feat: merge planar-brute-embed into the topola monorepo

- feat: use OrderedPair instead of custon BandName/BandUid (note: changes ordering of BandUid)
- fix(crates): rename planar-brute-embed to planar-incr-embed

Cargo.toml

@@ -34,7 +34,7 @@ features = ["serde-1"]
 
 [workspace.dependencies.serde]
 version = "1"
-features = ["derive"]
+features = ["derive", "rc"]
 
 [package]
 name = "topola"
@@ -59,6 +59,10 @@ serde.workspace = true
 spade.workspace = true
 thiserror.workspace = true
 
+[dependencies.planar-incr-embed]
+path = "crates/planar-incr-embed"
+features = ["serde"]
+
 [dependencies.specctra-core]
 path = "crates/specctra-core"
 features = ["rstar"]

LICENSES/Apache-2.0.txt

@@ -0,0 +1,73 @@
+Apache License
+Version 2.0, January 2004
+http://www.apache.org/licenses/
+
+TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
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+
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+9. Accepting Warranty or Additional Liability. While redistributing the Work or Derivative Works thereof, You may choose to offer, and charge a fee for, acceptance of support, warranty, indemnity, or other liability obligations and/or rights consistent with this License. However, in accepting such obligations, You may act only on Your own behalf and on Your sole responsibility, not on behalf of any other Contributor, and only if You agree to indemnify, defend, and hold each Contributor harmless for any liability incurred by, or claims asserted against, such Contributor by reason of your accepting any such warranty or additional liability.
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+
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README.md

@@ -45,10 +45,11 @@ repository on [GitHub](https://github.com/mikwielgus/topola).
 
 ## Licence
 
-Topola is licensed under the [MIT licence](LICENSE). Files present in
+Topola is licensed under the [MIT licence](LICENSES/MIT.txt). Files present in
 the `assets/` directory are dual-licensed as under MIT or
-[Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)
+[Creative Commons Attribution 4.0 International](LICENSES/CC-BY-4.0.txt)
-licence.
+licence. The file `crates/planar-incr-embed/src/math.rs` is dual-licensed as under
+MIT or [Apache 2.0](LICENSES/Apache-2.0.txt) license.
 
 ## Gallery
 

REUSE.toml

@@ -15,7 +15,12 @@ SPDX-FileCopyrightText = "2024 Topola contributors"
 SPDX-License-Identifier = "MIT"
 
 [[annotations]]
-path = ["tests/single_layer/**", "tests/multilayer/**"]
+path = [
+    "crates/planar-incr-embed/tests/**",
+    "crates/planar-incr-embed/src/planarr/snapshots/**",
+    "tests/single_layer/**",
+    "tests/multilayer/**"
+]
 SPDX-FileCopyrightText = "2024 Topola contributors"
 SPDX-License-Identifier = "MIT"
 

crates/planar-incr-embed/Cargo.toml

@@ -0,0 +1,33 @@
+# SPDX-FileCopyrightText: 2024 Topola contributors
+#
+# SPDX-License-Identifier: MIT
+
+[package]
+name = "planar-incr-embed"
+version = "0.1.0"
+edition = "2021"
+license = "MIT"
+
+[features]
+serde = ["dep:serde", "spade/serde"]
+
+[dependencies]
+log.workspace = true
+num-traits = "0.2"
+peeking_take_while = "1.0"
+spade.workspace = true
+thiserror.workspace = true
+
+[dependencies.serde]
+workspace = true
+optional = true
+
+[dev-dependencies]
+ron = "0.8"
+
+[dev-dependencies.insta]
+version = "1.42"
+features = ["json"]
+
+[dev-dependencies.serde]
+workspace = true

crates/planar-incr-embed/README.md

@@ -0,0 +1,9 @@
+<!--
+SPDX-FileCopyrightText: 2025 Topola contributors
+
+SPDX-License-Identifier: MIT
+-->
+
+# planar-incr-embed
+
+WIP implementation of incrementally finding planar graph embeddings modulo homotopy equivalence with fixed vertex positions.

crates/planar-incr-embed/src/algo/mod.rs

@@ -0,0 +1,118 @@
+// SPDX-FileCopyrightText: 2024 Topola contributors
+//
+// SPDX-License-Identifier: MIT
+//
+//! planar embedding / plane graph algorithms
+
+pub mod pmg_astar;
+
+use crate::{navmesh::NavmeshRef, NavmeshBase, NavmeshIndex};
+use alloc::{collections::BTreeSet, vec::Vec};
+
+/// The goal of one search iteration (a single path to be etched / embedded)
+#[derive(Clone, Debug)]
+pub struct Goal<PNI, EP> {
+    pub source: PNI,
+    pub target: BTreeSet<PNI>,
+    pub label: EP,
+}
+
+#[derive(Clone, Debug)]
+pub struct TargetNetwork<Scalar>(Vec<spade::Point2<Scalar>>);
+
+#[derive(Clone, Debug)]
+pub struct PreparedGoal<B: NavmeshBase> {
+    pub source: B::PrimalNodeIndex,
+    pub target: BTreeSet<B::PrimalNodeIndex>,
+    pub label: B::EtchedPath,
+
+    pub target_network: TargetNetwork<B::Scalar>,
+    pub minimal_costs: B::Scalar,
+}
+
+impl<PNI: Clone + Eq + Ord, EP: Clone + Eq> Goal<PNI, EP> {
+    pub fn target_network<B: NavmeshBase<PrimalNodeIndex = PNI, EtchedPath = EP>>(
+        &self,
+        navmesh: NavmeshRef<'_, B>,
+    ) -> TargetNetwork<B::Scalar> {
+        TargetNetwork(
+            self.target
+                .iter()
+                .cloned()
+                .map(|i| &navmesh.node_data(&NavmeshIndex::Primal(i)).unwrap().pos)
+                .cloned()
+                .collect(),
+        )
+    }
+
+    pub fn estimate_costs_for_source<B: NavmeshBase<PrimalNodeIndex = PNI, EtchedPath = EP>>(
+        &self,
+        navmesh: NavmeshRef<'_, B>,
+        source: &NavmeshIndex<PNI>,
+    ) -> B::Scalar
+    where
+        B::Scalar: num_traits::Float,
+    {
+        self.target_network(navmesh)
+            .estimate_costs(&navmesh.node_data(source).unwrap().pos)
+    }
+
+    pub fn estimate_costs<B: NavmeshBase<PrimalNodeIndex = PNI, EtchedPath = EP>>(
+        &self,
+        navmesh: NavmeshRef<'_, B>,
+    ) -> B::Scalar
+    where
+        B::Scalar: num_traits::Float,
+    {
+        self.estimate_costs_for_source(navmesh, &NavmeshIndex::Primal(self.source.clone()))
+    }
+
+    pub fn prepare<B: NavmeshBase<PrimalNodeIndex = PNI, EtchedPath = EP>>(
+        self,
+        navmesh: NavmeshRef<'_, B>,
+    ) -> PreparedGoal<B>
+    where
+        B::Scalar: num_traits::Float,
+    {
+        let target_network = self.target_network(navmesh);
+        let minimal_costs = target_network.estimate_costs(
+            &navmesh
+                .node_data(&NavmeshIndex::Primal(self.source.clone()))
+                .unwrap()
+                .pos,
+        );
+
+        PreparedGoal {
+            source: self.source,
+            target: self.target,
+            label: self.label,
+
+            target_network,
+            minimal_costs,
+        }
+    }
+}
+
+impl<Scalar: num_traits::Float> TargetNetwork<Scalar> {
+    pub fn estimate_costs(&self, source_pos: &spade::Point2<Scalar>) -> Scalar {
+        self.0
+            .iter()
+            .map(|i| crate::utils::euclidean_distance(source_pos, i))
+            .reduce(Scalar::min)
+            .unwrap()
+    }
+}
+
+impl<B: NavmeshBase> PreparedGoal<B>
+where
+    B::Scalar: num_traits::Float,
+{
+    pub fn estimate_costs_for_source<CT>(
+        &self,
+        navmesh: NavmeshRef<'_, B>,
+        source: &NavmeshIndex<B::PrimalNodeIndex>,
+    ) -> B::Scalar {
+        self.target_network
+            .estimate_costs(&navmesh.node_data(source).unwrap().pos)
+    }
+}

crates/planar-incr-embed/src/algo/pmg_astar.rs

@@ -0,0 +1,494 @@
+// SPDX-FileCopyrightText: 2025 Topola contributors
+// SPDX-FileCopyrightText: 2021 petgraph contributors
+//
+// SPDX-License-Identifier: MIT
+//
+//! planar multi-goal A*-like path search implementation
+
+use crate::{
+    algo::{Goal, PreparedGoal},
+    navmesh::{EdgeIndex, EdgePaths, Navmesh, NavmeshRef, NavmeshRefMut},
+    Edge, NavmeshBase, NavmeshIndex, RelaxedPath,
+};
+
+use alloc::collections::{BTreeMap, BinaryHeap};
+use alloc::{boxed::Box, sync::Arc, vec::Vec};
+use core::{cmp::Ordering, ops::ControlFlow};
+use num_traits::float::TotalOrder;
+
+/// A walk task
+#[derive(Clone, Debug)]
+pub struct Task<B: NavmeshBase> {
+    /// index of current goal
+    pub goal_idx: usize,
+
+    /// costs / weights accumulated so far
+    pub costs: B::Scalar,
+
+    /// estimated minimal costs until goal
+    pub estimated_remaining: B::Scalar,
+
+    /// estimated minimal costs for all remaining goals after this one
+    pub estimated_remaining_goals: B::Scalar,
+
+    /// the current navmesh edge paths
+    pub edge_paths: Box<[EdgePaths<B::EtchedPath, B::GapComment>]>,
+
+    /// the currently selected node
+    pub selected_node: NavmeshIndex<B::PrimalNodeIndex>,
+
+    /// the previously selected node
+    pub prev_node: NavmeshIndex<B::PrimalNodeIndex>,
+
+    /// the introduction position re: `selected_node`
+    pub cur_intro: usize,
+}
+
+/// Results after a [`Task`] is done.
+#[derive(Clone, Debug)]
+pub struct TaskResult<B: NavmeshBase> {
+    /// index of current goal
+    pub goal_idx: usize,
+
+    /// costs / weights accumulated so far
+    pub costs: B::Scalar,
+
+    /// the current navmesh edges
+    pub edge_paths: Box<[EdgePaths<B::EtchedPath, B::GapComment>]>,
+
+    /// the previously selected node
+    pub prev_node: NavmeshIndex<B::PrimalNodeIndex>,
+
+    /// the introduction position re: `target`
+    pub cur_intro: usize,
+}
+
+/// The main path search data structure
+#[derive(Clone, Debug)]
+pub struct PmgAstar<B: NavmeshBase> {
+    /// task queue, ordered by costs ascending
+    pub queue: BinaryHeap<Task<B>>,
+
+    // constant data
+    pub nodes:
+        Arc<BTreeMap<NavmeshIndex<B::PrimalNodeIndex>, crate::Node<B::PrimalNodeIndex, B::Scalar>>>,
+    pub edges: Arc<
+        BTreeMap<EdgeIndex<NavmeshIndex<B::PrimalNodeIndex>>, (Edge<B::PrimalNodeIndex>, usize)>,
+    >,
+    pub goals: Box<[PreparedGoal<B>]>,
+}
+
+impl<B: NavmeshBase> Task<B>
+where
+    B::Scalar: num_traits::Float,
+{
+    fn edge_paths_count(&self) -> usize {
+        self.edge_paths.iter().map(|i| i.len()).sum::<usize>()
+    }
+
+    fn estimated_full_costs(&self) -> B::Scalar {
+        self.costs + self.estimated_remaining + self.estimated_remaining_goals
+    }
+}
+
+impl<B: NavmeshBase> PartialEq for Task<B>
+where
+    B::PrimalNodeIndex: Ord,
+    B::EtchedPath: PartialOrd,
+    B::GapComment: PartialOrd,
+    B::Scalar: num_traits::Float + num_traits::float::TotalOrder + PartialOrd,
+{
+    fn eq(&self, other: &Self) -> bool {
+        self.estimated_full_costs()
+            .total_cmp(&other.estimated_full_costs())
+            == Ordering::Equal
+            && self.goal_idx == other.goal_idx
+            && other.edge_paths_count() == self.edge_paths_count()
+            && self.selected_node == other.selected_node
+            && self.prev_node == other.prev_node
+            && self.cur_intro == other.cur_intro
+            && self
+                .edge_paths
+                .partial_cmp(&other.edge_paths)
+                .map(|i| i == Ordering::Equal)
+                .unwrap_or(true)
+    }
+}
+
+impl<B: NavmeshBase> Eq for Task<B>
+where
+    B::PrimalNodeIndex: Ord,
+    B::EtchedPath: PartialOrd,
+    B::GapComment: PartialOrd,
+    B::Scalar: num_traits::Float + num_traits::float::TotalOrder + PartialOrd,
+{
+}
+
+// tasks are ordered such that smaller costs and higher goal indices are ordered as being larger (better)
+impl<B: NavmeshBase> Ord for Task<B>
+where
+    B::PrimalNodeIndex: Ord,
+    B::EtchedPath: PartialOrd,
+    B::GapComment: PartialOrd,
+    B::Scalar: num_traits::Float + num_traits::float::TotalOrder + PartialOrd,
+{
+    fn cmp(&self, other: &Self) -> Ordering {
+        // smaller costs are better
+        other
+            .estimated_full_costs()
+            .total_cmp(&self.estimated_full_costs())
+            // higher goal index is better
+            .then_with(|| self.goal_idx.cmp(&other.goal_idx))
+            // less inserted paths in edges are better
+            .then_with(|| other.edge_paths_count().cmp(&self.edge_paths_count()))
+            // tie-break on the rest
+            .then_with(|| self.selected_node.cmp(&other.selected_node))
+            .then_with(|| self.prev_node.cmp(&other.prev_node))
+            .then_with(|| self.cur_intro.cmp(&other.cur_intro))
+            .then_with(|| {
+                self.edge_paths
+                    .partial_cmp(&other.edge_paths)
+                    .unwrap_or(Ordering::Equal)
+            })
+    }
+}
+
+impl<B: NavmeshBase> PartialOrd for Task<B>
+where
+    B::PrimalNodeIndex: Ord,
+    B::EtchedPath: PartialOrd,
+    B::GapComment: PartialOrd,
+    B::Scalar: num_traits::Float + num_traits::float::TotalOrder + PartialOrd,
+{
+    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
+        Some(self.cmp(other))
+    }
+}
+
+impl<B: NavmeshBase<Scalar = Scalar>, Scalar: num_traits::Float + core::iter::Sum> PmgAstar<B> {
+    fn estimate_remaining_goals_costs(&self, start_goal_idx: usize) -> Scalar {
+        self.goals
+            .get(start_goal_idx + 1..)
+            .map(|rgoals| rgoals.iter().map(|i| i.minimal_costs).sum())
+            .unwrap_or_else(Scalar::zero)
+    }
+}
+
+impl<B: NavmeshBase> PreparedGoal<B>
+where
+    B::GapComment: Clone,
+    B::Scalar: num_traits::Float + core::iter::Sum,
+{
+    /// start processing the goal
+    fn start_pmga<'a, F: Fn(NavmeshRef<B>) -> Option<B::Scalar>>(
+        &'a self,
+        navmesh: NavmeshRef<'a, B>,
+        goal_idx: usize,
+        env: &'a PmgAstar<B>,
+        evaluate_navmesh: &'a F,
+    ) -> Option<impl Iterator<Item = Task<B>> + 'a> {
+        let source = NavmeshIndex::Primal(self.source.clone());
+        let estimated_remaining_goals = env.estimate_remaining_goals_costs(goal_idx);
+        Some(
+            navmesh
+                .node_data(&source)?
+                .neighs
+                .iter()
+                .filter_map({
+                    let source = source.clone();
+                    move |neigh| {
+                        navmesh
+                            .resolve_edge_data(source.clone(), neigh.clone())
+                            .map(|(_, epi)| {
+                                let edge_len = navmesh.access_edge_paths(epi).len();
+                                (neigh, epi, edge_len)
+                            })
+                    }
+                })
+                .flat_map(move |(neigh, epi, edge_len)| {
+                    let source = source.clone();
+                    // A*-like remaining costs estimation
+                    let estimated_remaining =
+                        self.estimate_costs_for_source::<B::GapComment>(navmesh, neigh);
+                    (0..=edge_len).filter_map(move |i| {
+                        let mut edge_paths = Box::from(navmesh.edge_paths);
+                        let mut navmesh = NavmeshRefMut {
+                            nodes: navmesh.nodes,
+                            edges: navmesh.edges,
+                            edge_paths: &mut edge_paths,
+                        };
+                        navmesh.access_edge_paths_mut(epi).with_borrow_mut(|mut j| {
+                            j.insert(i, RelaxedPath::Normal(self.label.clone()))
+                        });
+                        evaluate_navmesh(navmesh.as_ref()).map(|costs| Task {
+                            goal_idx,
+                            costs,
+                            estimated_remaining,
+                            estimated_remaining_goals,
+                            edge_paths,
+                            selected_node: neigh.clone(),
+                            prev_node: source.clone(),
+                            cur_intro: edge_len - i,
+                        })
+                    })
+                }),
+        )
+    }
+}
+
+impl<B: NavmeshBase> Task<B>
+where
+    B::EtchedPath: PartialOrd,
+    B::GapComment: Clone + PartialOrd,
+    B::Scalar: num_traits::Float + num_traits::float::TotalOrder,
+{
+    pub fn run<F>(
+        self,
+        env: &mut PmgAstar<B>,
+        evaluate_navmesh: F,
+    ) -> ControlFlow<TaskResult<B>, (Self, Vec<NavmeshIndex<B::PrimalNodeIndex>>)>
+    where
+        F: Fn(NavmeshRef<B>) -> Option<B::Scalar>,
+    {
+        if let NavmeshIndex::Primal(primal) = &self.selected_node {
+            if env.goals[self.goal_idx].target.contains(primal) {
+                let Self {
+                    goal_idx,
+                    costs,
+                    estimated_remaining: _,
+                    estimated_remaining_goals: _,
+                    edge_paths,
+                    prev_node,
+                    cur_intro,
+                    selected_node: _,
+                } = self;
+                return ControlFlow::Break(TaskResult {
+                    goal_idx,
+                    costs,
+                    edge_paths,
+                    prev_node,
+                    cur_intro,
+                });
+            } else {
+                panic!("wrong primal node selected");
+            }
+        }
+        let forks = self.progress(env, evaluate_navmesh);
+        ControlFlow::Continue((self, forks))
+    }
+
+    /// progress to the next step, splitting the task into new tasks (make sure to call `done` beforehand)
+    fn progress<F>(
+        &self,
+        env: &mut PmgAstar<B>,
+        evaluate_navmesh: F,
+    ) -> Vec<NavmeshIndex<B::PrimalNodeIndex>>
+    where
+        F: Fn(NavmeshRef<B>) -> Option<B::Scalar>,
+    {
+        let goal_idx = self.goal_idx;
+        let navmesh = NavmeshRef {
+            nodes: &env.nodes,
+            edges: &env.edges,
+            edge_paths: &self.edge_paths,
+        };
+        let goal = &env.goals[goal_idx];
+        let Some((_, other_ends)) = navmesh.planarr_find_all_other_ends(
+            &self.selected_node,
+            &self.prev_node,
+            self.cur_intro,
+            true,
+        ) else {
+            return Vec::new();
+        };
+
+        let mut ret = Vec::new();
+
+        env.queue
+            .extend(other_ends.filter_map(|(neigh, stop_data)| {
+                if let NavmeshIndex::Primal(primal) = &neigh {
+                    if !goal.target.contains(primal) {
+                        return None;
+                    }
+                }
+                // A*-like remaining costs estimation
+                let estimated_remaining =
+                    goal.estimate_costs_for_source::<B::GapComment>(navmesh, &neigh);
+                let mut edge_paths = self.edge_paths.clone();
+                let mut navmesh = NavmeshRefMut {
+                    nodes: &env.nodes,
+                    edges: &env.edges,
+                    edge_paths: &mut edge_paths,
+                };
+                let cur_intro = navmesh
+                    .edge_data_mut(self.selected_node.clone(), neigh.clone())
+                    .unwrap()
+                    .with_borrow_mut(|mut x| {
+                        x.insert(
+                            stop_data.insert_pos,
+                            RelaxedPath::Normal(goal.label.clone()),
+                        );
+                        x.len() - stop_data.insert_pos - 1
+                    });
+                ret.push(neigh.clone());
+                evaluate_navmesh(navmesh.as_ref()).map(|costs| Task {
+                    goal_idx,
+                    costs,
+                    estimated_remaining,
+                    estimated_remaining_goals: self.estimated_remaining_goals,
+                    edge_paths,
+                    selected_node: neigh.clone(),
+                    prev_node: self.selected_node.clone(),
+                    cur_intro,
+                })
+            }));
+
+        ret
+    }
+}
+
+#[derive(Clone, Debug, PartialEq)]
+pub struct IntermedResult<B: NavmeshBase> {
+    pub edge_paths: Box<[EdgePaths<B::EtchedPath, B::GapComment>]>,
+
+    pub goal_idx: usize,
+    pub forks: Vec<NavmeshIndex<B::PrimalNodeIndex>>,
+    pub selected_node: NavmeshIndex<B::PrimalNodeIndex>,
+
+    pub maybe_finished_goal: Option<B::Scalar>,
+}
+
+impl<B> PmgAstar<B>
+where
+    B: NavmeshBase,
+    B::EtchedPath: PartialOrd,
+    B::GapComment: Clone + PartialOrd,
+    B::Scalar: Default
+        + core::fmt::Debug
+        + core::iter::Sum
+        + num_traits::Float
+        + num_traits::float::TotalOrder,
+{
+    /// * `evaluate_navmesh` calculates the exact cost of a given navmesh (lower cost is better)
+    pub fn new<F>(
+        navmesh: &Navmesh<B>,
+        goals: Vec<Goal<B::PrimalNodeIndex, B::EtchedPath>>,
+        evaluate_navmesh: F,
+    ) -> Self
+    where
+        F: Fn(NavmeshRef<B>) -> Option<B::Scalar>,
+    {
+        let mut this = Self {
+            queue: BinaryHeap::new(),
+            goals: goals
+                .into_iter()
+                .map({
+                    let navmesh = navmesh.as_ref();
+                    move |i| i.prepare(navmesh)
+                })
+                .collect(),
+            nodes: navmesh.nodes.clone(),
+            edges: navmesh.edges.clone(),
+        };
+
+        // fill queue with first goal
+        if let Some(first_goal) = this.goals.first() {
+            this.queue = {
+                let navmesh = NavmeshRef {
+                    nodes: &this.nodes,
+                    edges: &this.edges,
+                    edge_paths: &navmesh.edge_paths,
+                };
+                let tmp = if let Some(iter) =
+                    first_goal.start_pmga(navmesh, 0, &this, &evaluate_navmesh)
+                {
+                    iter.collect()
+                } else {
+                    BinaryHeap::new()
+                };
+                tmp
+            };
+        }
+
+        this
+    }
+
+    pub fn queue_len(&self) -> usize {
+        self.queue.len()
+    }
+
+    /// run one step of the path-search
+    pub fn step<F>(
+        &mut self,
+        evaluate_navmesh: F,
+    ) -> ControlFlow<
+        Option<(B::Scalar, Box<[EdgePaths<B::EtchedPath, B::GapComment>]>)>,
+        IntermedResult<B>,
+    >
+    where
+        B::PrimalNodeIndex: core::fmt::Debug,
+        F: Fn(NavmeshRef<B>) -> Option<B::Scalar>,
+    {
+        let Some(task) = self.queue.pop() else {
+            log::info!("found no complete result");
+            return ControlFlow::Break(None);
+        };
+        ControlFlow::Continue(match task.run(self, &evaluate_navmesh) {
+            ControlFlow::Break(taskres) => {
+                let next_goal_idx = taskres.goal_idx + 1;
+                let navmesh = NavmeshRef {
+                    nodes: &self.nodes,
+                    edges: &self.edges,
+                    edge_paths: &taskres.edge_paths,
+                };
+                let edge_count = taskres.edge_paths.iter().map(|i| i.len()).sum::<usize>();
+                match self.goals.get(next_goal_idx) {
+                    None => {
+                        // done with all goals
+                        log::info!(
+                            "found result with {} edges and costs {:?}",
+                            edge_count,
+                            taskres.costs
+                        );
+                        return ControlFlow::Break(Some((taskres.costs, taskres.edge_paths)));
+                    }
+                    Some(next_goal) => {
+                        // prepare next goal
+                        log::debug!(
+                            "found partial result (goal {}) with {} edges and costs {:?}",
+                            taskres.goal_idx,
+                            edge_count,
+                            taskres.costs,
+                        );
+                        let mut tmp = if let Some(iter) =
+                            next_goal.start_pmga(navmesh, next_goal_idx, self, &evaluate_navmesh)
+                        {
+                            iter.collect()
+                        } else {
+                            BinaryHeap::new()
+                        };
+                        let forks = tmp.iter().map(|i| i.selected_node.clone()).collect();
+                        self.queue.append(&mut tmp);
+                        IntermedResult {
+                            goal_idx: taskres.goal_idx,
+                            forks,
+                            edge_paths: taskres.edge_paths,
+                            selected_node: NavmeshIndex::Primal(next_goal.source.clone()),
+                            maybe_finished_goal: Some(taskres.costs),
+                        }
+                    }
+                }
+            }
+            ControlFlow::Continue((task, forks)) => {
+                // task got further branched
+                IntermedResult {
+                    goal_idx: task.goal_idx,
+                    forks,
+                    edge_paths: task.edge_paths,
+                    selected_node: task.selected_node,
+                    maybe_finished_goal: None,
+                }
+            }
+        })
+    }
+}

crates/planar-incr-embed/src/lib.rs

@@ -0,0 +1,121 @@
+// SPDX-FileCopyrightText: 2025 Topola contributors
+//
+// SPDX-License-Identifier: MIT
+//
+//! WIP implementation of incrementally finding planar graph embeddings modulo homotopy equivalence with fixed vertex positions
+//!
+//! ## usually used generic parameter names
+//! * `EP`: type of etched path descriptor
+//! * `NI`: type of node indices
+//! * `PNI`: type of primal node indices
+//! * `Scalar`: type of coordinates of points and vectors (distances)
+
+#![allow(clippy::type_complexity)]
+#![no_std]
+
+extern crate alloc;
+
+pub mod algo;
+pub mod math;
+pub mod mayrev;
+pub mod navmesh;
+pub mod planarr;
+mod utils;
+
+use alloc::boxed::Box;
+use core::fmt;
+
+/// Immutable data associated to a topological navmesh edge
+#[derive(Clone, Copy, Debug, PartialEq, PartialOrd)]
+#[cfg_attr(feature = "serde", derive(serde::Deserialize, serde::Serialize))]
+pub struct Edge<PNI> {
+    pub lhs: Option<PNI>,
+    pub rhs: Option<PNI>,
+}
+
+impl<PNI> Edge<PNI> {
+    #[inline]
+    pub fn flip(&mut self) {
+        core::mem::swap(&mut self.lhs, &mut self.rhs);
+    }
+
+    #[inline]
+    pub fn as_ref(&self) -> Edge<&PNI> {
+        Edge {
+            lhs: self.lhs.as_ref(),
+            rhs: self.rhs.as_ref(),
+        }
+    }
+}
+
+#[derive(Clone, Copy, Debug, PartialEq, Eq, PartialOrd, Ord, Hash)]
+#[cfg_attr(
+    any(test, feature = "serde"),
+    derive(serde::Deserialize, serde::Serialize)
+)]
+pub enum RelaxedPath<EP, CT> {
+    Normal(EP),
+    Weak(CT),
+}
+
+pub trait GetIndex {
+    type Idx: Clone + Eq;
+
+    /// extract the index of the underlying node
+    fn get_index(&self) -> Self::Idx;
+}
+
+/// Trait as container for navmesh type-level parameters
+// in order to avoid extremely long type signatures
+pub trait NavmeshBase {
+    type PrimalNodeIndex: Clone + Eq + Ord + fmt::Debug;
+
+    /// type for `RelaxedPath::Normal` component
+    type EtchedPath: Clone + Eq + fmt::Debug;
+
+    /// type for `RelaxedPath::Weak` component
+    type GapComment: Clone + fmt::Debug;
+
+    type Scalar: Clone + fmt::Debug;
+}
+
+#[derive(Clone, Copy, Debug, PartialEq, Eq, PartialOrd, Ord, Hash)]
+#[cfg_attr(feature = "serde", derive(serde::Deserialize, serde::Serialize))]
+pub enum DualIndex {
+    /// refers to a Delaunay face
+    Inner(usize),
+    /// refers to a Delaunay edge
+    Outer(usize),
+}
+
+#[derive(Clone, Copy, Debug, PartialEq, Eq, PartialOrd, Ord, Hash)]
+#[cfg_attr(feature = "serde", derive(serde::Deserialize, serde::Serialize))]
+pub enum NavmeshIndex<PNI> {
+    Dual(DualIndex),
+    Primal(PNI),
+}
+
+#[derive(Clone, Debug, PartialEq, Eq, PartialOrd, Hash)]
+#[cfg_attr(feature = "serde", derive(serde::Deserialize, serde::Serialize))]
+pub struct Node<PNI, Scalar> {
+    pub neighs: Box<[NavmeshIndex<PNI>]>,
+    pub pos: spade::Point2<Scalar>,
+    /// if this node is `DualOuter`, then it has an `open_direction`
+    pub open_direction: Option<spade::Point2<Scalar>>,
+}
+
+impl<PNI, Scalar> Node<PNI, Scalar> {
+    pub fn dual_neighbors(&self) -> impl Iterator<Item = &DualIndex> {
+        self.neighs.iter().filter_map(|i| match i {
+            NavmeshIndex::Dual(dual) => Some(dual),
+            NavmeshIndex::Primal(_) => None,
+        })
+    }
+
+    pub fn primal_neighbors(&self) -> impl Iterator<Item = &PNI> {
+        self.neighs.iter().filter_map(|i| match i {
+            NavmeshIndex::Dual(_) => None,
+            NavmeshIndex::Primal(prim) => Some(prim),
+        })
+    }
+}

crates/planar-incr-embed/src/math.rs

@@ -0,0 +1,37 @@
+// SPDX-FileCopyrightText: 2025 Topola contributors
+// SPDX-FileCopyrightText: 2024 Spade contributors
+// SPDX-FileCopyrightText: 2024 Stefan Altmayer <stoeoef@gmail.com>
+//
+// SPDX-License-Identifier: MIT OR Apache-2.0
+
+use num_traits::float::Float;
+use spade::{Point2, SpadeNum};
+
+// source: https://github.com/Stoeoef/spade/blob/083b7744d91b994f4b482cdfaf0787a049e94858/src/delaunay_core/math.rs,
+// starting at line 359, modified to avoid private mothods of spade
+pub fn circumcenter<S>(positions: [Point2<S>; 3]) -> (Point2<S>, S)
+where
+    S: SpadeNum + Float,
+{
+    let [v0, v1, v2] = positions;
+    let b = Point2 {
+        x: v1.x - v0.x,
+        y: v1.y - v0.y,
+    };
+    let c = Point2 {
+        x: v2.x - v0.x,
+        y: v2.y - v0.y,
+    };
+
+    let one = S::one();
+    let two = one + one;
+    let d = two * (b.x * c.y - c.x * b.y);
+    let len_b = b.x * b.x + b.y * b.y;
+    let len_c = c.x * c.x + c.y * c.y;
+    let d_inv: S = one / d;
+
+    let x = (len_b * c.y - len_c * b.y) * d_inv;
+    let y = (-len_b * c.x + len_c * b.x) * d_inv;
+    let result = Point2::new(x + v0.x, y + v0.y);
+    (result, x * x + y * y)
+}

crates/planar-incr-embed/src/mayrev.rs

@@ -0,0 +1,294 @@
+// SPDX-FileCopyrightText: 2025 Topola contributors
+//
+// SPDX-License-Identifier: MIT
+//
+//! `MaybeReversed`: Structure making it easier to interact with a vector/slice and its reversal uniformly.
+
+use alloc::{sync::Arc, vec::Vec};
+use core::{borrow, iter::DoubleEndedIterator, marker::PhantomData, ops};
+
+/// Structure making it easier to interact with a vector/slice and its reversal uniformly.
+#[derive(Debug, PartialEq, Eq, PartialOrd, Ord, Hash)]
+pub struct MaybeReversed<I, T: ?Sized> {
+    pub inner: I,
+    pub reversed: bool,
+    item_marker: PhantomData<fn(T) -> T>,
+}
+
+impl<I: Clone, T: ?Sized> Clone for MaybeReversed<I, T> {
+    fn clone(&self) -> Self {
+        Self {
+            inner: self.inner.clone(),
+            reversed: self.reversed,
+            item_marker: PhantomData,
+        }
+    }
+}
+
+impl<I: Copy, T: ?Sized> Copy for MaybeReversed<I, T> {}
+
+impl<I, T> MaybeReversed<I, T> {
+    pub fn new(inner: I) -> Self {
+        Self {
+            inner,
+            reversed: false,
+            item_marker: PhantomData,
+        }
+    }
+
+    pub fn map<J, U, F>(self, f: F) -> MaybeReversed<J, U>
+    where
+        F: FnOnce(I) -> J,
+    {
+        let Self {
+            inner, reversed, ..
+        } = self;
+        MaybeReversed {
+            inner: f(inner),
+            reversed,
+            item_marker: PhantomData,
+        }
+    }
+
+    #[inline]
+    #[must_use]
+    pub fn flip(mut self) -> Self {
+        self.reversed ^= true;
+        self
+    }
+}
+
+impl<T> MaybeReversed<&mut Arc<[T]>, T> {
+    pub fn with_borrow_mut<R, F>(&mut self, f: F) -> R
+    where
+        F: FnOnce(MaybeReversed<&mut Vec<T>, T>) -> R,
+        T: Clone,
+    {
+        let mut inner: Vec<T> = self.inner.iter().cloned().collect();
+        let ret = f(MaybeReversed {
+            inner: &mut inner,
+            reversed: self.reversed,
+            item_marker: PhantomData,
+        });
+        *self.inner = Arc::from(inner.into_boxed_slice());
+        ret
+    }
+}
+
+impl<'a, I: ?Sized + borrow::Borrow<[T]>, T> MaybeReversed<&'a I, T> {
+    pub fn as_ref(&self) -> MaybeReversed<&'a [T], T> {
+        MaybeReversed {
+            inner: self.inner.borrow(),
+            reversed: self.reversed,
+            item_marker: PhantomData,
+        }
+    }
+
+    #[inline]
+    pub fn len(&self) -> usize {
+        self.inner.borrow().len()
+    }
+
+    pub fn resolve_index(&self, index: usize) -> usize {
+        if self.reversed {
+            self.len().checked_sub(index + 1).unwrap()
+        } else {
+            index
+        }
+    }
+
+    #[inline]
+    pub fn iter(&self) -> MaybeReversed<core::slice::Iter<'a, T>, T> {
+        MaybeReversed {
+            inner: self.inner.borrow().iter(),
+            reversed: self.reversed,
+            item_marker: PhantomData,
+        }
+    }
+}
+
+impl<I: ?Sized + borrow::Borrow<[T]>, T> MaybeReversed<&mut I, T> {
+    #[inline(always)]
+    pub fn as_ref(&self) -> MaybeReversed<&'_ I, T> {
+        MaybeReversed {
+            inner: &*self.inner,
+            reversed: self.reversed,
+            item_marker: PhantomData,
+        }
+    }
+
+    #[inline]
+    pub fn len(&self) -> usize {
+        self.inner.borrow().len()
+    }
+
+    #[inline]
+    pub fn is_empty(&self) -> bool {
+        self.inner.borrow().is_empty()
+    }
+
+    #[inline]
+    pub fn resolve_index(&self, index: usize) -> usize {
+        self.as_ref().resolve_index(index)
+    }
+
+    #[inline]
+    pub fn iter(&self) -> MaybeReversed<core::slice::Iter<'_, T>, T> {
+        self.as_ref().iter()
+    }
+}
+
+impl<T> MaybeReversed<&mut [T], T> {
+    #[inline]
+    pub fn iter_mut(&mut self) -> MaybeReversed<core::slice::IterMut<'_, T>, T> {
+        MaybeReversed {
+            inner: self.inner.iter_mut(),
+            reversed: self.reversed,
+            item_marker: PhantomData,
+        }
+    }
+}
+
+impl<T> MaybeReversed<&mut Vec<T>, T> {
+    #[inline(always)]
+    pub fn as_ref_slice(&self) -> MaybeReversed<&'_ [T], T> {
+        MaybeReversed {
+            inner: &self.inner[..],
+            reversed: self.reversed,
+            item_marker: PhantomData,
+        }
+    }
+
+    #[inline(always)]
+    pub fn as_mut_slice(&mut self) -> MaybeReversed<&'_ mut [T], T> {
+        MaybeReversed {
+            inner: &mut self.inner[..],
+            reversed: self.reversed,
+            item_marker: PhantomData,
+        }
+    }
+
+    pub fn insert(&mut self, index: usize, element: T) {
+        if self.reversed {
+            self.inner
+                .insert(self.len().checked_sub(index).unwrap(), element);
+        } else {
+            self.inner.insert(index, element);
+        }
+    }
+}
+
+impl<I: ?Sized + borrow::Borrow<[T]> + ops::Index<usize, Output = T>, T> ops::Index<usize>
+    for MaybeReversed<&I, T>
+{
+    type Output = <I as ops::Index<usize>>::Output;
+
+    fn index(&self, index: usize) -> &Self::Output {
+        self.inner.index(self.resolve_index(index))
+    }
+}
+
+impl<I: ?Sized + borrow::Borrow<[T]> + ops::Index<usize, Output = T>, T> ops::Index<usize>
+    for MaybeReversed<&mut I, T>
+{
+    type Output = <I as ops::Index<usize>>::Output;
+
+    fn index(&self, index: usize) -> &Self::Output {
+        self.inner.index(self.resolve_index(index))
+    }
+}
+
+impl<I: ?Sized + borrow::Borrow<[T]> + ops::IndexMut<usize, Output = T>, T> ops::IndexMut<usize>
+    for MaybeReversed<&mut I, T>
+{
+    fn index_mut(&mut self, index: usize) -> &mut Self::Output {
+        self.inner.index_mut(self.resolve_index(index))
+    }
+}
+
+#[inline]
+pub fn index<T>(obj: &[T], idx: MaybeReversed<usize, T>) -> &T {
+    use ops::Index;
+    obj.index(
+        MaybeReversed {
+            inner: obj,
+            reversed: idx.reversed,
+            item_marker: PhantomData,
+        }
+        .resolve_index(idx.inner),
+    )
+}
+
+#[inline]
+pub fn index_mut<T>(obj: &mut [T], idx: MaybeReversed<usize, T>) -> &mut T {
+    use ops::IndexMut;
+    obj.index_mut(
+        MaybeReversed {
+            inner: &obj[..],
+            reversed: idx.reversed,
+            item_marker: PhantomData,
+        }
+        .resolve_index(idx.inner),
+    )
+}
+
+#[inline]
+pub fn index_forward<T, U>(obj: &[T], idx: MaybeReversed<usize, U>) -> MaybeReversed<&T, U> {
+    MaybeReversed {
+        inner: &obj[idx.inner],
+        reversed: idx.reversed,
+        item_marker: PhantomData,
+    }
+}
+
+#[inline]
+pub fn index_mut_forward<T, U>(
+    obj: &mut [T],
+    idx: MaybeReversed<usize, U>,
+) -> MaybeReversed<&mut T, U> {
+    MaybeReversed {
+        inner: &mut obj[idx.inner],
+        reversed: idx.reversed,
+        item_marker: PhantomData,
+    }
+}
+
+impl<I: DoubleEndedIterator, T> Iterator for MaybeReversed<I, T> {
+    type Item = <I as Iterator>::Item;
+
+    fn next(&mut self) -> Option<<I as Iterator>::Item> {
+        match self.reversed {
+            false => self.inner.next(),
+            true => self.inner.next_back(),
+        }
+    }
+
+    fn fold<B, F>(self, init: B, f: F) -> B
+    where
+        F: FnMut(B, Self::Item) -> B,
+    {
+        match self.reversed {
+            false => self.inner.fold(init, f),
+            true => self.inner.rfold(init, f),
+        }
+    }
+}
+
+impl<I: DoubleEndedIterator, T> DoubleEndedIterator for MaybeReversed<I, T> {
+    fn next_back(&mut self) -> Option<<I as Iterator>::Item> {
+        match self.reversed {
+            false => self.inner.next_back(),
+            true => self.inner.next(),
+        }
+    }
+
+    fn rfold<B, F>(self, init: B, f: F) -> B
+    where
+        F: FnMut(B, Self::Item) -> B,
+    {
+        match self.reversed {
+            false => self.inner.rfold(init, f),
+            true => self.inner.fold(init, f),
+        }
+    }
+}

crates/planar-incr-embed/src/navmesh/generate.rs

@@ -0,0 +1,380 @@
+// SPDX-FileCopyrightText: 2025 Topola contributors
+// SPDX-FileCopyrightText: 2024 Spade contributors
+//
+// SPDX-License-Identifier: MIT
+//
+//! Topological navmesh generation from Delaunay triangulation
+// idea: see issue topola/topola#132
+
+use alloc::collections::{btree_map::Entry, BTreeMap, BTreeSet};
+use alloc::{boxed::Box, sync::Arc, vec::Vec};
+use core::ops;
+use num_traits::{Float, FloatConst};
+use spade::{
+    handles::{DirectedEdgeHandle, VoronoiVertex as VoroV},
+    HasPosition, Point2, Triangulation,
+};
+
+use crate::{
+    navmesh::{EdgeIndex, EdgePaths, NavmeshSer},
+    DualIndex, Edge, NavmeshBase, NavmeshIndex, Node,
+};
+
+#[derive(Clone, Debug, PartialEq)]
+pub struct TrianVertex<PNI, T: spade::SpadeNum> {
+    pub idx: PNI,
+    pub pos: Point2<T>,
+}
+
+impl<PNI, T: spade::SpadeNum> HasPosition for TrianVertex<PNI, T> {
+    type Scalar = T;
+
+    #[inline]
+    fn position(&self) -> spade::Point2<T> {
+        self.pos
+    }
+}
+
+#[derive(Clone, Copy, Debug)]
+struct EdgeMeta<PNI, Scalar> {
+    //hypot: Scalar,
+    /// `atan2`, but into the range `[0, 2π)`.
+    angle: Scalar,
+
+    data: Edge<PNI>,
+}
+
+impl<PNI, Scalar: Float + FloatConst + ops::AddAssign + ops::SubAssign> EdgeMeta<PNI, Scalar> {
+    /// rotate the angle by 180°
+    fn flip(&mut self) {
+        self.data.flip();
+        self.angle += Scalar::PI();
+        if self.angle >= Scalar::TAU() {
+            self.angle -= Scalar::TAU();
+        }
+    }
+}
+
+impl<B: NavmeshBase> NavmeshSer<B>
+where
+    B::Scalar: spade::SpadeNum
+        + Float
+        + FloatConst
+        + num_traits::float::TotalOrder
+        + ops::AddAssign
+        + ops::SubAssign,
+{
+    pub fn from_triangulation<T>(triangulation: &T) -> Self
+    where
+        T: Triangulation<Vertex = TrianVertex<B::PrimalNodeIndex, B::Scalar>>,
+    {
+        let mut nodes =
+            BTreeMap::<_, (Point2<B::Scalar>, BTreeSet<_>, Option<Point2<B::Scalar>>)>::new();
+        // note that all the directions are in the range [0, 2π).
+        let mut edges = BTreeMap::<
+            EdgeIndex<NavmeshIndex<B::PrimalNodeIndex>>,
+            EdgeMeta<B::PrimalNodeIndex, B::Scalar>,
+        >::new();
+
+        // insert edge for each Voronoi edge
+        for edge in triangulation.undirected_voronoi_edges() {
+            let edge = edge.as_directed();
+            let (a_vert, b_vert) = (edge.from(), edge.to());
+            let (a_idx, a) = insert_dual_node_position::<B, _, _, _>(&mut nodes, &a_vert, None);
+            let (b_idx, b) =
+                insert_dual_node_position::<B, _, _, _>(&mut nodes, &b_vert, Some(a_idx.clone()));
+            nodes.get_mut(&a_idx).unwrap().1.insert(b_idx.clone());
+            // https://docs.rs/spade/2.12.1/src/spade/delaunay_core/handles/public_handles.rs.html#305
+            let delaunay = edge.as_delaunay_edge();
+            insert_edge(
+                &mut edges,
+                a_idx,
+                &a,
+                b_idx,
+                &b,
+                Edge {
+                    lhs: Some(delaunay.from().data().idx.clone()),
+                    rhs: Some(delaunay.to().data().idx.clone()),
+                },
+            );
+        }
+
+        // insert edge for each {primal node} * {neighbors of that node}
+        for node in triangulation.vertices() {
+            // iterate over neighbors to generate sectors information
+            let idx = NavmeshIndex::Primal(node.data().idx.clone());
+            let a = node.data().pos;
+            let mut primal_neighs = BTreeSet::new();
+
+            for edge in node.as_voronoi_face().adjacent_edges() {
+                // to convert dual edges around a node into dual nodes around a node,
+                // we use the dual nodes that the edges point to.
+                let dual_node = edge.to();
+                let (dual_idx, b) = insert_dual_node_position::<B, _, _, _>(
+                    &mut nodes,
+                    &dual_node,
+                    Some(idx.clone()),
+                );
+                primal_neighs.insert(dual_idx.clone());
+                insert_edge(
+                    &mut edges,
+                    idx.clone(),
+                    &a,
+                    dual_idx,
+                    &b,
+                    Edge {
+                        lhs: None,
+                        rhs: None,
+                    },
+                );
+            }
+            assert!(nodes.insert(idx, (a, primal_neighs, None)).is_none());
+        }
+
+        // insert hull edges between `DualOuter` vertices
+        {
+            let convex_hull = triangulation.convex_hull().collect::<Vec<_>>();
+            // if the convex hull only consists of two entries, we only have two primals, and the
+            // convex hull generated by the code below would be invalid.
+            // but given we want to find shortest paths, and for two entries that is unique,
+            // we can just skip the generation in that case
+            if convex_hull.len() > 2 {
+                for cvhedges in convex_hull.windows(2) {
+                    let [edge1, edge2] = cvhedges else {
+                        continue;
+                    };
+                    insert_convex_hull_edge::<B, _, _, _>(&mut nodes, &mut edges, edge1, edge2);
+                }
+                insert_convex_hull_edge::<B, _, _, _>(
+                    &mut nodes,
+                    &mut edges,
+                    &convex_hull[convex_hull.len() - 1],
+                    &convex_hull[0],
+                );
+            }
+        }
+
+        let nodes = finalize_nodes::<B>(nodes, &edges);
+        let empty_edge: EdgePaths<B::EtchedPath, B::GapComment> =
+            Arc::from(Vec::new().into_boxed_slice());
+        Self {
+            nodes: Arc::new(nodes),
+            edges: edges
+                .into_iter()
+                .map(|(k, emeta)| (k, (emeta.data, empty_edge.clone())))
+                .collect(),
+        }
+    }
+}
+
+fn voronoi_vertex_get_index<V: HasPosition, DE, UE, F>(
+    vertex: &spade::handles::VoronoiVertex<'_, V, DE, UE, F>,
+) -> DualIndex {
+    match vertex {
+        VoroV::Inner(face) => DualIndex::Inner(face.index()),
+        VoroV::Outer(out) => DualIndex::Outer(out.index()),
+    }
+}
+
+// TODO: bound to root_bbox + some padding
+fn voronoi_vertex_get_position<V, DE, UE, F>(
+    vertex: &spade::handles::VoronoiVertex<'_, V, DE, UE, F>,
+) -> (
+    Point2<<V as HasPosition>::Scalar>,
+    Option<Point2<<V as HasPosition>::Scalar>>,
+)
+where
+    V: HasPosition,
+    <V as HasPosition>::Scalar: num_traits::float::Float,
+{
+    match vertex {
+        VoroV::Inner(face) => (face.circumcenter(), None),
+        VoroV::Outer(halfspace) => {
+            let delauney = halfspace.as_delaunay_edge();
+            let from = delauney.from().position();
+            let to = delauney.to().position();
+            let orth = Point2 {
+                x: -(to.y - from.y),
+                y: to.x - from.x,
+            };
+
+            (
+                Point2 {
+                    x: (from.x + to.x) / ((2.0).into()) + orth.x,
+                    y: (from.y + to.y) / ((2.0).into()) + orth.y,
+                },
+                Some(orth),
+            )
+        }
+    }
+}
+
+fn insert_edge<PNI, Scalar>(
+    edges: &mut BTreeMap<EdgeIndex<NavmeshIndex<PNI>>, EdgeMeta<PNI, Scalar>>,
+    a_idx: NavmeshIndex<PNI>,
+    a: &Point2<Scalar>,
+    b_idx: NavmeshIndex<PNI>,
+    b: &Point2<Scalar>,
+    data: Edge<PNI>,
+) where
+    PNI: Ord,
+    Scalar: Float + FloatConst + ops::AddAssign + ops::SubAssign,
+{
+    let direction = Point2 {
+        x: b.x - a.x,
+        y: b.y - a.y,
+    };
+
+    let angle = direction.y.atan2(direction.x);
+    let mut edgemeta = EdgeMeta {
+        // hypot: Scalar::hypot(direction.x, direction.y),
+        angle: if angle.is_sign_negative() {
+            angle + Scalar::TAU()
+        } else {
+            angle
+        },
+        data,
+    };
+
+    if a_idx > b_idx {
+        edgemeta.flip();
+    }
+
+    edges.insert(EdgeIndex::from((a_idx, b_idx)), edgemeta);
+}
+
+fn insert_dual_node_position<B: NavmeshBase, DE, UE, F>(
+    nodes: &mut BTreeMap<
+        NavmeshIndex<B::PrimalNodeIndex>,
+        (
+            Point2<B::Scalar>,
+            BTreeSet<NavmeshIndex<B::PrimalNodeIndex>>,
+            Option<Point2<B::Scalar>>,
+        ),
+    >,
+    vertex: &spade::handles::VoronoiVertex<
+        '_,
+        TrianVertex<B::PrimalNodeIndex, B::Scalar>,
+        DE,
+        UE,
+        F,
+    >,
+    new_neighbor: Option<NavmeshIndex<B::PrimalNodeIndex>>,
+) -> (NavmeshIndex<B::PrimalNodeIndex>, Point2<B::Scalar>)
+where
+    B::Scalar: spade::SpadeNum + Float,
+{
+    let idx = NavmeshIndex::Dual(voronoi_vertex_get_index(vertex));
+    let ret = match nodes.entry(idx.clone()) {
+        Entry::Occupied(occ) => occ.into_mut(),
+        Entry::Vacant(vac) => {
+            let (x, x_odir) = voronoi_vertex_get_position(vertex);
+            vac.insert((x, BTreeSet::new(), x_odir))
+        }
+    };
+    if let Some(neigh) = new_neighbor {
+        ret.1.insert(neigh);
+    }
+    (idx, ret.0)
+}
+
+fn insert_convex_hull_edge<B: NavmeshBase, DE, UE, F>(
+    nodes: &mut BTreeMap<
+        NavmeshIndex<B::PrimalNodeIndex>,
+        (
+            Point2<B::Scalar>,
+            BTreeSet<NavmeshIndex<B::PrimalNodeIndex>>,
+            Option<Point2<B::Scalar>>,
+        ),
+    >,
+    edges: &mut BTreeMap<
+        EdgeIndex<NavmeshIndex<B::PrimalNodeIndex>>,
+        EdgeMeta<B::PrimalNodeIndex, B::Scalar>,
+    >,
+    edge1: &DirectedEdgeHandle<TrianVertex<B::PrimalNodeIndex, B::Scalar>, DE, UE, F>,
+    edge2: &DirectedEdgeHandle<TrianVertex<B::PrimalNodeIndex, B::Scalar>, DE, UE, F>,
+) where
+    B::Scalar: spade::SpadeNum + Float + FloatConst + ops::AddAssign + ops::SubAssign,
+{
+    let (edge1to, edge2to) = (
+        edge1.as_voronoi_edge().from(),
+        edge2.as_voronoi_edge().from(),
+    );
+    assert!(matches!(edge1to, VoroV::Outer(_)));
+    assert!(matches!(edge2to, VoroV::Outer(_)));
+
+    let a_idx = NavmeshIndex::Dual(voronoi_vertex_get_index(&edge1to));
+    let b_idx = NavmeshIndex::Dual(voronoi_vertex_get_index(&edge2to));
+
+    let a_pos = {
+        let a = nodes.get_mut(&a_idx).unwrap();
+        a.1.insert(b_idx.clone());
+        a.0
+    };
+    let b_pos = {
+        let b = nodes.get_mut(&b_idx).unwrap();
+        b.1.insert(a_idx.clone());
+        b.0
+    };
+
+    // > The edges are returned in clockwise order as seen from any point in the triangulation.
+    let rhs_prim = edge1.to().data().idx.clone();
+    debug_assert!(edge2.from().data().idx == rhs_prim);
+
+    insert_edge(
+        edges,
+        a_idx,
+        &a_pos,
+        b_idx,
+        &b_pos,
+        Edge {
+            lhs: None,
+            rhs: Some(rhs_prim),
+        },
+    );
+}
+
+/// extracts sector information
+fn finalize_nodes<B: NavmeshBase>(
+    nodes: BTreeMap<
+        NavmeshIndex<B::PrimalNodeIndex>,
+        (
+            Point2<B::Scalar>,
+            BTreeSet<NavmeshIndex<B::PrimalNodeIndex>>,
+            Option<Point2<B::Scalar>>,
+        ),
+    >,
+    edges: &BTreeMap<
+        EdgeIndex<NavmeshIndex<B::PrimalNodeIndex>>,
+        EdgeMeta<B::PrimalNodeIndex, B::Scalar>,
+    >,
+) -> BTreeMap<NavmeshIndex<B::PrimalNodeIndex>, Node<B::PrimalNodeIndex, B::Scalar>>
+where
+    B::Scalar: Float + FloatConst + num_traits::float::TotalOrder + ops::AddAssign + ops::SubAssign,
+{
+    nodes
+        .into_iter()
+        .map(|(idx, (pos, neighs, open_direction))| {
+            let mut neighs: Box<[_]> = neighs.into_iter().collect();
+            neighs.sort_by(|a, b| {
+                let mut dir_a = edges[&EdgeIndex::from((idx.clone(), a.clone()))].clone();
+                if idx > *a {
+                    dir_a.flip();
+                }
+                let mut dir_b = edges[&EdgeIndex::from((idx.clone(), b.clone()))].clone();
+                if idx > *b {
+                    dir_b.flip();
+                }
+                <B::Scalar as num_traits::float::TotalOrder>::total_cmp(&dir_a.angle, &dir_b.angle)
+            });
+            (
+                idx,
+                Node {
+                    neighs,
+                    pos,
+                    open_direction,
+                },
+            )
+        })
+        .collect()
+}

crates/planar-incr-embed/src/navmesh/mod.rs

@@ -0,0 +1,477 @@
+// SPDX-FileCopyrightText: 2025 Topola contributors
+//
+// SPDX-License-Identifier: MIT
+//
+//! A topological navmesh implementation
+// idea: see issue topola/topola#132
+
+use alloc::collections::BTreeMap;
+use alloc::{boxed::Box, sync::Arc, vec::Vec};
+
+use crate::{mayrev::MaybeReversed, planarr, Edge, NavmeshBase, NavmeshIndex, Node, RelaxedPath};
+
+mod generate;
+mod ordered_pair;
+
+pub use generate::TrianVertex;
+pub use ordered_pair::OrderedPair;
+
+pub type EdgeIndex<T> = ordered_pair::OrderedPair<T>;
+pub type EdgePaths<EP, CT> = Arc<[RelaxedPath<EP, CT>]>;
+
+/// A topological navmesh (here in comfortably serializable form),
+/// built upon the merging of the primary and dual graph,
+/// and with an operation to create barriers.
+///
+/// This is basically a planar graph embedding.
+#[derive(Clone, Debug)]
+#[cfg_attr(feature = "serde", derive(serde::Deserialize, serde::Serialize))]
+#[cfg_attr(
+    feature = "serde",
+    serde(bound(
+        deserialize = "B: NavmeshBase,
+            B::PrimalNodeIndex: serde::Deserialize<'de>,
+            B::EtchedPath: serde::Deserialize<'de>,
+            B::GapComment: serde::Deserialize<'de>,
+            B::Scalar: serde::Deserialize<'de>",
+        serialize = "B: NavmeshBase,
+            B::PrimalNodeIndex: serde::Serialize,
+            B::EtchedPath: serde::Serialize,
+            B::GapComment: serde::Serialize,
+            B::Scalar: serde::Serialize"
+    ))
+)]
+pub struct NavmeshSer<B: NavmeshBase> {
+    pub nodes: Arc<BTreeMap<NavmeshIndex<B::PrimalNodeIndex>, Node<B::PrimalNodeIndex, B::Scalar>>>,
+    pub edges: BTreeMap<
+        EdgeIndex<NavmeshIndex<B::PrimalNodeIndex>>,
+        (
+            Edge<B::PrimalNodeIndex>,
+            EdgePaths<B::EtchedPath, B::GapComment>,
+        ),
+    >,
+}
+
+/// A topological navmesh,
+/// built upon the merging of the primary and dual graph,
+/// and with an operation to create barriers.
+///
+/// This is basically a planar graph embedding, and is used for enumeration of such embeddings.
+#[derive(Clone, Debug)]
+#[cfg_attr(feature = "serde", derive(serde::Deserialize, serde::Serialize))]
+#[cfg_attr(
+    feature = "serde",
+    serde(bound(
+        deserialize = "B: NavmeshBase,
+            B::PrimalNodeIndex: serde::Deserialize<'de>,
+            B::EtchedPath: serde::Deserialize<'de>,
+            B::GapComment: serde::Deserialize<'de>,
+            B::Scalar: serde::Deserialize<'de>",
+        serialize = "B: NavmeshBase,
+            B::PrimalNodeIndex: serde::Serialize,
+            B::EtchedPath: serde::Serialize,
+            B::GapComment: serde::Serialize,
+            B::Scalar: serde::Serialize"
+    ))
+)]
+pub struct Navmesh<B: NavmeshBase> {
+    pub nodes: Arc<BTreeMap<NavmeshIndex<B::PrimalNodeIndex>, Node<B::PrimalNodeIndex, B::Scalar>>>,
+    pub edges: Arc<
+        BTreeMap<EdgeIndex<NavmeshIndex<B::PrimalNodeIndex>>, (Edge<B::PrimalNodeIndex>, usize)>,
+    >,
+    pub edge_paths: Box<[EdgePaths<B::EtchedPath, B::GapComment>]>,
+}
+
+pub struct NavmeshRef<'a, B: NavmeshBase> {
+    pub nodes: &'a BTreeMap<NavmeshIndex<B::PrimalNodeIndex>, Node<B::PrimalNodeIndex, B::Scalar>>,
+    pub edges: &'a BTreeMap<
+        EdgeIndex<NavmeshIndex<B::PrimalNodeIndex>>,
+        (Edge<B::PrimalNodeIndex>, usize),
+    >,
+    pub edge_paths: &'a [EdgePaths<B::EtchedPath, B::GapComment>],
+}
+
+pub struct NavmeshRefMut<'a, B: NavmeshBase> {
+    pub nodes: &'a BTreeMap<NavmeshIndex<B::PrimalNodeIndex>, Node<B::PrimalNodeIndex, B::Scalar>>,
+    pub edges: &'a BTreeMap<
+        EdgeIndex<NavmeshIndex<B::PrimalNodeIndex>>,
+        (Edge<B::PrimalNodeIndex>, usize),
+    >,
+    pub edge_paths: &'a mut [EdgePaths<B::EtchedPath, B::GapComment>],
+}
+
+impl<B: NavmeshBase> Clone for NavmeshRef<'_, B> {
+    #[inline(always)]
+    fn clone(&self) -> Self {
+        *self
+    }
+}
+
+impl<B: NavmeshBase> Copy for NavmeshRef<'_, B> {}
+
+impl<B: NavmeshBase> Default for Navmesh<B> {
+    fn default() -> Self {
+        Self {
+            nodes: Arc::new(BTreeMap::new()),
+            edges: Arc::new(BTreeMap::new()),
+            edge_paths: Vec::new().into_boxed_slice(),
+        }
+    }
+}
+
+impl<B: NavmeshBase> NavmeshBase for NavmeshSer<B> {
+    type PrimalNodeIndex = B::PrimalNodeIndex;
+    type EtchedPath = B::EtchedPath;
+    type GapComment = B::GapComment;
+    type Scalar = B::Scalar;
+}
+
+impl<B: NavmeshBase> NavmeshBase for Navmesh<B> {
+    type PrimalNodeIndex = B::PrimalNodeIndex;
+    type EtchedPath = B::EtchedPath;
+    type GapComment = B::GapComment;
+    type Scalar = B::Scalar;
+}
+
+impl<B: NavmeshBase> NavmeshBase for NavmeshRef<'_, B> {
+    type PrimalNodeIndex = B::PrimalNodeIndex;
+    type EtchedPath = B::EtchedPath;
+    type GapComment = B::GapComment;
+    type Scalar = B::Scalar;
+}
+
+impl<B: NavmeshBase> NavmeshBase for NavmeshRefMut<'_, B> {
+    type PrimalNodeIndex = B::PrimalNodeIndex;
+    type EtchedPath = B::EtchedPath;
+    type GapComment = B::GapComment;
+    type Scalar = B::Scalar;
+}
+
+impl<B: NavmeshBase> From<NavmeshSer<B>> for Navmesh<B> {
+    fn from(this: NavmeshSer<B>) -> Navmesh<B> {
+        let mut edge_paths = Vec::with_capacity(this.edges.len());
+
+        let edges = this
+            .edges
+            .into_iter()
+            .map(|(key, (edge, paths))| {
+                let idx = edge_paths.len();
+                edge_paths.push(paths);
+                (key, (edge, idx))
+            })
+            .collect::<BTreeMap<_, _>>();
+
+        Self {
+            nodes: this.nodes,
+            edges: Arc::new(edges),
+            edge_paths: edge_paths.into_boxed_slice(),
+        }
+    }
+}
+
+impl<B: NavmeshBase> From<Navmesh<B>> for NavmeshSer<B> {
+    fn from(this: Navmesh<B>) -> NavmeshSer<B> {
+        Self {
+            nodes: this.nodes,
+            edges: this
+                .edges
+                .iter()
+                .map(|(key, (value, idx))| {
+                    (key.clone(), (value.clone(), this.edge_paths[*idx].clone()))
+                })
+                .collect(),
+        }
+    }
+}
+
+impl<B: NavmeshBase> Navmesh<B> {
+    #[inline(always)]
+    pub fn as_ref(&self) -> NavmeshRef<B> {
+        NavmeshRef {
+            nodes: &self.nodes,
+            edges: &self.edges,
+            edge_paths: &self.edge_paths,
+        }
+    }
+
+    #[inline(always)]
+    pub fn as_mut(&mut self) -> NavmeshRefMut<B> {
+        NavmeshRefMut {
+            nodes: &self.nodes,
+            edges: &self.edges,
+            edge_paths: &mut self.edge_paths,
+        }
+    }
+}
+
+pub(crate) fn resolve_edge_data<PNI: Ord, EP>(
+    edges: &BTreeMap<EdgeIndex<NavmeshIndex<PNI>>, (Edge<PNI>, usize)>,
+    from_node: NavmeshIndex<PNI>,
+    to_node: NavmeshIndex<PNI>,
+) -> Option<(Edge<&PNI>, MaybeReversed<usize, EP>)> {
+    let reversed = from_node > to_node;
+    let edge_idx: EdgeIndex<NavmeshIndex<PNI>> = (from_node, to_node).into();
+    let edge = edges.get(&edge_idx)?;
+    let mut data = edge.0.as_ref();
+    if reversed {
+        data.flip();
+    }
+    let mut ret = MaybeReversed::new(edge.1);
+    ret.reversed = reversed;
+    Some((data, ret))
+}
+
+impl<'a, B: NavmeshBase + 'a> NavmeshRefMut<'a, B> {
+    #[inline(always)]
+    pub fn as_ref(&'a self) -> NavmeshRef<'a, B> {
+        NavmeshRef {
+            nodes: self.nodes,
+            edges: self.edges,
+            edge_paths: self.edge_paths,
+        }
+    }
+
+    pub fn edge_data_mut(
+        &mut self,
+        from_node: NavmeshIndex<B::PrimalNodeIndex>,
+        to_node: NavmeshIndex<B::PrimalNodeIndex>,
+    ) -> Option<
+        MaybeReversed<
+            &mut Arc<[RelaxedPath<B::EtchedPath, B::GapComment>]>,
+            RelaxedPath<B::EtchedPath, B::GapComment>,
+        >,
+    > {
+        self.resolve_edge_data(from_node, to_node)
+            .map(|(_, item)| item)
+            .map(|item| self.access_edge_paths_mut(item))
+    }
+
+    #[inline(always)]
+    pub fn resolve_edge_data(
+        &self,
+        from_node: NavmeshIndex<B::PrimalNodeIndex>,
+        to_node: NavmeshIndex<B::PrimalNodeIndex>,
+    ) -> Option<(
+        Edge<&B::PrimalNodeIndex>,
+        MaybeReversed<usize, RelaxedPath<B::EtchedPath, B::GapComment>>,
+    )> {
+        resolve_edge_data(self.edges, from_node, to_node)
+    }
+
+    /// ## Panics
+    /// This function panics if the given `item` is out of bounds
+    /// (e.g. only happens when it was produced by a `Navmesh` with different edges)
+    #[inline(always)]
+    pub fn access_edge_paths_mut(
+        &mut self,
+        item: MaybeReversed<usize, RelaxedPath<B::EtchedPath, B::GapComment>>,
+    ) -> MaybeReversed<
+        &mut Arc<[RelaxedPath<B::EtchedPath, B::GapComment>]>,
+        RelaxedPath<B::EtchedPath, B::GapComment>,
+    > {
+        crate::mayrev::index_mut_forward(self.edge_paths, item)
+    }
+}
+
+impl<'a, B: NavmeshBase + 'a> NavmeshRef<'a, B> {
+    #[inline(always)]
+    pub fn resolve_edge_data(
+        &self,
+        from_node: NavmeshIndex<B::PrimalNodeIndex>,
+        to_node: NavmeshIndex<B::PrimalNodeIndex>,
+    ) -> Option<(
+        Edge<&B::PrimalNodeIndex>,
+        MaybeReversed<usize, RelaxedPath<B::EtchedPath, B::GapComment>>,
+    )> {
+        resolve_edge_data(self.edges, from_node, to_node)
+    }
+
+    #[inline(always)]
+    pub fn node_data(
+        &self,
+        node: &NavmeshIndex<B::PrimalNodeIndex>,
+    ) -> Option<&'a Node<B::PrimalNodeIndex, B::Scalar>> {
+        self.nodes.get(node)
+    }
+
+    pub fn edge_data(
+        &self,
+        from_node: NavmeshIndex<B::PrimalNodeIndex>,
+        to_node: NavmeshIndex<B::PrimalNodeIndex>,
+    ) -> Option<
+        MaybeReversed<
+            &'a Arc<[RelaxedPath<B::EtchedPath, B::GapComment>]>,
+            RelaxedPath<B::EtchedPath, B::GapComment>,
+        >,
+    > {
+        self.resolve_edge_data(from_node, to_node)
+            .map(|(_, item)| self.access_edge_paths(item))
+    }
+
+    /*
+    pub fn check_edge_rules<'b, ObjectKind: Copy + Eq + Ord>(
+        &self,
+        from_node: NavmeshIndex<B::PrimalNodeIndex>,
+        to_node: NavmeshIndex<B::PrimalNodeIndex>,
+    ) -> Option<(B::Scalar, bool)>
+    where
+        for<'i> &'i B::PrimalNodeIndex: topola_rules::GetConditions<'i, ObjectKind = ObjectKind>,
+        for<'i> &'i B::EtchedPath: topola_rules::GetConditions<'i, ObjectKind = ObjectKind>,
+        B::EtchedPath: topola_rules::GetWidth<Scalar = B::Scalar>,
+        R: topola_rules::AccessRules<Scalar = B::Scalar, ObjectKind = ObjectKind>,
+        B::Scalar: Default + num_traits::Float + core::iter::Sum,
+    {
+        let edgd = self.edge_data(from_node.clone(), to_node.clone())?;
+        if edgd.inner.is_empty() {
+            return Some((B::Scalar::default(), true));
+        }
+        let (NavmeshIndex::Dual(_), NavmeshIndex::Dual(_)) = (from_node.clone(), to_node.clone())
+        else {
+            // we only check dual-dual connections for now
+            return Some((B::Scalar::default(), true));
+        };
+        // decode dual nodes into the unique orthogonal primal nodes
+        let start_node_data = self.node_data(&from_node)?;
+        let start_node_neighs = &start_node_data.neighs;
+
+        let start_target_pos = start_node_neighs
+            .iter()
+            .enumerate()
+            .find(|(_, i)| **i == from_node)?
+            .0;
+        let prev = &start_node_neighs
+            [(start_node_neighs.len() + start_target_pos - 1) % start_node_neighs.len()];
+        let next = &start_node_neighs[(start_target_pos + 1) % start_node_neighs.len()];
+
+        let filtered_edgd: Vec<_> = Iterator::filter_map(edgd.iter(), |i| match i {
+            RelaxedPath::Normal(i) => Some(i),
+            RelaxedPath::Weak(_) => None,
+        })
+        .collect();
+
+        let usage_width: B::Scalar =
+            Iterator::map(filtered_edgd.iter(), topola_rules::GetWidth::width).sum();
+
+        let conds: Vec<_> = filtered_edgd
+            .iter()
+            .filter_map(|i| i.conditions())
+            .collect();
+        let mut usage = usage_width
+            + conds
+                .windows(2)
+                .filter_map(|x| if let [i, j] = x { Some((i, j)) } else { None })
+                .map(|(i, j)| self.rules.clearance((i, j).into()))
+                .sum();
+
+        let (NavmeshIndex::Primal(prev), NavmeshIndex::Primal(next)) = (prev, next) else {
+            return if let (
+                NavmeshIndex::Dual(DualIndex::Outer(_)),
+                NavmeshIndex::Dual(DualIndex::Outer(_)),
+            ) = (from_node, to_node)
+            {
+                // `DualOuter`-`DualOuter` are only associated to a single primal
+                // TODO: but even those should have a maximum capacity (e.g. up to PCB border)
+                // TODO: handle (more difficult) how large polygons are and such...
+                Some((usage, true))
+            } else {
+                // something is wrong
+                None
+            };
+        };
+
+        let stop_node_data = self.node_data(&to_node)?;
+        let to_primals: BTreeSet<_> = stop_node_data.primal_neighbors().collect();
+        assert!(to_primals.contains(&prev));
+        assert!(to_primals.contains(&next));
+
+        use topola_rules::GetConditions;
+        let prev_cond = prev.conditions();
+        let next_cond = next.conditions();
+
+        if let Some(prev_cond) = prev_cond {
+            usage = usage
+                + self
+                    .rules
+                    .clearance((&prev_cond, conds.first().unwrap()).into());
+        }
+
+        if let Some(next_cond) = next_cond {
+            usage = usage
+                + self
+                    .rules
+                    .clearance((&next_cond, conds.last().unwrap()).into());
+        }
+
+        // TODO: handle (more difficult) how large polygons are and such...
+        Some((
+            usage,
+            usage
+                <= B::Scalar::hypot(
+                    stop_node_data.pos.x - start_node_data.pos.x,
+                    stop_node_data.pos.y - start_node_data.pos.y,
+                ),
+        ))
+    }
+    */
+
+    /// ## Panics
+    /// This function panics if the given `item` is out of bounds
+    /// (e.g. only happens when it was produced by a `Navmesh` with different edges)
+    #[inline(always)]
+    pub fn access_edge_paths(
+        &self,
+        item: MaybeReversed<usize, RelaxedPath<B::EtchedPath, B::GapComment>>,
+    ) -> MaybeReversed<
+        &'a Arc<[RelaxedPath<B::EtchedPath, B::GapComment>]>,
+        RelaxedPath<B::EtchedPath, B::GapComment>,
+    > {
+        crate::mayrev::index_forward(self.edge_paths, item)
+    }
+
+    /// See [`find_other_end`](planarr::find_other_end).
+    pub fn planarr_find_other_end(
+        self,
+        node: &NavmeshIndex<B::PrimalNodeIndex>,
+        start: &NavmeshIndex<B::PrimalNodeIndex>,
+        pos: usize,
+        already_inserted_at_start: bool,
+        stop: &NavmeshIndex<B::PrimalNodeIndex>,
+    ) -> Option<(usize, planarr::OtherEnd)> {
+        planarr::find_other_end(
+            self.nodes[node].neighs.iter().map(move |neigh| {
+                let edge = self
+                    .edge_data(node.clone(), neigh.clone())
+                    .expect("unable to resolve neighbor");
+                (neigh.clone(), edge)
+            }),
+            start,
+            pos,
+            already_inserted_at_start,
+            stop,
+        )
+    }
+
+    /// See [`find_all_other_ends`](planarr::find_all_other_ends).
+    pub fn planarr_find_all_other_ends(
+        self,
+        node: &'a NavmeshIndex<B::PrimalNodeIndex>,
+        start: &'a NavmeshIndex<B::PrimalNodeIndex>,
+        pos: usize,
+        already_inserted_at_start: bool,
+    ) -> Option<(
+        usize,
+        impl Iterator<Item = (NavmeshIndex<B::PrimalNodeIndex>, planarr::OtherEnd)> + 'a,
+    )> {
+        planarr::find_all_other_ends(
+            self.nodes[node].neighs.iter().map(move |neigh| {
+                let edge = self
+                    .edge_data(node.clone(), neigh.clone())
+                    .expect("unable to resolve neighbor");
+                (neigh.clone(), edge)
+            }),
+            start,
+            pos,
+            already_inserted_at_start,
+        )
+    }
+}

crates/planar-incr-embed/src/navmesh/ordered_pair.rs

@@ -0,0 +1,70 @@
+// SPDX-FileCopyrightText: 2025 Topola contributors
+//
+// SPDX-License-Identifier: MIT
+
+#[derive(Clone, Copy, Debug, PartialEq, Eq, PartialOrd, Ord, Hash)]
+#[cfg_attr(feature = "serde", derive(serde::Deserialize))]
+#[cfg_attr(feature = "serde", serde(from = "(T, T)"))]
+#[cfg_attr(
+    feature = "serde",
+    serde(bound(deserialize = "T: serde::Deserialize<'de> + Ord"))
+)]
+pub struct OrderedPair<T>(T, T);
+
+impl<T> core::ops::Index<bool> for OrderedPair<T> {
+    type Output = T;
+
+    #[inline]
+    fn index(&self, index: bool) -> &T {
+        if index {
+            &self.1
+        } else {
+            &self.0
+        }
+    }
+}
+
+impl<T: Ord> From<(T, T)> for OrderedPair<T> {
+    fn from(mut x: (T, T)) -> Self {
+        if x.0 > x.1 {
+            core::mem::swap(&mut x.0, &mut x.1);
+        }
+        let (a, b) = x;
+        Self(a, b)
+    }
+}
+
+impl<T> From<OrderedPair<T>> for (T, T) {
+    #[inline(always)]
+    fn from(OrderedPair(a, b): OrderedPair<T>) -> (T, T) {
+        (a, b)
+    }
+}
+
+impl<'a, T> From<&'a OrderedPair<T>> for (&'a T, &'a T) {
+    #[inline(always)]
+    fn from(OrderedPair(a, b): &'a OrderedPair<T>) -> (&'a T, &'a T) {
+        (a, b)
+    }
+}
+
+#[cfg(feature = "serde")]
+impl<T: serde::Serialize> serde::Serialize for OrderedPair<T> {
+    #[inline]
+    fn serialize<S: serde::Serializer>(&self, serializer: S) -> Result<S::Ok, S::Error> {
+        use serde::ser::SerializeTuple;
+        let mut tuple = match serializer.serialize_tuple(2) {
+            Ok(x) => x,
+            Err(e) => return Err(e),
+        };
+        match tuple.serialize_element(&self.0) {
+            Ok(x) => x,
+            Err(e) => return Err(e),
+        }
+        match tuple.serialize_element(&self.1) {
+            Ok(x) => x,
+            Err(e) => return Err(e),
+        }
+        tuple.end()
+    }
+}

crates/planar-incr-embed/src/planarr/mod.rs

@@ -0,0 +1,207 @@
+// SPDX-FileCopyrightText: 2025 Topola contributors
+//
+// SPDX-License-Identifier: MIT
+//
+//! per-node planar arrangement structures
+//! * `NI`... type of node indices
+//! * `EP`... type of etched path descriptor
+
+use crate::{
+    mayrev::MaybeReversed,
+    utils::{handle_lifo_relaxed, rotate_iter},
+    RelaxedPath,
+};
+use alloc::vec::Vec;
+
+/// Data about the other end of a path going through an planar arrangement
+#[derive(Clone, Debug, PartialEq, Eq, PartialOrd, Ord)]
+#[cfg_attr(
+    any(test, feature = "serde"),
+    derive(serde::Deserialize, serde::Serialize)
+)]
+pub struct OtherEnd {
+    /// the index / position of the target section
+    pub section_idx: usize,
+    /// the position to be used inside the target section
+    pub insert_pos: usize,
+}
+
+/// Find the appropriate other end (in `stop`) position of a path
+/// starting between `pos - 1` and `pos`
+/// (at `pos` exactly if `already_inserted_at_start` is set) in `start`.
+/// Returns `Option<start_idx, stop_data>`.
+///
+/// ## Edge cases
+/// Note that this function "works" if `start == stop`, but does introduce a bias
+/// (currently meaning that routes are introduced before instead of after this)
+/// into further routes to resolve the resulting ambiguity
+/// and should therefore be avoided entirely.
+///
+/// ## Failure
+/// If the input data is invalid:
+/// * the `start` or `stop` doesn't exist, or
+/// * `NI`'s are non-unique (`self.0.iter().map(|i| &i.0)` should never contain duplicates)
+/// * the `[EP]`'s aren't LIFO-ordered as expected, or
+/// * the `pos` is out of bounds,
+///
+/// this function returns `None`.
+pub fn find_other_end<'a, NI, EP, CT, Iter, EPB>(
+    this: Iter,
+    start: &NI,
+    pos: usize,
+    already_inserted_at_start: bool,
+    stop: &NI,
+) -> Option<(usize, OtherEnd)>
+where
+    Iter: Clone
+        + Iterator<Item = (NI, MaybeReversed<&'a EPB, RelaxedPath<EP, CT>>)>
+        + core::iter::ExactSizeIterator,
+    NI: Eq,
+    EP: Clone + Eq + 'a,
+    EPB: core::borrow::Borrow<[RelaxedPath<EP, CT>]> + 'a,
+{
+    let mut stack = Vec::new();
+
+    // iteration in counter-clockwise order
+    let (start_idx, mut it) = rotate_iter(
+        this.map(|(i, j)| (i, j.as_ref())).enumerate(),
+        move |(_, (i, _))| i == start,
+    );
+
+    // 1. handle start
+    {
+        let (_, (_, start_eps)) = it.next().unwrap();
+        if start == stop {
+            return Some((
+                start_idx,
+                OtherEnd {
+                    section_idx: start_idx,
+                    insert_pos: pos + 1,
+                },
+            ));
+        }
+        for i in start_eps
+            .as_ref()
+            .iter()
+            .skip(pos + usize::from(already_inserted_at_start))
+        {
+            handle_lifo_relaxed(&mut stack, i);
+        }
+    }
+
+    // 2. handle rest
+    for (nni, (ni, eps)) in it {
+        if &ni == stop {
+            // find insertion point (one of `eps.len()+1` positions)
+            return if stack.is_empty() {
+                Some((
+                    start_idx,
+                    OtherEnd {
+                        section_idx: nni,
+                        insert_pos: 0,
+                    },
+                ))
+            } else {
+                for (n, i) in eps.as_ref().iter().enumerate() {
+                    handle_lifo_relaxed(&mut stack, i);
+                    if stack.is_empty() {
+                        return Some((
+                            start_idx,
+                            OtherEnd {
+                                section_idx: nni,
+                                insert_pos: n + 1,
+                            },
+                        ));
+                    }
+                }
+                None
+            };
+        } else {
+            for i in eps.as_ref().iter() {
+                handle_lifo_relaxed(&mut stack, i);
+            }
+        }
+    }
+
+    None
+}
+
+/// Find the appropriate other ends of a path
+/// starting between `pos - 1` and `pos`
+/// (at `pos` exactly if `already_inserted_at_start` is set) in `start`.
+/// Returns `Option<start_idx, Vec<(stop_ni, stop_data)>>`.
+///
+/// ## Edge cases
+/// Note that this function won't report possible entries with `start_idx == stop_idx`.
+///
+/// ## Failure
+/// If the input data is invalid:
+/// * the `start` doesn't exist, or
+/// * `NI`'s are non-unique (`self.0.iter().map(|i| &i.0)` should never contain duplicates)
+/// * the `[EP]`'s aren't LIFO-ordered as expected, or
+/// * the `pos` is out of bounds,
+///
+/// this function returns `None`.
+pub fn find_all_other_ends<'a, NI, EP, CT, Iter, EPB>(
+    this: Iter,
+    start: &'a NI,
+    pos: usize,
+    already_inserted_at_start: bool,
+) -> Option<(usize, impl Iterator<Item = (NI, OtherEnd)> + 'a)>
+where
+    Iter: Clone
+        + Iterator<Item = (NI, MaybeReversed<&'a EPB, RelaxedPath<EP, CT>>)>
+        + core::iter::ExactSizeIterator
+        + 'a,
+    NI: Clone + Eq,
+    EP: Clone + Eq + 'a,
+    CT: 'a,
+    EPB: core::borrow::Borrow<[RelaxedPath<EP, CT>]> + 'a,
+{
+    let mut stack = Vec::new();
+
+    // iteration in counter-clockwise order
+    let (start_idx, mut it) = rotate_iter(this.enumerate(), move |(_, (i, _))| i == start);
+
+    // 1. handle start
+    {
+        let (_, (st_, start_eps)) = it.next().unwrap();
+        if &st_ != start {
+            panic!();
+        }
+        for i in start_eps
+            .iter()
+            .skip(pos + usize::from(already_inserted_at_start))
+        {
+            handle_lifo_relaxed(&mut stack, i);
+        }
+    }
+
+    // 2. handle rest
+    Some((
+        start_idx,
+        it.filter_map(move |(section_idx, (ni, eps))| {
+            // find possible insertion point
+            // (at most one of `eps.len()+1` positions)
+            let mut pos = if stack.is_empty() { Some(0) } else { None };
+            for (n, i) in eps.iter().enumerate() {
+                handle_lifo_relaxed(&mut stack, i);
+                if pos.is_none() && stack.is_empty() {
+                    pos = Some(n + 1);
+                }
+            }
+            pos.map(|insert_pos| {
+                (
+                    ni,
+                    OtherEnd {
+                        section_idx,
+                        insert_pos,
+                    },
+                )
+            })
+        }),
+    ))
+}
+
+#[cfg(test)]
+mod tests;

crates/planar-incr-embed/src/planarr/snapshots/planar_incr_embed__planarr__tests__simple00-2.snap

@@ -0,0 +1,5 @@
+---
+source: src/planarr.rs
+expression: "(tmp.0, tmp.1.collect::<Vec<_>>())"
+---
+[1, [[2, {"section_idx": 2, "insert_pos": 0}], [0, {"section_idx": 0, "insert_pos": 1}]]]

crates/planar-incr-embed/src/planarr/snapshots/planar_incr_embed__planarr__tests__simple00-3.snap

@@ -0,0 +1,45 @@
+---
+source: src/planarr.rs
+expression: s.0
+---
+[
+  [
+    0,
+    [
+      {
+        "Normal": "c"
+      },
+      {
+        "Normal": "b"
+      },
+      {
+        "Normal": "a"
+      }
+    ]
+  ],
+  [
+    1,
+    [
+      {
+        "Normal": "a"
+      },
+      {
+        "Normal": "b"
+      },
+      {
+        "Normal": "d"
+      }
+    ]
+  ],
+  [
+    2,
+    [
+      {
+        "Normal": "d"
+      },
+      {
+        "Normal": "c"
+      }
+    ]
+  ]
+]

crates/planar-incr-embed/src/planarr/snapshots/planar_incr_embed__planarr__tests__simple00.snap

@@ -0,0 +1,5 @@
+---
+source: src/planarr.rs
+expression: "(tmp.0, tmp.1.collect::<Vec<_>>())"
+---
+[0, [[1, {"section_idx": 1, "insert_pos": 2}], [2, {"section_idx": 2, "insert_pos": 0}]]]

crates/planar-incr-embed/src/planarr/snapshots/planar_incr_embed__planarr__tests__simple01.snap

@@ -0,0 +1,45 @@
+---
+source: src/planarr.rs
+expression: s.0
+---
+[
+  [
+    0,
+    [
+      {
+        "Normal": "c"
+      },
+      {
+        "Normal": "b"
+      },
+      {
+        "Normal": "a"
+      }
+    ]
+  ],
+  [
+    1,
+    [
+      {
+        "Normal": "a"
+      },
+      {
+        "Normal": "b"
+      },
+      {
+        "Normal": "d"
+      }
+    ]
+  ],
+  [
+    2,
+    [
+      {
+        "Normal": "c"
+      },
+      {
+        "Normal": "d"
+      }
+    ]
+  ]
+]

crates/planar-incr-embed/src/planarr/tests.rs

@@ -0,0 +1,150 @@
+// SPDX-FileCopyrightText: 2025 Topola contributors
+//
+// SPDX-License-Identifier: MIT
+//
+//! per-node planar arrangement structures
+//! * `NI`... type of node indices
+//! * `EP`... type of etched path descriptor
+
+extern crate std;
+use super::*;
+use alloc::{boxed::Box, sync::Arc};
+use insta::assert_compact_json_snapshot;
+
+#[derive(Clone, Debug, PartialEq, Eq, PartialOrd, Ord)]
+#[cfg_attr(feature = "serde", derive(serde::Deserialize, serde::Serialize))]
+struct PlanarArrangement<NI, EP, CT>(
+    /// counter-clockwise (CCW) ordered sectors, containing CCW ordered paths
+    pub Box<[(NI, Arc<[RelaxedPath<EP, CT>]>)]>,
+);
+
+impl<NI: Clone, EP, CT> PlanarArrangement<NI, EP, CT> {
+    pub fn from_node_indices(idxs: impl Iterator<Item = NI>) -> Self {
+        let empty_edge: Arc<[RelaxedPath<EP, CT>]> = Arc::from(Vec::new().into_boxed_slice());
+        Self(idxs.map(|i| (i, empty_edge.clone())).collect())
+    }
+
+    pub fn as_mut(&mut self) -> PlanarArrangementRefMut<'_, NI, EP, CT> {
+        PlanarArrangementRefMut(
+            self.0
+                .iter_mut()
+                .map(|(i, j)| (i.clone(), MaybeReversed::new(j)))
+                .collect(),
+        )
+    }
+}
+
+struct PlanarArrangementRefMut<'a, NI, EP, CT>(
+    /// counter-clockwise (CCW) ordered sectors, containing CCW ordered paths
+    pub  Box<
+        [(
+            NI,
+            MaybeReversed<&'a mut Arc<[RelaxedPath<EP, CT>]>, RelaxedPath<EP, CT>>,
+        )],
+    >,
+);
+
+impl<NI: Clone + Eq, EP: Clone + Eq, CT> PlanarArrangementRefMut<'_, NI, EP, CT> {
+    /// See [`find_other_end`].
+    #[inline(always)]
+    pub fn find_other_end(
+        &self,
+        start: &NI,
+        pos: usize,
+        already_inserted_at_start: bool,
+        stop: &NI,
+    ) -> Option<(usize, OtherEnd)> {
+        find_other_end(
+            self.0.iter().map(|(i, j)| (i.clone(), j.as_ref())),
+            start,
+            pos,
+            already_inserted_at_start,
+            stop,
+        )
+    }
+
+    /// See [`find_all_other_ends`].
+    #[inline(always)]
+    pub fn find_all_other_ends<'a>(
+        &'a self,
+        start: &'a NI,
+        pos: usize,
+        already_inserted_at_start: bool,
+    ) -> Option<(usize, impl Iterator<Item = (NI, OtherEnd)> + 'a)> {
+        find_all_other_ends(
+            self.0.iter().map(|(i, j)| (i.clone(), j.as_ref())),
+            start,
+            pos,
+            already_inserted_at_start,
+        )
+    }
+
+    /// Insert a path into the current sectors arrangement,
+    /// starting at position `pos_start` in sector `start`, and finding
+    /// the appropriate other end position in `stop`, and inserting the path there.
+    ///
+    /// See also [`find_other_end`]
+    /// (which does implement the search, look there for failure and edge cases).
+    ///
+    /// If given valid input `self`, this function won't make `self` invalid.
+    ///
+    /// The result in the success case is the inverted stop position
+    /// (which can be passed to the next `insert_path` of the neighbor `stop`'s node)
+    pub fn insert_path(
+        &mut self,
+        start: &NI,
+        pos_start: usize,
+        stop: &NI,
+        path: EP,
+    ) -> Result<usize, EP>
+    where
+        CT: Clone,
+    {
+        match self.find_other_end(start, pos_start, false, stop) {
+            None => Err(path),
+            Some((idx_start, stop_data)) => {
+                let path = RelaxedPath::Normal(path);
+
+                self.0[idx_start].1.with_borrow_mut(|mut j| {
+                    j.insert(pos_start, path.clone());
+                });
+
+                self.0[stop_data.section_idx].1.with_borrow_mut(|mut j| {
+                    j.insert(stop_data.insert_pos, path);
+                    Ok(j.len() - stop_data.insert_pos - 1)
+                })
+            }
+        }
+    }
+}
+
+#[test]
+fn simple00() {
+    let mut s = PlanarArrangement::<_, _, ()>::from_node_indices(0..3);
+    let mut s_ = s.as_mut();
+    assert_eq!(s_.insert_path(&0, 0, &1, 'a'), Ok(0));
+    assert_eq!(s_.insert_path(&0, 0, &1, 'b'), Ok(0));
+    {
+        let tmp = s_.find_all_other_ends(&0, 0, false).unwrap();
+        assert_compact_json_snapshot!((tmp.0, tmp.1.collect::<Vec<_>>()));
+    }
+    assert_eq!(s_.insert_path(&0, 0, &2, 'c'), Ok(0));
+    {
+        let tmp = s_.find_all_other_ends(&1, 2, false).unwrap();
+        assert_compact_json_snapshot!((tmp.0, tmp.1.collect::<Vec<_>>()));
+    }
+    assert_eq!(s_.insert_path(&1, 2, &2, 'd'), Ok(1));
+    assert_compact_json_snapshot!(s.0);
+}
+
+#[test]
+fn simple01() {
+    let mut s = PlanarArrangement::<_, _, ()>::from_node_indices(0..3);
+    let mut s_ = s.as_mut();
+    s_.0[2].1.reversed = true;
+    assert_eq!(s_.insert_path(&0, 0, &1, 'a'), Ok(0));
+    assert_eq!(s_.insert_path(&0, 0, &1, 'b'), Ok(0));
+    assert_eq!(s_.insert_path(&0, 0, &2, 'c'), Ok(0));
+    assert_eq!(s_.insert_path(&1, 2, &2, 'd'), Ok(1));
+    assert_compact_json_snapshot!(s.0);
+}

crates/planar-incr-embed/src/utils.rs

@@ -0,0 +1,50 @@
+// SPDX-FileCopyrightText: 2025 Topola contributors
+//
+// SPDX-License-Identifier: MIT
+
+use crate::RelaxedPath;
+use alloc::vec::Vec;
+
+fn handle_lifo<EP: Clone + Eq>(stack: &mut Vec<EP>, item: &EP) {
+    if stack.last() == Some(item) {
+        stack.pop();
+    } else {
+        stack.push(item.clone());
+    }
+}
+
+pub fn handle_lifo_relaxed<EP: Clone + Eq, CT>(stack: &mut Vec<EP>, item: &RelaxedPath<EP, CT>) {
+    match item {
+        RelaxedPath::Normal(item) => handle_lifo(stack, item),
+        RelaxedPath::Weak(_) => {}
+    }
+}
+
+/// Rotates a finite iterator around such that it starts at `start`, and note the start index
+pub fn rotate_iter<Item, Iter, F>(iter: Iter, is_start: F) -> (usize, impl Iterator<Item = Item>)
+where
+    Iter: Clone + Iterator<Item = Item>,
+    F: Clone + Fn(&Item) -> bool,
+{
+    use peeking_take_while::PeekableExt;
+    let not_is_start = move |i: &Item| !is_start(i);
+
+    let mut it_first = iter.clone().peekable();
+    let start_idx = it_first
+        .by_ref()
+        .peeking_take_while(not_is_start.clone())
+        .count();
+
+    (start_idx, it_first.chain(iter.take_while(not_is_start)))
+}
+
+pub fn euclidean_distance<Scalar>(a: &spade::Point2<Scalar>, b: &spade::Point2<Scalar>) -> Scalar
+where
+    Scalar: num_traits::Float,
+{
+    let delta = spade::Point2 {
+        x: a.x - b.x,
+        y: a.y - b.y,
+    };
+    delta.y.hypot(delta.x)
+}

crates/planar-incr-embed/tests/complex.rs

@@ -0,0 +1,86 @@
+// SPDX-FileCopyrightText: 2024 Topola contributors
+//
+// SPDX-License-Identifier: MIT
+
+#![cfg(feature = "serde")]
+
+use pie::{DualIndex, NavmeshIndex, RelaxedPath};
+use planar_incr_embed as pie;
+
+#[derive(
+    Clone, Copy, Debug, PartialEq, Eq, PartialOrd, Ord, serde::Deserialize, serde::Serialize,
+)]
+enum PrimitiveIndex {
+    FixedDot(usize),
+}
+
+#[derive(
+    Clone, Copy, Debug, PartialEq, Eq, PartialOrd, Ord, serde::Deserialize, serde::Serialize,
+)]
+enum LayoutNodeIndex {
+    Primitive(PrimitiveIndex),
+}
+
+#[derive(Clone)]
+struct MyNavmeshBase;
+type EtchedPath = pie::navmesh::EdgeIndex<LayoutNodeIndex>;
+
+impl pie::NavmeshBase for MyNavmeshBase {
+    type PrimalNodeIndex = LayoutNodeIndex;
+    type EtchedPath = EtchedPath;
+    type GapComment = ();
+    type Scalar = f64;
+}
+
+type Navmesh = pie::navmesh::Navmesh<MyNavmeshBase>;
+
+#[test]
+fn tht_3pin_xlr_to_tht_3pin_xlr() {
+    // the intermediate navmesh
+
+    let navmesh_ser: pie::navmesh::NavmeshSer<MyNavmeshBase> = ron::from_str(
+        &std::fs::read_to_string("tests/tht_3pin_xlr_to_tht_3pin_xlr/navmesh_intermed.ron")
+            .unwrap(),
+    )
+    .unwrap();
+
+    let mut navmesh: Navmesh = navmesh_ser.into();
+
+    /*
+    let _goals: Vec<EtchedPath> = ron::from_str(
+        &std::fs::read_to_string("tests/tht_3pin_xlr_to_tht_3pin_xlr/goals.ron").unwrap(),
+    )
+    .unwrap();
+    */
+
+    // execute the path of the second goal "2 -> 8"
+
+    let p2 = LayoutNodeIndex::Primitive(PrimitiveIndex::FixedDot(2));
+    let p8 = LayoutNodeIndex::Primitive(PrimitiveIndex::FixedDot(8));
+
+    let label = RelaxedPath::Normal(EtchedPath::from((p2, p8)));
+    let p2 = NavmeshIndex::Primal(p2);
+    let d5 = NavmeshIndex::Dual(DualIndex::Inner(5));
+    let d6 = NavmeshIndex::Dual(DualIndex::Inner(6));
+
+    let next_pos = navmesh
+        .as_ref()
+        .planarr_find_other_end(&d6, &p2, 0, false, &d5)
+        .unwrap()
+        .1;
+    let mut tmp = navmesh.as_mut();
+    tmp.edge_data_mut(d6, p2).unwrap().with_borrow_mut(|mut j| {
+        j.insert(0, label.clone());
+    });
+    let next_pos = tmp.edge_data_mut(d6, d5).unwrap().with_borrow_mut(|mut j| {
+        j.insert(next_pos.insert_pos, label);
+        j.len() - next_pos.insert_pos - 1
+    });
+
+    insta::assert_json_snapshot!(navmesh
+        .as_ref()
+        .planarr_find_all_other_ends(&d5, &d6, next_pos, true)
+        .unwrap()
+        .1
+        .collect::<Vec<_>>());
+}

crates/planar-incr-embed/tests/snapshots/complex__tht_3pin_xlr_to_tht_3pin_xlr.snap

@@ -0,0 +1,43 @@
+---
+source: tests/complex.rs
+expression: "navmesh.as_ref().planarr_find_all_other_ends(&d5, &d6, next_pos,\ntrue).unwrap().1.collect::<Vec<_>>()"
+---
+[
+  [
+    {
+      "Primal": {
+        "Primitive": {
+          "FixedDot": 0
+        }
+      }
+    },
+    {
+      "section_idx": 5,
+      "insert_pos": 0
+    }
+  ],
+  [
+    {
+      "Dual": {
+        "Inner": 2
+      }
+    },
+    {
+      "section_idx": 2,
+      "insert_pos": 1
+    }
+  ],
+  [
+    {
+      "Primal": {
+        "Primitive": {
+          "FixedDot": 4
+        }
+      }
+    },
+    {
+      "section_idx": 3,
+      "insert_pos": 0
+    }
+  ]
+]

crates/planar-incr-embed/tests/tht_3pin_xlr_to_tht_3pin_xlr/goals.ron

@@ -0,0 +1,5 @@
+[
+  (Primitive(FixedDot(0)), Primitive(FixedDot(6))),
+  (Primitive(FixedDot(2)), Primitive(FixedDot(8))),
+  (Primitive(FixedDot(4)), Primitive(FixedDot(10)))
+]

crates/planar-incr-embed/tests/tht_3pin_xlr_to_tht_3pin_xlr/navmesh_intermed.ron

@@ -0,0 +1,233 @@
+(
+    nodes: {
+        Dual(Inner(1)): (
+            neighs: [
+                Primal(Primitive(FixedDot(2))),
+                Dual(Inner(6)),
+                Primal(Primitive(FixedDot(4))),
+                Dual(Inner(2)),
+                Primal(Primitive(FixedDot(10))),
+                Dual(Inner(3)),
+            ],
+            pos: (x: 0.0, y: 0.0),
+            open_direction: None,
+        ),
+        Dual(Inner(2)): (
+            neighs: [
+                Dual(Inner(5)),
+                Primal(Primitive(FixedDot(8))),
+                Dual(Inner(4)),
+                Primal(Primitive(FixedDot(10))),
+                Dual(Inner(1)),
+                Primal(Primitive(FixedDot(4))),
+            ],
+            pos: (x: 0.0, y: 0.0),
+            open_direction: None,
+        ),
+        Dual(Inner(3)): (
+            neighs: [
+                Primal(Primitive(FixedDot(2))),
+                Dual(Inner(1)),
+                Primal(Primitive(FixedDot(10))),
+                Dual(Inner(4)),
+                Primal(Primitive(FixedDot(6))),
+                Dual(Outer(13)),
+            ],
+            pos: (x: 0.0, y: 0.0),
+            open_direction: None,
+        ),
+        Dual(Inner(4)): (
+            neighs: [
+                Primal(Primitive(FixedDot(10))),
+                Dual(Inner(2)),
+                Primal(Primitive(FixedDot(8))),
+                Dual(Outer(15)),
+                Primal(Primitive(FixedDot(6))),
+                Dual(Inner(3)),
+            ],
+            pos: (x: 0.0, y: 0.0),
+            open_direction: None,
+        ),
+        Dual(Inner(5)): (
+            neighs: [
+                Dual(Outer(19)),
+                Primal(Primitive(FixedDot(8))),
+                Dual(Inner(2)),
+                Primal(Primitive(FixedDot(4))),
+                Dual(Inner(6)),
+                Primal(Primitive(FixedDot(0))),
+            ],
+            pos: (x: 0.0, y: 0.0),
+            open_direction: None,
+        ),
+        Dual(Inner(6)): (
+            neighs: [
+                Primal(Primitive(FixedDot(0))),
+                Dual(Inner(5)),
+                Primal(Primitive(FixedDot(4))),
+                Dual(Inner(1)),
+                Primal(Primitive(FixedDot(2))),
+                Dual(Outer(21)),
+            ],
+            pos: (x: 0.0, y: 0.0),
+            open_direction: None,
+        ),
+        Dual(Outer(13)): (
+            neighs: [
+                Dual(Outer(21)),
+                Dual(Inner(3)),
+                Primal(Primitive(FixedDot(6))),
+                Dual(Outer(15)),
+            ],
+            pos: (x: 0.0, y: 0.0),
+            open_direction: Some((
+                x: -0.000000000014551915228366852,
+                y: -13970.0,
+            )),
+        ),
+        Dual(Outer(15)): (
+            neighs: [
+                Primal(Primitive(FixedDot(8))),
+                Dual(Outer(19)),
+                Dual(Outer(13)),
+                Dual(Inner(4)),
+            ],
+            pos: (x: 0.0, y: 0.0),
+            open_direction: Some((
+                x: -7620.0,
+                y: 635.0,
+            )),
+        ),
+        Dual(Outer(19)): (
+            neighs: [
+                Dual(Outer(15)),
+                Dual(Inner(5)),
+                Primal(Primitive(FixedDot(0))),
+                Dual(Outer(21)),
+            ],
+            pos: (x: 0.0, y: 0.0),
+            open_direction: Some((
+                x: 0.000000000014551915228366852,
+                y: 13970.0,
+            )),
+        ),
+        Dual(Outer(21)): (
+            neighs: [
+                Dual(Outer(19)),
+                Dual(Inner(6)),
+                Primal(Primitive(FixedDot(2))),
+                Dual(Outer(13)),
+            ],
+            pos: (x: 0.0, y: 0.0),
+            open_direction: Some((
+                x: 7620.0,
+                y: -635.0,
+            )),
+        ),
+        Primal(Primitive(FixedDot(0))): (
+            neighs: [
+                Dual(Outer(19)),
+                Dual(Inner(5)),
+                Dual(Inner(6)),
+            ],
+            pos: (x: 0.0, y: 0.0),
+            open_direction: None,
+        ),
+        Primal(Primitive(FixedDot(2))): (
+            neighs: [
+                Dual(Outer(21)),
+                Dual(Inner(6)),
+                Dual(Inner(1)),
+                Dual(Inner(3)),
+            ],
+            pos: (x: 0.0, y: 0.0),
+            open_direction: None,
+        ),
+        Primal(Primitive(FixedDot(4))): (
+            neighs: [
+                Dual(Inner(6)),
+                Dual(Inner(5)),
+                Dual(Inner(2)),
+                Dual(Inner(1)),
+            ],
+            pos: (x: 0.0, y: 0.0),
+            open_direction: None,
+        ),
+        Primal(Primitive(FixedDot(6))): (
+            neighs: [
+                Dual(Inner(4)),
+                Dual(Outer(13)),
+                Dual(Inner(3)),
+            ],
+            pos: (x: 0.0, y: 0.0),
+            open_direction: None,
+        ),
+        Primal(Primitive(FixedDot(8))): (
+            neighs: [
+                Dual(Inner(2)),
+                Dual(Inner(5)),
+                Dual(Outer(15)),
+                Dual(Inner(4)),
+            ],
+            pos: (x: 0.0, y: 0.0),
+            open_direction: None,
+        ),
+        Primal(Primitive(FixedDot(10))): (
+            neighs: [
+                Dual(Inner(2)),
+                Dual(Inner(4)),
+                Dual(Inner(3)),
+                Dual(Inner(1)),
+            ],
+            pos: (x: 0.0, y: 0.0),
+            open_direction: None,
+        ),
+    },
+    edges: {
+        (Dual(Inner(1)), Dual(Inner(2))): ((), []),
+        (Dual(Inner(1)), Dual(Inner(3))): ((), []),
+        (Dual(Inner(1)), Dual(Inner(6))): ((), []),
+        (Dual(Inner(1)), Primal(Primitive(FixedDot(2)))): ((), []),
+        (Dual(Inner(1)), Primal(Primitive(FixedDot(4)))): ((), []),
+        (Dual(Inner(1)), Primal(Primitive(FixedDot(10)))): ((), []),
+        (Dual(Inner(2)), Dual(Inner(4))): ((), [
+            Normal((Primitive(FixedDot(0)), Primitive(FixedDot(6)))),
+        ]),
+        (Dual(Inner(2)), Dual(Inner(5))): ((), [
+            Normal((Primitive(FixedDot(0)), Primitive(FixedDot(6)))),
+        ]),
+        (Dual(Inner(2)), Primal(Primitive(FixedDot(4)))): ((), []),
+        (Dual(Inner(2)), Primal(Primitive(FixedDot(8)))): ((), []),
+        (Dual(Inner(2)), Primal(Primitive(FixedDot(10)))): ((), []),
+        (Dual(Inner(3)), Dual(Inner(4))): ((), []),
+        (Dual(Inner(3)), Dual(Outer(13))): ((), []),
+        (Dual(Inner(3)), Primal(Primitive(FixedDot(2)))): ((), []),
+        (Dual(Inner(3)), Primal(Primitive(FixedDot(6)))): ((), []),
+        (Dual(Inner(3)), Primal(Primitive(FixedDot(10)))): ((), []),
+        (Dual(Inner(4)), Dual(Outer(15))): ((), []),
+        (Dual(Inner(4)), Primal(Primitive(FixedDot(6)))): ((), [
+            Normal((Primitive(FixedDot(0)), Primitive(FixedDot(6)))),
+        ]),
+        (Dual(Inner(4)), Primal(Primitive(FixedDot(8)))): ((), []),
+        (Dual(Inner(4)), Primal(Primitive(FixedDot(10)))): ((), []),
+        (Dual(Inner(5)), Dual(Inner(6))): ((), []),
+        (Dual(Inner(5)), Dual(Outer(19))): ((), []),
+        (Dual(Inner(5)), Primal(Primitive(FixedDot(0)))): ((), [
+            Normal((Primitive(FixedDot(0)), Primitive(FixedDot(6)))),
+        ]),
+        (Dual(Inner(5)), Primal(Primitive(FixedDot(4)))): ((), []),
+        (Dual(Inner(5)), Primal(Primitive(FixedDot(8)))): ((), []),
+        (Dual(Inner(6)), Dual(Outer(21))): ((), []),
+        (Dual(Inner(6)), Primal(Primitive(FixedDot(0)))): ((), []),
+        (Dual(Inner(6)), Primal(Primitive(FixedDot(2)))): ((), []),
+        (Dual(Inner(6)), Primal(Primitive(FixedDot(4)))): ((), []),
+        (Dual(Outer(13)), Dual(Outer(15))): ((), []),
+        (Dual(Outer(13)), Dual(Outer(21))): ((), []),
+        (Dual(Outer(13)), Primal(Primitive(FixedDot(6)))): ((), []),
+        (Dual(Outer(15)), Dual(Outer(19))): ((), []),
+        (Dual(Outer(15)), Primal(Primitive(FixedDot(8)))): ((), []),
+        (Dual(Outer(19)), Dual(Outer(21))): ((), []),
+        (Dual(Outer(19)), Primal(Primitive(FixedDot(0)))): ((), []),
+        (Dual(Outer(21)), Primal(Primitive(FixedDot(2)))): ((), []),
+    }
+)

crates/planar-incr-embed/tests/tht_3pin_xlr_to_tht_3pin_xlr/navmesh_invalid.ron

@@ -0,0 +1,59 @@
+(
+  nodes:{
+    Dual(Inner(1)):(neighs:[Primal(Primitive(FixedDot(2))),Dual(Inner(6)),Primal(Primitive(FixedDot(4))),Dual(Inner(2)),Primal(Primitive(FixedDot(10))),Dual(Inner(3))],open_direction:None),
+    Dual(Inner(2)):(neighs:[Dual(Inner(5)),Primal(Primitive(FixedDot(8))),Dual(Inner(4)),Primal(Primitive(FixedDot(10))),Dual(Inner(1)),Primal(Primitive(FixedDot(4)))],open_direction:None),
+    Dual(Inner(3)):(neighs:[Primal(Primitive(FixedDot(2))),Dual(Inner(1)),Primal(Primitive(FixedDot(10))),Dual(Inner(4)),Primal(Primitive(FixedDot(6))),Dual(Outer(13))],open_direction:None),
+    Dual(Inner(4)):(neighs:[Primal(Primitive(FixedDot(10))),Dual(Inner(2)),Primal(Primitive(FixedDot(8))),Dual(Outer(15)),Primal(Primitive(FixedDot(6))),Dual(Inner(3))],open_direction:None),
+    Dual(Inner(5)):(neighs:[Dual(Outer(19)),Primal(Primitive(FixedDot(8))),Dual(Inner(2)),Primal(Primitive(FixedDot(4))),Dual(Inner(6)),Primal(Primitive(FixedDot(0)))],open_direction:None),
+    Dual(Inner(6)):(neighs:[Primal(Primitive(FixedDot(0))),Dual(Inner(5)),Primal(Primitive(FixedDot(4))),Dual(Inner(1)),Primal(Primitive(FixedDot(2))),Dual(Outer(21))],open_direction:None),
+    Dual(Outer(13)):(neighs:[Dual(Outer(21)),Dual(Inner(3)),Primal(Primitive(FixedDot(6))),Dual(Outer(15))],open_direction:Some((x:-0.000000000014551915228366852,y:-13970.0))),
+    Dual(Outer(15)):(neighs:[Primal(Primitive(FixedDot(8))),Dual(Outer(19)),Dual(Outer(13)),Dual(Inner(4))],open_direction:Some((x:-7620.0,y:635.0))),
+    Dual(Outer(19)):(neighs:[Dual(Outer(15)),Dual(Inner(5)),Primal(Primitive(FixedDot(0))),Dual(Outer(21))],open_direction:Some((x:0.000000000014551915228366852,y:13970.0))),
+    Dual(Outer(21)):(neighs:[Dual(Outer(19)),Dual(Inner(6)),Primal(Primitive(FixedDot(2))),Dual(Outer(13))],open_direction:Some((x:7620.0,y:-635.0))),
+    Primal(Primitive(FixedDot(0))):(neighs:[Dual(Outer(19)),Dual(Inner(5)),Dual(Inner(6))],open_direction:None),
+    Primal(Primitive(FixedDot(2))):(neighs:[Dual(Outer(21)),Dual(Inner(6)),Dual(Inner(1)),Dual(Inner(3))],open_direction:None),
+    Primal(Primitive(FixedDot(4))):(neighs:[Dual(Inner(6)),Dual(Inner(5)),Dual(Inner(2)),Dual(Inner(1))],open_direction:None),
+    Primal(Primitive(FixedDot(6))):(neighs:[Dual(Inner(4)),Dual(Outer(13)),Dual(Inner(3))],open_direction:None),
+    Primal(Primitive(FixedDot(8))):(neighs:[Dual(Inner(2)),Dual(Inner(5)),Dual(Outer(15)),Dual(Inner(4))],open_direction:None),
+    Primal(Primitive(FixedDot(10))):(neighs:[Dual(Inner(2)),Dual(Inner(4)),Dual(Inner(3)),Dual(Inner(1))],open_direction:None)
+  },
+  edges:{
+    (Dual(Inner(1)),Dual(Inner(2))):(paths:[],weight:13342.493438320249),
+    (Dual(Inner(1)),Dual(Inner(3))):(paths:[],weight:854.5080618564726),
+    (Dual(Inner(1)),Dual(Inner(6))):(paths:[],weight:9463.450638488148),
+    (Dual(Inner(1)),Primal(Primitive(FixedDot(2)))):(paths:[],weight:7255.50060560296),
+    (Dual(Inner(1)),Primal(Primitive(FixedDot(4)))):(paths:[],weight:7255.5006056029515),
+    (Dual(Inner(1)),Primal(Primitive(FixedDot(10)))):(paths:[],weight:7255.5006056029415),
+    (Dual(Inner(2)),Dual(Inner(4))):(paths:[(Primitive(FixedDot(0)),Primitive(FixedDot(6)))],weight:9463.450638488148),
+    (Dual(Inner(2)),Dual(Inner(5))):(paths:[(Primitive(FixedDot(0)),Primitive(FixedDot(6)))],weight:854.5080618564726),
+    (Dual(Inner(2)),Primal(Primitive(FixedDot(4)))):(paths:[(Primitive(FixedDot(4)),Primitive(FixedDot(10)))],weight:7255.5006056029415),
+    (Dual(Inner(2)),Primal(Primitive(FixedDot(8)))):(paths:[],weight:7255.50060560296),
+    (Dual(Inner(2)),Primal(Primitive(FixedDot(10)))):(paths:[(Primitive(FixedDot(4)),Primitive(FixedDot(10)))],weight:7255.5006056029515),
+    (Dual(Inner(3)),Dual(Inner(4))):(paths:[],weight:9794.094419218618),
+    (Dual(Inner(3)),Dual(Outer(13))):(paths:[],weight:10315.419947506583),
+    (Dual(Inner(3)),Primal(Primitive(FixedDot(2)))):(paths:[],weight:7883.284871174122),
+    (Dual(Inner(3)),Primal(Primitive(FixedDot(6)))):(paths:[],weight:7883.284871174128),
+    (Dual(Inner(3)),Primal(Primitive(FixedDot(10)))):(paths:[],weight:7883.284871174124),
+    (Dual(Inner(4)),Dual(Outer(15))):(paths:[],weight:7945.163814846131),
+    (Dual(Inner(4)),Primal(Primitive(FixedDot(6)))):(paths:[(Primitive(FixedDot(0)),Primitive(FixedDot(6)))],weight:3834.860957550632),
+    (Dual(Inner(4)),Primal(Primitive(FixedDot(8)))):(paths:[],weight:3834.8609575506225),
+    (Dual(Inner(4)),Primal(Primitive(FixedDot(10)))):(paths:[],weight:3834.8609575506225),
+    (Dual(Inner(5)),Dual(Inner(6))):(paths:[(Primitive(FixedDot(2)),Primitive(FixedDot(8)))],weight:9794.094419218618),
+    (Dual(Inner(5)),Dual(Outer(19))):(paths:[],weight:10315.419947506569),
+    (Dual(Inner(5)),Primal(Primitive(FixedDot(0)))):(paths:[(Primitive(FixedDot(0)),Primitive(FixedDot(6)))],weight:7883.284871174128),
+    (Dual(Inner(5)),Primal(Primitive(FixedDot(4)))):(paths:[],weight:7883.284871174124),
+    (Dual(Inner(5)),Primal(Primitive(FixedDot(8)))):(paths:[(Primitive(FixedDot(2)),Primitive(FixedDot(8)))],weight:7883.284871174122),
+    (Dual(Inner(6)),Dual(Outer(21))):(paths:[],weight:7945.163814846131),
+    (Dual(Inner(6)),Primal(Primitive(FixedDot(0)))):(paths:[],weight:3834.860957550632),
+    (Dual(Inner(6)),Primal(Primitive(FixedDot(2)))):(paths:[(Primitive(FixedDot(2)),Primitive(FixedDot(8)))],weight:3834.8609575506225),
+    (Dual(Inner(6)),Primal(Primitive(FixedDot(4)))):(paths:[],weight:3834.8609575506225),
+    (Dual(Outer(13)),Dual(Outer(15))):(paths:[],weight:23307.614233335862),
+    (Dual(Outer(13)),Dual(Outer(21))):(paths:[],weight:22729.54093795121),
+    (Dual(Outer(13)),Primal(Primitive(FixedDot(6)))):(paths:[],weight:15618.934822836045),
+    (Dual(Outer(15)),Dual(Outer(19))):(paths:[],weight:22729.5409379512),
+    (Dual(Outer(15)),Primal(Primitive(FixedDot(8)))):(paths:[],weight:8548.949131326026),
+    (Dual(Outer(19)),Dual(Outer(21))):(paths:[],weight:23307.61423333585),
+    (Dual(Outer(19)),Primal(Primitive(FixedDot(0)))):(paths:[],weight:15618.93482283603),
+    (Dual(Outer(21)),Primal(Primitive(FixedDot(2)))):(paths:[],weight:8548.949131326026)
+  }
+)

crates/specctra-core/src/mesadata.rs

@@ -178,19 +178,11 @@ impl SpecctraMesadata {
 }
 
 impl AccessRules for SpecctraMesadata {
-    fn clearance(&self, conditions1: &Conditions, conditions2: &Conditions) -> f64 {
+    fn clearance(&self, conditions1: &Conditions<'_>, conditions2: &Conditions<'_>) -> f64 {
-        let (Some(net1), Some(net2)) = (conditions1.maybe_net, conditions2.maybe_net) else {
+        let clr1 = self.get_rule(conditions1.net).clearance;
-            return 0.0;
+        let clr2 = self.get_rule(conditions2.net).clearance;
-        };
 
-        let clr1 = self.get_rule(net1).clearance;
+        f64::max(clr1, clr2)
-        let clr2 = self.get_rule(net2).clearance;
-
-        if clr1 > clr2 {
-            clr1
-        } else {
-            clr2
-        }
     }
 
     fn largest_clearance(&self, _maybe_net: Option<usize>) -> f64 {

crates/specctra-core/src/rules.rs

@@ -2,18 +2,35 @@
 //
 // SPDX-License-Identifier: MIT
 
-pub trait GetConditions {
+use std::borrow::Cow;
-    fn conditions(&self) -> Conditions;
+
+pub trait GetConditions<'a> {
+    fn conditions(self) -> Option<Conditions<'a>>;
 }
 
-#[derive(Debug, Default)]
+#[derive(
-pub struct Conditions {
+    Clone,
-    pub maybe_net: Option<usize>,
+    Debug,
-    pub maybe_region: Option<String>,
+    Default,
-    pub maybe_layer: Option<String>,
+    PartialEq,
+    Eq,
+    PartialOrd,
+    Ord,
+    Hash,
+    serde::Deserialize,
+    serde::Serialize,
+)]
+pub struct Conditions<'a> {
+    pub net: usize,
+
+    #[serde(borrow)]
+    pub maybe_region: Option<Cow<'a, str>>,
+
+    #[serde(borrow)]
+    pub maybe_layer: Option<Cow<'a, str>>,
 }
 
 pub trait AccessRules {
-    fn clearance(&self, conditions1: &Conditions, conditions2: &Conditions) -> f64;
+    fn clearance(&self, conditions1: &Conditions<'_>, conditions2: &Conditions<'_>) -> f64;
     fn largest_clearance(&self, net: Option<usize>) -> f64;
 }

src/autorouter/measure_length.rs

@@ -43,7 +43,7 @@ impl MeasureLengthExecutionStepper {
             let mut length = 0.0;
 
             for selector in self.selection.selectors() {
-                let band = autorouter.board.bandname_band(&selector.band).unwrap().0;
+                let band = autorouter.board.bandname_band(&selector.band).unwrap()[false];
                 length += band.ref_(autorouter.board.layout().drawing()).length();
             }
 

src/autorouter/remove_bands.rs

@@ -41,7 +41,7 @@ impl RemoveBandsExecutionStepper {
 
             let mut edit = LayoutEdit::new();
             for selector in self.selection.selectors() {
-                let band = autorouter.board.bandname_band(&selector.band).unwrap().0;
+                let band = autorouter.board.bandname_band(&selector.band).unwrap()[false];
                 autorouter.board.layout_mut().remove_band(&mut edit, band);
             }
             Ok(Some(edit))

src/board/mod.rs

@@ -8,11 +8,9 @@
 
 pub use specctra_core::mesadata::AccessMesadata;
 
-use std::{cmp::Ordering, collections::BTreeMap};
-
 use bimap::BiBTreeMap;
 use derive_getters::Getters;
-use serde::{Deserialize, Serialize};
+use std::collections::BTreeMap;
 
 use crate::{
     drawing::{
@@ -33,21 +31,7 @@ use crate::{
 };
 
 /// Represents a band between two pins.
-#[derive(Clone, Debug, Deserialize, Eq, PartialOrd, Ord, PartialEq, Serialize)]
+pub type BandName = planar_incr_embed::navmesh::OrderedPair<String>;
-pub struct BandName(String, String);
-
-impl BandName {
-    /// Creates a new [`BandName`] and manages their order.
-    ///
-    /// This function ensures that the two pin names are sorted in lexicographical order, so that the smaller name always comes first.
-    pub fn new(pinname1: String, pinname2: String) -> Self {
-        if pinname1.cmp(&pinname2) == Ordering::Greater {
-            BandName(pinname2, pinname1)
-        } else {
-            BandName(pinname1, pinname2)
-        }
-    }
-}
 
 #[derive(Clone, Debug, PartialEq, Eq, PartialOrd, Ord, Hash)]
 pub enum ResolvedSelector<'a> {
@@ -284,14 +268,17 @@ impl<M: AccessMesadata> Board<M> {
             .unwrap()
             .to_string();
         self.band_bandname
-            .insert(band, BandName::new(source_pinname, target_pinname));
+            .insert(band, BandName::from((source_pinname, target_pinname)));
     }
 
     /// Finds a band between two pin names.
     pub fn band_between_pins(&self, pinname1: &str, pinname2: &str) -> Option<BandUid> {
         self.band_bandname
             // note: it doesn't matter in what order pinnames are given, the constructor sorts them
-            .get_by_right(&BandName::new(pinname1.to_string(), pinname2.to_string()))
+            .get_by_right(&BandName::from((
+                pinname1.to_string(),
+                pinname2.to_string(),
+            )))
             .copied()
     }
 

src/drawing/band.rs

@@ -2,7 +2,6 @@
 //
 // SPDX-License-Identifier: MIT
 
-use core::{cmp, hash};
 use enum_dispatch::enum_dispatch;
 use petgraph::stable_graph::NodeIndex;
 
@@ -20,54 +19,10 @@ use super::{
     Drawing,
 };
 
-#[derive(Clone, Copy, Debug)]
+pub type BandUid = planar_incr_embed::navmesh::OrderedPair<BandTermsegIndex>;
-pub struct BandUid(pub BandTermsegIndex, pub BandTermsegIndex);
-
-impl BandUid {
-    pub fn new(first_seg1: BandTermsegIndex, first_seg2: BandTermsegIndex) -> Self {
-        if first_seg1.petgraph_index() <= first_seg2.petgraph_index() {
-            BandUid(first_seg1, first_seg2)
-        } else {
-            BandUid(first_seg2, first_seg1)
-        }
-    }
-}
-
-impl PartialEq for BandUid {
-    fn eq(&self, other: &Self) -> bool {
-        self.0.petgraph_index() == other.0.petgraph_index()
-            && self.1.petgraph_index() == other.1.petgraph_index()
-    }
-}
-
-impl Eq for BandUid {}
-
-impl hash::Hash for BandUid {
-    fn hash<H: hash::Hasher>(&self, state: &mut H) {
-        self.0.petgraph_index().hash(state);
-        self.1.petgraph_index().hash(state);
-    }
-}
-
-impl cmp::PartialOrd for BandUid {
-    fn partial_cmp(&self, other: &Self) -> Option<cmp::Ordering> {
-        Some(self.cmp(other))
-    }
-}
-
-impl cmp::Ord for BandUid {
-    fn cmp(&self, other: &Self) -> cmp::Ordering {
-        use cmp::Ordering as O;
-        match self.0.petgraph_index().cmp(&other.0.petgraph_index()) {
-            O::Less => O::Less,
-            O::Greater => O::Greater,
-            O::Equal => self.1.petgraph_index().cmp(&other.1.petgraph_index()),
-        }
-    }
-}
 
 #[enum_dispatch(GetPetgraphIndex)]
-#[derive(Clone, Copy, Debug, Eq, Ord, PartialEq, PartialOrd)]
+#[derive(Clone, Copy, Debug, Eq, Ord, PartialEq, PartialOrd, Hash)]
 pub enum BandTermsegIndex {
     Straight(LoneLooseSegIndex),
     Bended(SeqLooseSegIndex),

src/drawing/collect.rs

@@ -27,10 +27,10 @@ pub trait Collect {
 
 impl<CW: Copy, R: AccessRules> Collect for Drawing<CW, R> {
     fn loose_band_uid(&self, start_loose: LooseIndex) -> BandUid {
-        BandUid::new(
+        BandUid::from((
             self.loose_band_first_seg(start_loose),
             self.loose_band_last_seg(start_loose),
-        )
+        ))
     }
 
     fn bend_bow(&self, bend: LooseBendIndex) -> Vec<PrimitiveIndex> {

src/drawing/drawing.rs

@@ -981,8 +981,12 @@ impl<CW: Copy, R: AccessRules> Drawing<CW, R> {
 
                 let epsilon = 1.0;
                 inflated_shape = node.primitive(self).shape().inflate(
-                    (self.rules.clearance(&conditions, &infringee_conditions) - epsilon)
+                    match (&conditions, infringee_conditions) {
-                        .clamp(0.0, f64::INFINITY),
+                        (None, _) | (_, None) => 0.0,
+                        (Some(lhs), Some(rhs)) => {
+                            (self.rules.clearance(lhs, &rhs) - epsilon).clamp(0.0, f64::INFINITY)
+                        }
+                    },
                 );
 
                 inflated_shape

src/drawing/guide.rs

@@ -97,7 +97,8 @@ impl<CW: Copy, R: AccessRules> Guide for Drawing<CW, R> {
         width: f64,
     ) -> Result<(Line, Line), NoTangents> {
         let from_circle = self.head_circle(head, width);
-        let to_circle = self.dot_circle(around, width, &self.conditions(head.face().into()));
+        let to_circle =
+            self.dot_circle(around, width, self.conditions(head.face().into()).as_ref());
 
         let from_cw = self.head_cw(head);
         let tangents: Vec<Line> =
@@ -113,16 +114,17 @@ impl<CW: Copy, R: AccessRules> Guide for Drawing<CW, R> {
         width: f64,
     ) -> Result<Line, NoTangents> {
         let from_circle = self.head_circle(head, width);
-        let to_circle = self.dot_circle(around, width, &self.conditions(head.face().into()));
+        let to_circle =
+            self.dot_circle(around, width, self.conditions(head.face().into()).as_ref());
 
         let from_cw = self.head_cw(head);
         math::tangent_segment(from_circle, from_cw, to_circle, Some(cw))
     }
 
     fn head_around_dot_offset(&self, head: &Head, around: DotIndex, _width: f64) -> f64 {
-        self.rules().clearance(
+        self.clearance(
-            &self.conditions(around.into()),
+            self.conditions(around.into()).as_ref(),
-            &self.conditions(head.face().into()),
+            self.conditions(head.face().into()).as_ref(),
         )
     }
 
@@ -133,7 +135,8 @@ impl<CW: Copy, R: AccessRules> Guide for Drawing<CW, R> {
         width: f64,
     ) -> Result<(Line, Line), NoTangents> {
         let from_circle = self.head_circle(head, width);
-        let to_circle = self.bend_circle(around, width, &self.conditions(head.face().into()));
+        let to_circle =
+            self.bend_circle(around, width, self.conditions(head.face().into()).as_ref());
 
         let from_cw = self.head_cw(head);
         let tangents: Vec<Line> =
@@ -149,16 +152,17 @@ impl<CW: Copy, R: AccessRules> Guide for Drawing<CW, R> {
         width: f64,
     ) -> Result<Line, NoTangents> {
         let from_circle = self.head_circle(head, width);
-        let to_circle = self.bend_circle(around, width, &self.conditions(head.face().into()));
+        let to_circle =
+            self.bend_circle(around, width, self.conditions(head.face().into()).as_ref());
 
         let from_cw = self.head_cw(head);
         math::tangent_segment(from_circle, from_cw, to_circle, Some(cw))
     }
 
     fn head_around_bend_offset(&self, head: &Head, around: BendIndex, _width: f64) -> f64 {
-        self.rules().clearance(
+        self.clearance(
-            &self.conditions(head.face().into()),
+            self.conditions(head.face().into()).as_ref(),
-            &self.conditions(around.into()),
+            self.conditions(around.into()).as_ref(),
         )
     }
 
@@ -196,18 +200,37 @@ impl<CW: Copy, R: AccessRules> Guide for Drawing<CW, R> {
 }
 
 trait GuidePrivate {
+    fn clearance(&self, lhs: Option<&Conditions<'_>>, rhs: Option<&Conditions<'_>>) -> f64;
+
     fn head_circle(&self, head: &Head, width: f64) -> Circle;
 
-    fn bend_circle(&self, bend: BendIndex, width: f64, guide_conditions: &Conditions) -> Circle;
+    fn bend_circle(
+        &self,
+        bend: BendIndex,
+        width: f64,
+        guide_conditions: Option<&Conditions<'_>>,
+    ) -> Circle;
 
-    fn dot_circle(&self, dot: DotIndex, width: f64, guide_conditions: &Conditions) -> Circle;
+    fn dot_circle(
+        &self,
+        dot: DotIndex,
+        width: f64,
+        guide_conditions: Option<&Conditions<'_>>,
+    ) -> Circle;
 
     fn rear(&self, head: CaneHead) -> DotIndex;
 
-    fn conditions(&self, node: PrimitiveIndex) -> Conditions;
+    fn conditions(&self, node: PrimitiveIndex) -> Option<Conditions<'_>>;
 }
 
 impl<CW: Copy, R: AccessRules> GuidePrivate for Drawing<CW, R> {
+    fn clearance(&self, lhs: Option<&Conditions<'_>>, rhs: Option<&Conditions<'_>>) -> f64 {
+        match (lhs, rhs) {
+            (None, _) | (_, None) => 0.0,
+            (Some(lhs), Some(rhs)) => self.rules().clearance(lhs, rhs),
+        }
+    }
+
     fn head_circle(&self, head: &Head, width: f64) -> Circle {
         match *head {
             Head::Bare(head) => Circle {
@@ -216,19 +239,28 @@ impl<CW: Copy, R: AccessRules> GuidePrivate for Drawing<CW, R> {
             },
             Head::Cane(head) => {
                 if let Some(inner) = self.primitive(head.cane.bend).inner() {
-                    self.bend_circle(inner.into(), width, &self.conditions(head.face().into()))
+                    self.bend_circle(
+                        inner.into(),
+                        width,
+                        self.conditions(head.face().into()).as_ref(),
+                    )
                 } else {
                     self.dot_circle(
                         self.primitive(head.cane.bend).core().into(),
                         width,
-                        &self.conditions(head.face().into()),
+                        self.conditions(head.face().into()).as_ref(),
                     )
                 }
             }
         }
     }
 
-    fn bend_circle(&self, bend: BendIndex, width: f64, guide_conditions: &Conditions) -> Circle {
+    fn bend_circle(
+        &self,
+        bend: BendIndex,
+        width: f64,
+        guide_conditions: Option<&Conditions<'_>>,
+    ) -> Circle {
         let outer_circle = match bend.primitive(self).shape() {
             PrimitiveShape::Bend(shape) => shape.outer_circle(),
             _ => unreachable!(),
@@ -238,21 +270,22 @@ impl<CW: Copy, R: AccessRules> GuidePrivate for Drawing<CW, R> {
             pos: outer_circle.pos,
             r: outer_circle.r
                 + width / 2.0
-                + self
+                + self.clearance(self.conditions(bend.into()).as_ref(), guide_conditions),
-                    .rules()
-                    .clearance(&self.conditions(bend.into()), guide_conditions),
         }
     }
 
-    fn dot_circle(&self, dot: DotIndex, width: f64, guide_conditions: &Conditions) -> Circle {
+    fn dot_circle(
+        &self,
+        dot: DotIndex,
+        width: f64,
+        guide_conditions: Option<&Conditions<'_>>,
+    ) -> Circle {
         let shape = dot.primitive(self).shape();
         Circle {
             pos: shape.center(),
             r: shape.width() / 2.0
                 + width / 2.0
-                + self
+                + self.clearance(self.conditions(dot.into()).as_ref(), guide_conditions),
-                    .rules()
-                    .clearance(&self.conditions(dot.into()), guide_conditions),
         }
     }
 
@@ -261,7 +294,7 @@ impl<CW: Copy, R: AccessRules> GuidePrivate for Drawing<CW, R> {
             .other_joint(head.cane.dot.into())
     }
 
-    fn conditions(&self, node: PrimitiveIndex) -> Conditions {
+    fn conditions(&self, node: PrimitiveIndex) -> Option<Conditions<'_>> {
         node.primitive(self).conditions()
     }
 }

src/drawing/loose.rs

@@ -12,13 +12,12 @@ use crate::{
         dot::{DotIndex, LooseDotIndex},
         graph::{MakePrimitive, PrimitiveIndex},
         primitive::{GetJoints, LoneLooseSeg, LooseBend, LooseDot, Primitive, SeqLooseSeg},
+        rules::AccessRules,
         seg::{LoneLooseSegIndex, SeqLooseSegIndex},
     },
     graph::GetPetgraphIndex,
 };
 
-use super::rules::AccessRules;
-
 #[enum_dispatch]
 pub trait GetPrevNextLoose {
     fn next_loose(&self, maybe_prev: Option<LooseIndex>) -> Option<LooseIndex>;

src/drawing/primitive.rs

@@ -10,6 +10,7 @@ use crate::{
         bend::{BendIndex, FixedBendWeight, LooseBendIndex, LooseBendWeight},
         dot::{DotIndex, DotWeight, FixedDotIndex, FixedDotWeight, LooseDotIndex, LooseDotWeight},
         graph::{GetMaybeNet, PrimitiveIndex, PrimitiveWeight},
+        rules::{AccessRules, Conditions, GetConditions},
         seg::{FixedSegWeight, LoneLooseSegWeight, SegIndex, SeqLooseSegIndex, SeqLooseSegWeight},
         Drawing,
     },
@@ -17,8 +18,6 @@ use crate::{
     graph::{GenericIndex, GetPetgraphIndex},
 };
 
-use specctra_core::rules::{AccessRules, Conditions, GetConditions};
-
 #[enum_dispatch]
 pub trait GetDrawing<'a, R: AccessRules> {
     fn drawing(&self) -> &Drawing<impl Copy, R>;
@@ -171,16 +170,16 @@ pub enum Primitive<'a, CW: Copy, R: AccessRules> {
     LooseBend(LooseBend<'a, CW, R>),
 }
 
-impl<'a, CW: Copy, R: AccessRules> specctra_core::rules::GetConditions for Primitive<'a, CW, R> {
+impl<'a, CW: Copy, R: AccessRules> GetConditions<'a> for &Primitive<'a, CW, R> {
-    fn conditions(&self) -> specctra_core::rules::Conditions {
+    fn conditions(self) -> Option<Conditions<'a>> {
         match self {
-            Self::FixedDot(x) => x.conditions(),
+            Primitive::FixedDot(x) => x.conditions(),
-            Self::LooseDot(x) => x.conditions(),
+            Primitive::LooseDot(x) => x.conditions(),
-            Self::FixedSeg(x) => x.conditions(),
+            Primitive::FixedSeg(x) => x.conditions(),
-            Self::LoneLooseSeg(x) => x.conditions(),
+            Primitive::LoneLooseSeg(x) => x.conditions(),
-            Self::SeqLooseSeg(x) => x.conditions(),
+            Primitive::SeqLooseSeg(x) => x.conditions(),
-            Self::FixedBend(x) => x.conditions(),
+            Primitive::FixedBend(x) => x.conditions(),
-            Self::LooseBend(x) => x.conditions(),
+            Primitive::LooseBend(x) => x.conditions(),
         }
     }
 }
@@ -240,16 +239,16 @@ where
     }
 }
 
-impl<'a, W, CW: Copy, R: AccessRules> GetConditions for GenericPrimitive<'a, W, CW, R>
+impl<'a, W, CW: Copy, R: AccessRules> GetConditions<'a> for &GenericPrimitive<'a, W, CW, R>
 where
     GenericPrimitive<'a, W, CW, R>: GetMaybeNet,
 {
-    fn conditions(&self) -> Conditions {
+    fn conditions(self) -> Option<Conditions<'a>> {
-        Conditions {
+        self.maybe_net().map(|net| Conditions {
-            maybe_net: self.maybe_net(),
+            net,
-            maybe_region: Some("A".to_string()),
+            maybe_region: Some("A".into()),
-            maybe_layer: Some("F.Cu".to_string()),
+            maybe_layer: Some("F.Cu".into()),
-        }
+        })
     }
 }
 

src/graph.rs

@@ -80,6 +80,13 @@ impl<W> Ord for GenericIndex<W> {
     }
 }
 
+impl<W> core::hash::Hash for GenericIndex<W> {
+    #[inline]
+    fn hash<H: core::hash::Hasher>(&self, state: &mut H) {
+        self.node_index.hash(state);
+    }
+}
+
 impl<W> GetPetgraphIndex for GenericIndex<W> {
     #[inline]
     fn petgraph_index(&self) -> NodeIndex<usize> {

tests/common/mod.rs

@@ -205,7 +205,7 @@ pub fn assert_band_length(
     rel_err: f64,
 ) {
     let band = board.band_between_pins(source_pin, target_pin).unwrap();
-    let band_length = band.0.ref_(board.layout().drawing()).length();
+    let band_length = band[false].ref_(board.layout().drawing()).length();
     assert!(
         (band_length - expected_length).abs() < expected_length * rel_err,
         "band_length = {}, expected_length = {}, epsilon = {}",