mirror of https://codeberg.org/topola/topola.git
refactor(math): put tangents stuff into separate module
This commit is contained in:
Alain Emilia Anna Zscheile
mikolaj
parent
c9b5c39b3d
commit
4529ac1ba3
|
|
@ -0,0 +1,128 @@
|
|||
// SPDX-FileCopyrightText: 2024 Topola contributors
|
||||
//
|
||||
// SPDX-License-Identifier: MIT
|
||||
|
||||
use geo::algorithm::line_measures::{Distance, Euclidean};
|
||||
use geo::{geometry::Point, point, Line};
|
||||
pub use specctra_core::math::{Circle, PointWithRotation};
|
||||
|
||||
mod tangents;
|
||||
pub use tangents::*;
|
||||
|
||||
pub fn intersect_circles(circle1: &Circle, circle2: &Circle) -> Vec<Point> {
|
||||
let delta = circle2.pos - circle1.pos;
|
||||
let d = Euclidean::distance(&circle2.pos, &circle1.pos);
|
||||
|
||||
if d > circle1.r + circle2.r {
|
||||
// No intersection.
|
||||
return vec![];
|
||||
}
|
||||
|
||||
if d < (circle2.r - circle1.r).abs() {
|
||||
// One contains the other.
|
||||
return vec![];
|
||||
}
|
||||
|
||||
// Distance from `circle1.pos` to the intersection of the diagonals.
|
||||
let a = (circle1.r * circle1.r - circle2.r * circle2.r + d * d) / (2.0 * d);
|
||||
|
||||
// Intersection of the diagonals.
|
||||
let p = circle1.pos + delta * (a / d);
|
||||
let h = (circle1.r * circle1.r - a * a).sqrt();
|
||||
|
||||
if h == 0.0 {
|
||||
return [p].into();
|
||||
}
|
||||
|
||||
let r = point! {x: -delta.x(), y: delta.y()} * (h / d);
|
||||
|
||||
[p + r, p - r].into()
|
||||
}
|
||||
|
||||
pub fn intersect_circle_segment(circle: &Circle, segment: &Line) -> Vec<Point> {
|
||||
let delta: Point = segment.delta().into();
|
||||
let from = segment.start_point();
|
||||
let to = segment.end_point();
|
||||
let epsilon = 1e-9;
|
||||
let interval01 = 0.0..=1.0;
|
||||
|
||||
let a = delta.dot(delta);
|
||||
let b =
|
||||
2.0 * (delta.x() * (from.x() - circle.pos.x()) + delta.y() * (from.y() - circle.pos.y()));
|
||||
let c = circle.pos.dot(circle.pos) + from.dot(from)
|
||||
- 2.0 * circle.pos.dot(from)
|
||||
- circle.r * circle.r;
|
||||
let discriminant = b * b - 4.0 * a * c;
|
||||
|
||||
if a.abs() < epsilon || discriminant < 0.0 {
|
||||
return [].into();
|
||||
}
|
||||
|
||||
if discriminant == 0.0 {
|
||||
let u = -b / (2.0 * a);
|
||||
|
||||
return if interval01.contains(&u) {
|
||||
vec![from + (to - from) * -b / (2.0 * a)]
|
||||
} else {
|
||||
vec![]
|
||||
};
|
||||
}
|
||||
|
||||
let mut v = vec![];
|
||||
|
||||
let u1 = (-b + discriminant.sqrt()) / (2.0 * a);
|
||||
|
||||
if interval01.contains(&u1) {
|
||||
v.push(from + (to - from) * u1);
|
||||
}
|
||||
|
||||
let u2 = (-b - discriminant.sqrt()) / (2.0 * a);
|
||||
|
||||
if interval01.contains(&u2) {
|
||||
v.push(from + (to - from) * u2);
|
||||
}
|
||||
|
||||
v
|
||||
}
|
||||
|
||||
pub fn between_vectors(p: Point, from: Point, to: Point) -> bool {
|
||||
let cross = cross_product(from, to);
|
||||
|
||||
if cross > 0.0 {
|
||||
cross_product(from, p) >= 0.0 && cross_product(p, to) >= 0.0
|
||||
} else if cross < 0.0 {
|
||||
cross_product(from, p) >= 0.0 || cross_product(p, to) >= 0.0
|
||||
} else {
|
||||
false
|
||||
}
|
||||
}
|
||||
|
||||
/// Computes the (directed) angle between the positive X axis and the vector.
|
||||
///
|
||||
/// The result is measured counterclockwise and normalized into range (-pi, pi] (like atan2).
|
||||
pub fn vector_angle(vector: Point) -> f64 {
|
||||
vector.y().atan2(vector.x())
|
||||
}
|
||||
|
||||
/// Computes the (directed) angle between two vectors.
|
||||
///
|
||||
/// The result is measured counterclockwise and normalized into range (-pi, pi] (like atan2).
|
||||
pub fn angle_between(v1: Point, v2: Point) -> f64 {
|
||||
cross_product(v1, v2).atan2(dot_product(v1, v2))
|
||||
}
|
||||
|
||||
pub fn seq_cross_product(start: Point, stop: Point, reference: Point) -> f64 {
|
||||
let dx1 = stop.x() - start.x();
|
||||
let dy1 = stop.y() - start.y();
|
||||
let dx2 = reference.x() - stop.x();
|
||||
let dy2 = reference.y() - stop.y();
|
||||
cross_product((dx1, dy1).into(), (dx2, dy2).into())
|
||||
}
|
||||
|
||||
pub fn dot_product(v1: Point, v2: Point) -> f64 {
|
||||
v1.x() * v2.x() + v1.y() * v2.y()
|
||||
}
|
||||
|
||||
pub fn cross_product(v1: Point, v2: Point) -> f64 {
|
||||
v1.x() * v2.y() - v1.y() * v2.x()
|
||||
}
|
||||
|
|
@ -4,8 +4,11 @@
|
|||
|
||||
use geo::algorithm::line_measures::{Distance, Euclidean};
|
||||
use geo::{geometry::Point, point, Line};
|
||||
use specctra_core::math::Circle;
|
||||
use thiserror::Error;
|
||||
|
||||
use super::seq_cross_product;
|
||||
|
||||
#[derive(Error, Debug, Clone, Copy, PartialEq)]
|
||||
#[error("no tangents for {0:?} and {1:?}")] // TODO add real error message
|
||||
pub struct NoTangents(pub Circle, pub Circle);
|
||||
|
|
@ -17,8 +20,6 @@ pub struct CanonicalLine {
|
|||
pub c: f64,
|
||||
}
|
||||
|
||||
pub use specctra_core::math::{Circle, PointWithRotation};
|
||||
|
||||
fn _tangent(center: Point, r1: f64, r2: f64) -> Result<CanonicalLine, ()> {
|
||||
let epsilon = 1e-9;
|
||||
let dr = r2 - r1;
|
||||
|
|
@ -130,121 +131,3 @@ pub fn tangent_segment(
|
|||
.next()
|
||||
.unwrap())
|
||||
}
|
||||
|
||||
pub fn intersect_circles(circle1: &Circle, circle2: &Circle) -> Vec<Point> {
|
||||
let delta = circle2.pos - circle1.pos;
|
||||
let d = Euclidean::distance(&circle2.pos, &circle1.pos);
|
||||
|
||||
if d > circle1.r + circle2.r {
|
||||
// No intersection.
|
||||
return vec![];
|
||||
}
|
||||
|
||||
if d < (circle2.r - circle1.r).abs() {
|
||||
// One contains the other.
|
||||
return vec![];
|
||||
}
|
||||
|
||||
// Distance from `circle1.pos` to the intersection of the diagonals.
|
||||
let a = (circle1.r * circle1.r - circle2.r * circle2.r + d * d) / (2.0 * d);
|
||||
|
||||
// Intersection of the diagonals.
|
||||
let p = circle1.pos + delta * (a / d);
|
||||
let h = (circle1.r * circle1.r - a * a).sqrt();
|
||||
|
||||
if h == 0.0 {
|
||||
return [p].into();
|
||||
}
|
||||
|
||||
let r = point! {x: -delta.x(), y: delta.y()} * (h / d);
|
||||
|
||||
[p + r, p - r].into()
|
||||
}
|
||||
|
||||
pub fn intersect_circle_segment(circle: &Circle, segment: &Line) -> Vec<Point> {
|
||||
let delta: Point = segment.delta().into();
|
||||
let from = segment.start_point();
|
||||
let to = segment.end_point();
|
||||
let epsilon = 1e-9;
|
||||
let interval01 = 0.0..=1.0;
|
||||
|
||||
let a = delta.dot(delta);
|
||||
let b =
|
||||
2.0 * (delta.x() * (from.x() - circle.pos.x()) + delta.y() * (from.y() - circle.pos.y()));
|
||||
let c = circle.pos.dot(circle.pos) + from.dot(from)
|
||||
- 2.0 * circle.pos.dot(from)
|
||||
- circle.r * circle.r;
|
||||
let discriminant = b * b - 4.0 * a * c;
|
||||
|
||||
if a.abs() < epsilon || discriminant < 0.0 {
|
||||
return [].into();
|
||||
}
|
||||
|
||||
if discriminant == 0.0 {
|
||||
let u = -b / (2.0 * a);
|
||||
|
||||
return if interval01.contains(&u) {
|
||||
vec![from + (to - from) * -b / (2.0 * a)]
|
||||
} else {
|
||||
vec![]
|
||||
};
|
||||
}
|
||||
|
||||
let mut v = vec![];
|
||||
|
||||
let u1 = (-b + discriminant.sqrt()) / (2.0 * a);
|
||||
|
||||
if interval01.contains(&u1) {
|
||||
v.push(from + (to - from) * u1);
|
||||
}
|
||||
|
||||
let u2 = (-b - discriminant.sqrt()) / (2.0 * a);
|
||||
|
||||
if interval01.contains(&u2) {
|
||||
v.push(from + (to - from) * u2);
|
||||
}
|
||||
|
||||
v
|
||||
}
|
||||
|
||||
pub fn between_vectors(p: Point, from: Point, to: Point) -> bool {
|
||||
let cross = cross_product(from, to);
|
||||
|
||||
if cross > 0.0 {
|
||||
cross_product(from, p) >= 0.0 && cross_product(p, to) >= 0.0
|
||||
} else if cross < 0.0 {
|
||||
cross_product(from, p) >= 0.0 || cross_product(p, to) >= 0.0
|
||||
} else {
|
||||
false
|
||||
}
|
||||
}
|
||||
|
||||
/// Computes the (directed) angle between the positive X axis and the vector.
|
||||
///
|
||||
/// The result is measured counterclockwise and normalized into range (-pi, pi] (like atan2).
|
||||
pub fn vector_angle(vector: Point) -> f64 {
|
||||
vector.y().atan2(vector.x())
|
||||
}
|
||||
|
||||
/// Computes the (directed) angle between two vectors.
|
||||
///
|
||||
/// The result is measured counterclockwise and normalized into range (-pi, pi] (like atan2).
|
||||
pub fn angle_between(v1: Point, v2: Point) -> f64 {
|
||||
cross_product(v1, v2).atan2(dot_product(v1, v2))
|
||||
}
|
||||
|
||||
pub fn seq_cross_product(start: Point, stop: Point, reference: Point) -> f64 {
|
||||
let dx1 = stop.x() - start.x();
|
||||
let dy1 = stop.y() - start.y();
|
||||
let dx2 = reference.x() - stop.x();
|
||||
let dy2 = reference.y() - stop.y();
|
||||
cross_product((dx1, dy1).into(), (dx2, dy2).into())
|
||||
}
|
||||
|
||||
pub fn dot_product(v1: Point, v2: Point) -> f64 {
|
||||
v1.x() * v2.x() + v1.y() * v2.y()
|
||||
}
|
||||
|
||||
pub fn cross_product(v1: Point, v2: Point) -> f64 {
|
||||
v1.x() * v2.y() - v1.y() * v2.x()
|
||||
}
|
||||
Loading…
Reference in New Issue