refactor(math/line): Rename `NormalLine` to `LineInGeneralForm`

The previous name sounded as if it was a normal (to some surface), which
is not the case.

src/layout/collect_bands.rs

@@ -26,7 +26,7 @@ use crate::{
     },
     graph::GetPetgraphIndex,
     layout::{Layout, NodeIndex},
-    math::{intersect_linestring_and_ray, LineIntersection, NormalLine},
+    math::{intersect_linestring_and_ray, LineInGeneralForm, LineIntersection},
 };
 
 impl<R: AccessRules> Layout<R> {
@@ -45,7 +45,7 @@ impl<R: AccessRules> Layout<R> {
             to: right_pos,
             width: f64::EPSILON * 16.0,
         };
-        let mut orig_hline = NormalLine::from(ltr_line);
+        let mut orig_hline = LineInGeneralForm::from(ltr_line);
         orig_hline.make_normal_unit();
         let orig_hline = orig_hline;
         let location_denom = orig_hline.segment_interval(&ltr_line);
@@ -78,7 +78,7 @@ impl<R: AccessRules> Layout<R> {
                 let band_uid = self.drawing.loose_band_uid(loose).ok()?;
                 let loose_hline = orig_hline.orthogonal_through(&match shape {
                     PrimitiveShape::Seg(seg) => {
-                        let seg_hline = NormalLine::from(seg.middle_line());
+                        let seg_hline = LineInGeneralForm::from(seg.middle_line());
                         match orig_hline.intersects(&seg_hline) {
                             LineIntersection::Empty => return None,
                             LineIntersection::Overlapping => shape.center(),
@@ -92,7 +92,7 @@ impl<R: AccessRules> Layout<R> {
                         shape.center()
                     }
                 });
-                let location = (loose_hline.offset - location_start) / location_denom;
+                let location = (loose_hline.c - location_start) / location_denom;
                 log::trace!(
                     "intersection ({:?}) with {:?} is at {:?}",
                     band_uid,

src/math/line.rs

@@ -14,13 +14,13 @@ pub enum LineIntersection {
 
 /// A line in the normal form: `x0*y + y0*y + offset = 0`.
 #[derive(Clone, Copy, Debug, PartialEq)]
-pub struct NormalLine {
+pub struct LineInGeneralForm {
-    pub x: f64,
+    pub a: f64,
-    pub y: f64,
+    pub b: f64,
-    pub offset: f64,
+    pub c: f64, // On the same equation side as a and b, not on the other.
 }
 
-impl From<Line> for NormalLine {
+impl From<Line> for LineInGeneralForm {
     fn from(l: Line) -> Self {
         // the normal vector is perpendicular to the line
         let normal = point! {
@@ -28,28 +28,28 @@ impl From<Line> for NormalLine {
             y: -l.dx(),
         };
         Self {
-            x: normal.0.x,
+            a: normal.0.x,
-            y: normal.0.y,
+            b: normal.0.y,
-            offset: -perp_dot_product(l.end.into(), l.start.into()),
+            c: -perp_dot_product(l.end.into(), l.start.into()),
         }
     }
 }
 
-impl NormalLine {
+impl LineInGeneralForm {
     pub fn evaluate_at(&self, pt: Point) -> f64 {
-        self.x * pt.x() + self.y * pt.y() + self.offset
+        self.a * pt.x() + self.b * pt.y() + self.c
     }
 
     pub fn angle(&self) -> f64 {
-        self.y.atan2(self.x)
+        self.b.atan2(self.a)
     }
 
     pub fn make_normal_unit(&mut self) {
-        let normal_len = self.y.hypot(self.x);
+        let normal_len = self.b.hypot(self.a);
         if normal_len > (f64::EPSILON * 16.0) {
-            self.x /= normal_len;
+            self.a /= normal_len;
-            self.y /= normal_len;
+            self.b /= normal_len;
-            self.offset /= normal_len;
+            self.c /= normal_len;
         }
     }
 
@@ -58,11 +58,11 @@ impl NormalLine {
         const ALMOST_ZERO: f64 = f64::EPSILON * 16.0;
         let (mut a, mut b) = (*self, *b);
         let _ = (a.make_normal_unit(), b.make_normal_unit());
-        let apt = geo::point! { x: a.x, y: a.y };
+        let apt = geo::point! { x: a.a, y: a.b };
-        let bpt = geo::point! { x: b.x, y: b.y };
+        let bpt = geo::point! { x: b.a, y: b.b };
         let det = perp_dot_product(apt, bpt);
-        let rpx = b.y * a.offset - a.y * b.offset;
+        let rpx = b.b * a.c - a.b * b.c;
-        let rpy = -b.x * a.offset + a.x * b.offset;
+        let rpy = -b.a * a.c + a.a * b.c;
 
         if det.abs() > ALMOST_ZERO {
             LineIntersection::Point(geo::point! { x: rpx, y: rpy } / det)
@@ -79,17 +79,17 @@ impl NormalLine {
     pub fn orthogonal_through(&self, pt: &Point) -> Self {
         Self {
             // recover the original parallel vector
-            x: -self.y,
+            a: -self.b,
-            y: self.x,
+            b: self.a,
-            offset: self.x * pt.0.y - self.y * pt.0.x,
+            c: self.a * pt.0.y - self.b * pt.0.x,
         }
     }
 
     pub fn segment_interval(&self, line: &Line) -> core::ops::RangeInclusive<f64> {
         // recover the original parallel vector
         let parv = geo::point! {
-            x: -self.y,
+            x: -self.b,
-            y: self.x,
+            y: self.a,
         };
         dot_product(parv, line.start.into())..=dot_product(parv, line.end.into())
     }
@@ -106,8 +106,8 @@ impl NormalLine {
 
 /// Returns `Some(p)` when `p` lies in the intersection of the given lines.
 pub fn intersect_lines(line1: &Line, line2: &Line) -> Option<Point> {
-    let nline1 = NormalLine::from(*line1);
+    let nline1 = LineInGeneralForm::from(*line1);
-    let nline2 = NormalLine::from(*line2);
+    let nline2 = LineInGeneralForm::from(*line2);
 
     match nline1.intersects(&nline2) {
         LineIntersection::Empty | LineIntersection::Overlapping => None,
@@ -139,8 +139,8 @@ pub fn intersect_lines(line1: &Line, line2: &Line) -> Option<Point> {
 /// Returns `Some(p)` when `p` lies in the intersection of a line and a ray
 /// (line which is only bounded at one side, i.e. point + directon)
 pub fn intersect_line_and_ray(line1: &Line, ray2: &Line) -> Option<Point> {
-    let nline1 = NormalLine::from(*line1);
+    let nline1 = LineInGeneralForm::from(*line1);
-    let nray2 = NormalLine::from(*ray2);
+    let nray2 = LineInGeneralForm::from(*ray2);
 
     match nline1.intersects(&nray2) {
         LineIntersection::Empty | LineIntersection::Overlapping => None,

src/math/tangents.rs

@@ -6,13 +6,13 @@ use geo::{geometry::Point, Line};
 use specctra_core::math::Circle;
 use thiserror::Error;
 
-use super::{seq_perp_dot_product, NormalLine, RotationSense};
+use super::{seq_perp_dot_product, LineInGeneralForm, RotationSense};
 
 #[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);
 
-fn _tangent(center: Point, r1: f64, r2: f64) -> Result<NormalLine, ()> {
+fn _tangent(center: Point, r1: f64, r2: f64) -> Result<LineInGeneralForm, ()> {
     let epsilon = 1e-9;
     let dr = r2 - r1;
     let norm = center.x() * center.x() + center.y() * center.y();
@@ -24,15 +24,15 @@ fn _tangent(center: Point, r1: f64, r2: f64) -> Result<NormalLine, ()> {
 
     let sqrt_discriminant = f64::sqrt(f64::abs(discriminant));
 
-    Ok(NormalLine {
+    Ok(LineInGeneralForm {
-        x: (center.x() * dr + center.y() * sqrt_discriminant) / norm,
+        a: (center.x() * dr + center.y() * sqrt_discriminant) / norm,
-        y: (center.y() * dr - center.x() * sqrt_discriminant) / norm,
+        b: (center.y() * dr - center.x() * sqrt_discriminant) / norm,
-        offset: r1,
+        c: r1,
     })
 }
 
-fn _tangents(circle1: Circle, circle2: Circle) -> Result<[NormalLine; 4], ()> {
+fn _tangents(circle1: Circle, circle2: Circle) -> Result<[LineInGeneralForm; 4], ()> {
-    let mut tgs: [NormalLine; 4] = [
+    let mut tgs: [LineInGeneralForm; 4] = [
         _tangent((circle2 - circle1).pos, -circle1.r, -circle2.r)?,
         _tangent((circle2 - circle1).pos, -circle1.r, circle2.r)?,
         _tangent((circle2 - circle1).pos, circle1.r, -circle2.r)?,
@@ -40,18 +40,18 @@ fn _tangents(circle1: Circle, circle2: Circle) -> Result<[NormalLine; 4], ()> {
     ];
 
     for tg in tgs.iter_mut() {
-        tg.offset -= tg.x * circle1.pos.x() + tg.y * circle1.pos.y();
+        tg.c -= tg.a * circle1.pos.x() + tg.b * circle1.pos.y();
     }
 
     Ok(tgs)
 }
 
-fn cast_point_to_canonical_line(pt: Point, line: NormalLine) -> Point {
+fn cast_point_to_canonical_line(pt: Point, line: LineInGeneralForm) -> Point {
     (
-        (line.y * (line.y * pt.x() - line.x * pt.y()) - line.x * line.offset)
+        (line.b * (line.b * pt.x() - line.a * pt.y()) - line.a * line.c)
-            / (line.x * line.x + line.y * line.y),
+            / (line.a * line.a + line.b * line.b),
-        (line.x * (-line.y * pt.x() + line.x * pt.y()) - line.y * line.offset)
+        (line.a * (-line.b * pt.x() + line.a * pt.y()) - line.b * line.c)
-            / (line.x * line.x + line.y * line.y),
+            / (line.a * line.a + line.b * line.b),
     )
         .into()
 }