Refactor curve approximation code

crates/fj-kernel/src/algorithms/approx/curve.rs

@@ -8,30 +8,28 @@ use super::{Approx, Tolerance};
 
 impl Approx for Curve {
     type Approximation = Vec<(Point<1>, Point<3>)>;
-
-    fn approx(&self, tolerance: Tolerance) -> Self::Approximation {
-        self.global().approx(tolerance)
+    type Params = RangeOnCurve;
+
+    fn approx(
+        &self,
+        tolerance: Tolerance,
+        range: Self::Params,
+    ) -> Self::Approximation {
+        self.global().approx(tolerance, range)
     }
 }
 
 impl Approx for GlobalCurve {
     type Approximation = Vec<(Point<1>, Point<3>)>;
+    type Params = RangeOnCurve;
 
-    /// Approximate the global curve
-    ///
-    /// # Implementation Note
-    ///
-    /// This only works as-is, because only circles need to be approximated
-    /// right now and because only edges that are full circles are supported, as
-    /// opposed to edges that only inhabit part of the circle.
-    ///
-    /// To support that, we will need additional information here, to define
-    /// between which points the curve needs to be approximated.
-    fn approx(&self, tolerance: Tolerance) -> Self::Approximation {
+    fn approx(
+        &self,
+        tolerance: Tolerance,
+        range: Self::Params,
+    ) -> Self::Approximation {
         match self.kind() {
-            CurveKind::Circle(curve) => {
-                approx_circle(curve, [[Scalar::ZERO], [Scalar::TAU]], tolerance)
-            }
+            CurveKind::Circle(curve) => approx_circle(curve, range, tolerance),
             CurveKind::Line(_) => Vec::new(),
         }
     }
@@ -41,29 +39,27 @@ impl Approx for GlobalCurve {
 ///
 /// `tolerance` specifies how much the approximation is allowed to deviate
 /// from the circle.
-pub fn approx_circle(
+fn approx_circle(
     circle: &Circle<3>,
-    between: [impl Into<Point<1>>; 2],
+    range: impl Into<RangeOnCurve>,
     tolerance: Tolerance,
 ) -> Vec<(Point<1>, Point<3>)> {
-    let mut points = Vec::new();
-
     let radius = circle.a().magnitude();
-
-    let [start, end] = between.map(Into::into);
-    let range = (end - start).t;
+    let range = range.into();
 
     // To approximate the circle, we use a regular polygon for which
     // the circle is the circumscribed circle. The `tolerance`
     // parameter is the maximum allowed distance between the polygon
     // and the circle. This is the same as the difference between
     // the circumscribed circle and the incircle.
 
-    let n = number_of_vertices_for_circle(tolerance, radius, range.abs());
+    let n = number_of_vertices_for_circle(tolerance, radius, range.length());
+
+    let mut points = Vec::new();
 
     for i in 0..n {
-        let angle =
-            start.t + (Scalar::TAU / n as f64 * i as f64) * range.sign();
+        let angle = range.start().t
+            + (Scalar::TAU / n as f64 * i as f64) * range.direction();
 
         let point_curve = Point::from([angle]);
         let point_global = circle.point_from_circle_coords(point_curve);
@@ -86,6 +82,32 @@ fn number_of_vertices_for_circle(
     max(n, 3)
 }
 
+pub struct RangeOnCurve {
+    pub boundary: [Point<1>; 2],
+}
+
+impl RangeOnCurve {
+    fn start(&self) -> Point<1> {
+        self.boundary[0]
+    }
+
+    fn end(&self) -> Point<1> {
+        self.boundary[1]
+    }
+
+    fn signed_length(&self) -> Scalar {
+        (self.end() - self.start()).t
+    }
+
+    fn length(&self) -> Scalar {
+        self.signed_length().abs()
+    }
+
+    fn direction(&self) -> Scalar {
+        self.signed_length().sign()
+    }
+}
+
 #[cfg(test)]
 mod tests {
     use fj_math::Scalar;

crates/fj-kernel/src/algorithms/approx/cycle.rs

@@ -6,12 +6,17 @@ use super::{Approx, Tolerance};
 
 impl Approx for Cycle {
     type Approximation = CycleApprox;
+    type Params = ();
 
-    fn approx(&self, tolerance: Tolerance) -> Self::Approximation {
+    fn approx(
+        &self,
+        tolerance: Tolerance,
+        (): Self::Params,
+    ) -> Self::Approximation {
         let mut points = Vec::new();
 
         for edge in self.edges() {
-            let edge_points = edge.approx(tolerance);
+            let edge_points = edge.approx(tolerance, ());
 
             points.extend(edge_points.into_iter().map(|point| {
                 let (point_curve, point_global) = point;

crates/fj-kernel/src/algorithms/approx/edge.rs

@@ -1,14 +1,25 @@
-use fj_math::Point;
+use fj_math::{Point, Scalar};
 
 use crate::objects::{Edge, Vertex, VerticesOfEdge};
 
-use super::Approx;
+use super::{curve::RangeOnCurve, Approx};
 
 impl Approx for Edge {
     type Approximation = Vec<(Point<1>, Point<3>)>;
-
-    fn approx(&self, tolerance: super::Tolerance) -> Self::Approximation {
-        let mut points = self.curve().approx(tolerance);
+    type Params = ();
+
+    fn approx(
+        &self,
+        tolerance: super::Tolerance,
+        (): Self::Params,
+    ) -> Self::Approximation {
+        let mut points = self.curve().approx(
+            tolerance,
+            // The range is only used for circles right now.
+            RangeOnCurve {
+                boundary: [[Scalar::ZERO].into(), [Scalar::TAU].into()],
+            },
+        );
         approx_edge(*self.vertices(), &mut points);
 
         points

crates/fj-kernel/src/algorithms/approx/face.rs

@@ -8,8 +8,13 @@ use super::{Approx, CycleApprox, Tolerance};
 
 impl Approx for Face {
     type Approximation = FaceApprox;
+    type Params = ();
 
-    fn approx(&self, tolerance: Tolerance) -> Self::Approximation {
+    fn approx(
+        &self,
+        tolerance: Tolerance,
+        (): Self::Params,
+    ) -> Self::Approximation {
         // Curved faces whose curvature is not fully defined by their edges
         // are not supported yet. For that reason, we can fully ignore `face`'s
         // `surface` field and just pass the edges to `Self::for_edges`.
@@ -28,13 +33,13 @@ impl Approx for Face {
         let mut interiors = HashSet::new();
 
         for cycle in self.exteriors() {
-            let cycle = cycle.approx(tolerance);
+            let cycle = cycle.approx(tolerance, ());
 
             points.extend(cycle.points.iter().copied());
             exteriors.push(cycle);
         }
         for cycle in self.interiors() {
-            let cycle = cycle.approx(tolerance);
+            let cycle = cycle.approx(tolerance, ());
 
             points.extend(cycle.points.iter().copied());
             interiors.insert(cycle);
@@ -118,7 +123,7 @@ mod tests {
         let g = (g, g.to_xyz());
         let h = (h, h.to_xyz());
 
-        let approx = face.approx(tolerance);
+        let approx = face.approx(tolerance, ());
         let expected = FaceApprox {
             points: set![a, b, c, d, e, f, g, h],
             exterior: CycleApprox {

crates/fj-kernel/src/algorithms/approx/mod.rs

@@ -17,9 +17,16 @@ pub trait Approx {
     /// The approximation of the object
     type Approximation;
 
+    /// Additional parameters required for the approximation
+    type Params;
+
     /// Approximate the object
     ///
     /// `tolerance` defines how far the approximation is allowed to deviate from
     /// the actual object.
-    fn approx(&self, tolerance: Tolerance) -> Self::Approximation;
+    fn approx(
+        &self,
+        tolerance: Tolerance,
+        params: Self::Params,
+    ) -> Self::Approximation;
 }

crates/fj-kernel/src/algorithms/sweep/edge.rs

@@ -119,7 +119,7 @@ fn create_continuous_side_face(
     let placeholder = Surface::xy_plane();
 
     let cycle = Cycle::new(placeholder).with_edges([edge]);
-    let approx = cycle.approx(tolerance);
+    let approx = cycle.approx(tolerance, ());
 
     let mut quads = Vec::new();
     for segment in approx.segments() {

crates/fj-kernel/src/algorithms/triangulate/mod.rs

@@ -27,7 +27,7 @@ pub fn triangulate(
         }
 
         let surface = face.surface();
-        let approx = face.approx(tolerance);
+        let approx = face.approx(tolerance, ());
 
         let points: Vec<_> = approx
             .points