Merge pull request #811 from hannobraun/intersection

Return local curves from surface-surface intersection

crates/fj-kernel/src/algorithms/intersection/surface_surface.rs

@@ -3,14 +3,23 @@ use fj_math::{Line, Point, Scalar, Vector};
 use crate::objects::{Curve, Surface};
 
 /// Test intersection between two surfaces
-pub fn surface_surface(a: &Surface, b: &Surface) -> Option<Curve<3>> {
+pub fn surface_surface(
+    a: &Surface,
+    b: &Surface,
+) -> Option<(Curve<2>, Curve<2>, Curve<3>)> {
     // Algorithm from Real-Time Collision Detection by Christer Ericson. See
     // section 5.4.4, Intersection of Two Planes.
+    //
+    // Adaptations were made to get the intersection curves in local coordinates
+    // for each surface.
 
-    let (a_normal, a_distance) = extract_plane(a);
-    let (b_normal, b_distance) = extract_plane(b);
+    let a_parametric = PlaneParametric::extract_from_surface(a);
+    let b_parametric = PlaneParametric::extract_from_surface(b);
 
-    let direction = a_normal.cross(&b_normal);
+    let a = PlaneConstantNormal::from_parametric_plane(&a_parametric);
+    let b = PlaneConstantNormal::from_parametric_plane(&b_parametric);
+
+    let direction = a.normal.cross(&b.normal);
 
     let denom = direction.dot(&direction);
     if denom == Scalar::ZERO {
@@ -24,36 +33,97 @@ pub fn surface_surface(a: &Surface, b: &Surface) -> Option<Curve<3>> {
         return None;
     }
 
-    let origin = (b_normal * a_distance - a_normal * b_distance)
+    let origin = (b.normal * a.distance - a.normal * b.distance)
         .cross(&direction)
         / denom;
     let origin = Point { coords: origin };
 
-    Some(Curve::Line(Line { origin, direction }))
+    let line = Line { origin, direction };
+
+    let curve_a = project_line_into_plane(&line, &a_parametric);
+    let curve_b = project_line_into_plane(&line, &b_parametric);
+    let curve_global = Curve::Line(Line { origin, direction });
+
+    Some((curve_a, curve_b, curve_global))
 }
 
-/// Extract a plane in constant-normal form from a `Surface`
-///
-/// Panics, if the given `Surface` is not a plane.
-fn extract_plane(surface: &Surface) -> (Vector<3>, Scalar) {
-    let Surface::SweptCurve(surface) = surface;
-    let line = match surface.curve {
-        Curve::Line(line) => line,
-        _ => todo!("Only plane-plane intersection is currently supported."),
-    };
+/// A plane in parametric form
+struct PlaneParametric {
+    pub origin: Point<3>,
+    pub u: Vector<3>,
+    pub v: Vector<3>,
+}
 
-    // Convert plane from parametric form to three-point form.
-    let a = line.origin;
-    let b = line.origin + line.direction;
-    let c = line.origin + surface.path;
+impl PlaneParametric {
+    pub fn extract_from_surface(surface: &Surface) -> Self {
+        let Surface::SweptCurve(surface) = surface;
+        let line = match surface.curve {
+            Curve::Line(line) => line,
+            _ => todo!("Only plane-plane intersection is currently supported."),
+        };
+
+        Self {
+            origin: line.origin,
+            u: line.direction,
+            v: surface.path,
+        }
+    }
+}
 
-    // Convert plane from three-point form to constant-normal form. See
-    // Real-Time Collision Detection by Christer Ericson, section 3.6, Planes
-    // and Halfspaces.
-    let normal = (b - a).cross(&(c - a)).normalize();
-    let distance = normal.dot(&a.coords);
+/// A plane in constant-normal form
+struct PlaneConstantNormal {
+    pub distance: Scalar,
+    pub normal: Vector<3>,
+}
 
-    (normal, distance)
+impl PlaneConstantNormal {
+    /// Extract a plane in constant-normal form from a `Surface`
+    ///
+    /// Panics, if the given `Surface` is not a plane.
+    pub fn from_parametric_plane(plane: &PlaneParametric) -> Self {
+        // Convert plane from parametric form to three-point form.
+        let a = plane.origin;
+        let b = plane.origin + plane.u;
+        let c = plane.origin + plane.v;
+
+        // Convert plane from three-point form to constant-normal form. See
+        // Real-Time Collision Detection by Christer Ericson, section 3.6, Planes
+        // and Halfspaces.
+        let normal = (b - a).cross(&(c - a)).normalize();
+        let distance = normal.dot(&a.coords);
+
+        PlaneConstantNormal { distance, normal }
+    }
+}
+
+fn project_line_into_plane(
+    line: &Line<3>,
+    plane: &PlaneParametric,
+) -> Curve<2> {
+    let line_origin_relative_to_plane = line.origin - plane.origin;
+    dbg!(&line_origin_relative_to_plane);
+    let line_origin_in_plane = Vector::from([
+        plane
+            .u
+            .scalar_projection_onto(&line_origin_relative_to_plane),
+        plane
+            .v
+            .scalar_projection_onto(&line_origin_relative_to_plane),
+    ]);
+
+    let line_direction_in_plane = Vector::from([
+        plane.u.scalar_projection_onto(&line.direction),
+        plane.v.scalar_projection_onto(&line.direction),
+    ]);
+
+    let line = Line {
+        origin: Point {
+            coords: line_origin_in_plane,
+        },
+        direction: line_direction_in_plane,
+    };
+
+    Curve::Line(line)
 }
 
 #[cfg(test)]
@@ -69,6 +139,7 @@ mod tests {
         let xy = Surface::xy_plane();
         let xz = Surface::xz_plane();
 
+        // Coincident and parallel planes don't have an intersection curve.
         assert_eq!(surface_surface(&xy, &xy), None);
         assert_eq!(
             surface_surface(
@@ -77,6 +148,14 @@ mod tests {
             ),
             None,
         );
-        assert_eq!(surface_surface(&xy, &xz), Some(Curve::x_axis()));
+
+        let expected_xy = Curve::u_axis();
+        let expected_xz = Curve::u_axis();
+        let expected_global = Curve::x_axis();
+
+        assert_eq!(
+            surface_surface(&xy, &xz),
+            Some((expected_xy, expected_xz, expected_global))
+        );
     }
 }