Implement textured coordinates

assignment-1c/grading-criteria.md

@@ -34,7 +34,7 @@ Due: Friday March 3rd
       color in the Phong illumination model when it is evaluated at that point.
       (25 pts)
 
-- [ ] The program is capable of rendering textured triangles. The texture
+- [x] The program is capable of rendering textured triangles. The texture
       coordinate at the ray/triangle intersection point is correctly
       interpolated from the texture coordinates defined at each of the three
       triangle vertices. The interpolated texture coordinate is used to retrieve

assignment-1c/src/scene/illumination.rs

@@ -37,7 +37,9 @@ impl Scene {
 
     let diffuse_color = match object.texture_idx {
       Some(texture_idx) => {
-        let (u, v) = object.kind.get_texture_coord(&intersection_context)?;
+        let (u, v) = object
+          .kind
+          .get_texture_coord(&self, &intersection_context)?;
 
         let texture = match self.textures.get(texture_idx) {
           Some(v) => v,

assignment-1c/src/scene/object.rs

@@ -49,12 +49,13 @@ impl ObjectKind {
   /// the intersection point
   pub fn get_texture_coord(
     &self,
+    scene: &Scene,
     ctx: &IntersectionContext,
   ) -> Result<(f64, f64)> {
     match self {
       ObjectKind::Sphere(sphere) => sphere.get_texture_coord(ctx),
       ObjectKind::Cylinder(cylinder) => todo!(),
-      ObjectKind::Triangle(triangle) => todo!(),
+      ObjectKind::Triangle(triangle) => triangle.get_texture_coord(scene, ctx),
     }
   }
 }

assignment-1c/src/scene/triangle.rs

@@ -4,6 +4,7 @@ use ordered_float::NotNan;
 
 use crate::ray::Ray;
 use crate::utils::{cross, dot};
+use crate::{Point, Vector};
 
 use super::illumination::IntersectionContext;
 use super::Scene;
@@ -11,7 +12,11 @@ use super::Scene;
 #[derive(Debug)]
 pub struct Triangle {
   pub vertices: Vector3<usize>,
+
+  /// Indexes into the scene's normal coordinates list
   pub normals: Option<Vector3<usize>>,
+
+  /// Indexes into the scene's texture coordinates list
   pub textures: Option<Vector3<usize>>,
 }
 
@@ -21,17 +26,13 @@ impl Triangle {
     scene: &Scene,
     ray: &Ray,
   ) -> Result<Option<IntersectionContext>> {
-    let p0 = scene.triangle_vertices[self.vertices.x];
-    let p1 = scene.triangle_vertices[self.vertices.y];
-    let p2 = scene.triangle_vertices[self.vertices.z];
+    let (p0, e1, e2) = self.basis_vectors(scene);
 
     // Solve for the plane equation coefficients A, B, C, D such that:
     //
     // $$
     //     Ax + By + Cz + D = 0
     // $$
-    let e1 = p1 - p0;
-    let e2 = p2 - p0;
     let n = cross(e1, e2);
     let a = n.x;
     let b = n.y;
@@ -63,21 +64,10 @@ impl Triangle {
     // p = p0 + beta * e1 + gamma * e2
     // Using the whack linear algebra approach derived on slide 57
     let ep = point - p0;
-    let d = Matrix2::new(dot(e1, e1), dot(e1, e2), dot(e2, e1), dot(e2, e2));
     let p = Vector2::new(dot(e1, ep), dot(e2, ep));
 
-    let d_inv = match d.try_inverse() {
-      Some(v) => v,
-      // TODO: Whack
-      None => return Ok(None),
-    };
-
-    let sol = d_inv * p;
-    let beta = sol.x;
-    let gamma = sol.y;
-
-    // Slide 46
-    let alpha = 1.0 - beta - gamma;
+    let (alpha, beta, gamma) =
+      self.compute_barycentric_coordinates(scene, p)?;
 
     // Each of alpha, beta, and gamma must be between 0 and 1
     if ![alpha, beta, gamma].into_iter().all(|v| 0.0 < v && v < 1.0) {
@@ -103,4 +93,80 @@ impl Triangle {
       normal,
     }))
   }
+
+  pub fn get_texture_coord(
+    &self,
+    scene: &Scene,
+    ctx: &IntersectionContext,
+  ) -> Result<(f64, f64)> {
+    let texture_coordinates = match self.textures {
+      Some(v) => v,
+      None => {
+        bail!("Textured triangle requested without providing coordinates")
+      }
+    };
+
+    let p0 = scene.texture_vertices[texture_coordinates.x];
+    let p1 = scene.texture_vertices[texture_coordinates.y];
+    let p2 = scene.texture_vertices[texture_coordinates.z];
+
+    let p = self.convert_point(scene, ctx.point);
+    let (alpha, beta, gamma) =
+      self.compute_barycentric_coordinates(scene, p)?;
+
+    let u = alpha * p0.x + beta * p1.x + gamma * p2.x;
+    let v = alpha * p0.y + beta * p1.y + gamma * p2.y;
+
+    Ok((u, v))
+  }
+
+  fn convert_point(&self, scene: &Scene, point: Point) -> Vector2<f64> {
+    let (p0, e1, e2) = self.basis_vectors(scene);
+
+    let ep = point - p0;
+    Vector2::new(dot(e1, ep), dot(e2, ep))
+  }
+
+  /// Fetch the corners of the triangles from the scene
+  #[inline]
+  fn corner_coordinates(&self, scene: &Scene) -> (Point, Point, Point) {
+    let p0 = scene.triangle_vertices[self.vertices.x];
+    let p1 = scene.triangle_vertices[self.vertices.y];
+    let p2 = scene.triangle_vertices[self.vertices.z];
+
+    (p0, p1, p2)
+  }
+
+  /// Get the new basis vectors using p0 as the origin.
+  #[inline]
+  fn basis_vectors(&self, scene: &Scene) -> (Vector, Vector, Vector) {
+    let (p0, p1, p2) = self.corner_coordinates(scene);
+    let e1 = p1 - p0;
+    let e2 = p2 - p0;
+    (p0, e1, e2)
+  }
+
+  fn compute_barycentric_coordinates(
+    &self,
+    scene: &Scene,
+    p: Vector2<f64>,
+  ) -> Result<(f64, f64, f64)> {
+    let (_, e1, e2) = self.basis_vectors(scene);
+    let d = Matrix2::new(dot(e1, e1), dot(e1, e2), dot(e2, e1), dot(e2, e2));
+
+    let d_inv = match d.try_inverse() {
+      Some(v) => v,
+      // TODO: Whack
+      None => bail!("No inverse..."),
+    };
+
+    let sol = d_inv * p;
+    let beta = sol.x;
+    let gamma = sol.y;
+
+    // Slide 46
+    let alpha = 1.0 - beta - gamma;
+
+    Ok((alpha, beta, gamma))
+  }
 }