shapes: implement plane geometry.

rtchallenge/src/shapes.rs

@@ -4,12 +4,15 @@ use crate::{
     matrices::Matrix4x4,
     rays::Ray,
     tuples::{dot, Tuple},
+    EPSILON,
 };
 
 #[derive(Debug, PartialEq, Clone)]
 enum Geometry {
     /// Sphere represents the unit-sphere (radius of unit 1.) at the origin 0., 0., 0.
     Sphere,
+    /// Flat surface that extends infinitely in the XZ axes.
+    Plane,
 }
 
 /// Shape represents visible objects.  A signal instance of Shape can generically represent one of
@@ -55,6 +58,14 @@ impl Shape {
             geometry: Geometry::Sphere,
         }
     }
+    pub fn plane() -> Shape {
+        Shape {
+            transform: Matrix4x4::identity(),
+            inverse_transform: Matrix4x4::identity(),
+            material: Material::default(),
+            geometry: Geometry::Plane,
+        }
+    }
     /// Find the normal at the point on the sphere.
     ///
     /// # Examples
@@ -118,12 +129,28 @@ impl Shape {
     ///     -(2. as Float).sqrt() / 2.,
     /// ));
     /// assert_eq!(n, Tuple::vector(0., 0.97014, -0.24254));
+    ///
+    /// // Normal of a plane is constant everywhere.
+    /// let p = Shape::plane();
+    /// assert_eq!(
+    ///     p.normal_at(Tuple::point(0., 0., 0.)),
+    ///     Tuple::vector(0., 1., 0.)
+    /// );
+    /// assert_eq!(
+    ///     p.normal_at(Tuple::point(10., 0., -10.)),
+    ///     Tuple::vector(0., 1., 0.)
+    /// );
+    /// assert_eq!(
+    ///     p.normal_at(Tuple::point(-5., 0., 150.)),
+    ///     Tuple::vector(0., 1., 0.)
+    /// );
     /// ```
     #[cfg(not(feature = "disable-inverse-cache"))]
     pub fn normal_at(&self, world_point: Tuple) -> Tuple {
         let object_point = self.inverse_transform * world_point;
         let object_normal = match self.geometry {
             Geometry::Sphere => object_point - Tuple::point(0., 0., 0.),
+            Geometry::Plane => Tuple::vector(0., 1., 0.),
         };
         let mut world_normal = self.inverse_transform.transpose() * object_normal;
         world_normal.w = 0.;
@@ -134,6 +161,7 @@ impl Shape {
         let object_point = self.transform.inverse() * world_point;
         let object_normal = match self.geometry {
             Geometry::Sphere => object_point - Tuple::point(0., 0., 0.),
+            Geometry::Plane => Tuple::vector(0., 1., 0.),
         };
         let mut world_normal = self.transform.inverse().transpose() * object_normal;
         world_normal.w = 0.;
@@ -210,14 +238,40 @@ impl Shape {
 /// s.set_transform(Matrix4x4::translation(5., 0., 0.));
 /// let xs = intersect(&s, &r);
 /// assert_eq!(xs.len(), 0);
+///
+/// // Intersect with a ray parallel to the plane.
+/// let p = Shape::plane();
+/// let r = Ray::new(Tuple::point(0., 10., 0.), Tuple::vector(0., 0., 1.));
+/// let xs = intersect(&p, &r);
+/// assert_eq!(xs.len(), 0);
+///
+/// // Intersect with a coplanar.
+/// let r = Ray::new(Tuple::point(0., 0., 0.), Tuple::vector(0., 0., 1.));
+/// let xs = intersect(&p, &r);
+/// assert_eq!(xs.len(), 0);
+///
+/// // A ray intersecting a plane from above.
+/// let r = Ray::new(Tuple::point(0., 1., 0.), Tuple::vector(0., -1., 0.));
+/// let xs = intersect(&p, &r);
+/// assert_eq!(xs.len(), 1);
+/// assert_eq!(xs[0].t, 1.);
+/// assert_eq!(xs[0].object, &p);
+///
+/// // A ray intersecting a plane from below.
+/// let r = Ray::new(Tuple::point(0., -1., 0.), Tuple::vector(0., 1., 0.));
+/// let xs = intersect(&p, &r);
+/// assert_eq!(xs.len(), 1);
+/// assert_eq!(xs[0].t, 1.);
+/// assert_eq!(xs[0].object, &p);
 /// ```
 pub fn intersect<'s>(shape: &'s Shape, ray: &Ray) -> Intersections<'s> {
     match shape.geometry {
-        Geometry::Sphere => intersect_rtc(shape, ray),
+        Geometry::Sphere => intersect_sphere(shape, ray),
+        Geometry::Plane => intersect_plane(shape, ray),
     }
 }
 
-fn intersect_rtc<'s>(shape: &'s Shape, ray: &Ray) -> Intersections<'s> {
+fn intersect_sphere<'s>(shape: &'s Shape, ray: &Ray) -> Intersections<'s> {
     let ray = ray.transform(shape.inverse_transform);
     let sphere_to_ray = ray.origin - Tuple::point(0., 0., 0.);
     let a = dot(ray.direction, ray.direction);
@@ -232,18 +286,12 @@ fn intersect_rtc<'s>(shape: &'s Shape, ray: &Ray) -> Intersections<'s> {
         Intersection::new((-b + discriminant.sqrt()) / (2. * a), &shape),
     ])
 }
-fn intersect_rtiow<'s>(shape: &'s Shape, ray: &Ray) -> Intersections<'s> {
+fn intersect_plane<'s>(shape: &'s Shape, ray: &Ray) -> Intersections<'s> {
-    let ray = ray.transform(shape.inverse_transform);
+    if (ray.direction.y).abs() < EPSILON {
-    let oc = ray.origin - Tuple::point(0., 0., 0.);
-    let a = dot(ray.direction, ray.direction);
-    let b = dot(oc, ray.direction);
-    let c = dot(oc, oc) - 1.;
-    let discriminant = b * b - a * c;
-    if discriminant < 0. {
         return Intersections::default();
     }
-    Intersections::new(vec![
+    Intersections::new(vec![Intersection::new(
-        Intersection::new((-b - discriminant.sqrt()) / a, &shape),
+        -ray.origin.y / ray.direction.y,
-        Intersection::new((-b + discriminant.sqrt()) / a, &shape),
+        &shape,
-    ])
+    )])
 }