Cross product

assignment-1/Cargo.lock

@@ -14,8 +14,15 @@ version = "0.1.0"
 dependencies = [
  "anyhow",
  "clap",
+ "num",
 ]
 
+[[package]]
+name = "autocfg"
+version = "1.1.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "d468802bab17cbc0cc575e9b053f41e72aa36bfa6b7f55e3529ffa43161b97fa"
+
 [[package]]
 name = "bitflags"
 version = "1.3.2"
@@ -135,6 +142,85 @@ version = "0.1.4"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "f051f77a7c8e6957c0696eac88f26b0117e54f52d3fc682ab19397a8812846a4"
 
+[[package]]
+name = "num"
+version = "0.4.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "43db66d1170d347f9a065114077f7dccb00c1b9478c89384490a3425279a4606"
+dependencies = [
+ "num-bigint",
+ "num-complex",
+ "num-integer",
+ "num-iter",
+ "num-rational",
+ "num-traits",
+]
+
+[[package]]
+name = "num-bigint"
+version = "0.4.3"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "f93ab6289c7b344a8a9f60f88d80aa20032336fe78da341afc91c8a2341fc75f"
+dependencies = [
+ "autocfg",
+ "num-integer",
+ "num-traits",
+ "serde",
+]
+
+[[package]]
+name = "num-complex"
+version = "0.4.3"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "02e0d21255c828d6f128a1e41534206671e8c3ea0c62f32291e808dc82cff17d"
+dependencies = [
+ "num-traits",
+ "serde",
+]
+
+[[package]]
+name = "num-integer"
+version = "0.1.45"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "225d3389fb3509a24c93f5c29eb6bde2586b98d9f016636dff58d7c6f7569cd9"
+dependencies = [
+ "autocfg",
+ "num-traits",
+]
+
+[[package]]
+name = "num-iter"
+version = "0.1.43"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "7d03e6c028c5dc5cac6e2dec0efda81fc887605bb3d884578bb6d6bf7514e252"
+dependencies = [
+ "autocfg",
+ "num-integer",
+ "num-traits",
+]
+
+[[package]]
+name = "num-rational"
+version = "0.4.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "0638a1c9d0a3c0914158145bc76cff373a75a627e6ecbfb71cbe6f453a5a19b0"
+dependencies = [
+ "autocfg",
+ "num-bigint",
+ "num-integer",
+ "num-traits",
+ "serde",
+]
+
+[[package]]
+name = "num-traits"
+version = "0.2.15"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "578ede34cf02f8924ab9447f50c28075b4d3e5b269972345e7e0372b38c6cdcd"
+dependencies = [
+ "autocfg",
+]
+
 [[package]]
 name = "once_cell"
 version = "1.17.0"
@@ -203,6 +289,12 @@ dependencies = [
  "windows-sys",
 ]
 
+[[package]]
+name = "serde"
+version = "1.0.152"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "bb7d1f0d3021d347a83e556fc4683dea2ea09d87bccdf88ff5c12545d89d5efb"
+
 [[package]]
 name = "strsim"
 version = "0.10.0"

assignment-1/Cargo.toml

@@ -8,3 +8,4 @@ edition = "2021"
 [dependencies]
 anyhow = "1.0.68"
 clap = { version = "4.1.4", features = ["derive"] }
+num = { version = "0.4.0", features = ["serde"] }

assignment-1/src/main.rs

@@ -1,6 +1,8 @@
 mod input_file;
 mod ray;
 mod scene_data;
+mod view;
+mod vec3;
 
 use std::path::PathBuf;
 

assignment-1/src/ray.rs

@@ -1,18 +1,23 @@
-use crate::scene_data::{Sphere, Vec3};
+use crate::scene_data::Sphere;
+use crate::vec3::Vec3;
 
-/// A normalized Ray
+/// A normalized parametric Ray of the form (origin + direction * time)
+///
+/// That means at any time t: f64, the point represented by origin + direction * time occurs on the
+/// ray.
 pub struct Ray {
   origin: Vec3,
   direction: Vec3,
 }
 
 impl Ray {
+  /// Evaluate the ray at a certain point in time, yielding a point
   pub fn eval(&self, time: f64) -> Vec3 {
     self.origin + self.direction * time
   }
 }
 
-/// Given a ray and a sphere, returns the first point at which this ray intersects the sphere.
+/// Given a ray and a sphere, returns the first time at which this ray intersects the sphere.
 ///
 /// If there is no intersection point, returns None.
 pub fn ray_intersection_time(ray: &Ray, sphere: &Sphere) -> Option<f64> {
@@ -43,13 +48,16 @@ pub fn ray_intersection_time(ray: &Ray, sphere: &Sphere) -> Option<f64> {
 
       return Some(solution_1.min(solution_2));
     }
+
+    // Probably hit some NaN or Infinity value due to faulty inputs...
     _ => unreachable!("Invalid determinant value: {discriminant}"),
   }
 }
 
 #[cfg(test)]
 mod tests {
-  use crate::scene_data::{Sphere, Vec3};
+  use crate::scene_data::Sphere;
+  use crate::vec3::Vec3;
 
   use super::{ray_intersection_time, Ray};
 
@@ -64,7 +72,24 @@ mod tests {
       radius: 4.0,
     };
 
-    let t = ray_intersection_time(&ray, &sphere).unwrap();
+    let point = ray_intersection_time(&ray, &sphere).map(|t| ray.eval(t));
-    assert_eq!(ray.eval(t), Vec3::new(0.0, 0.0, -6.0));
+
+    // the intersection point in this case is (0, 0, –6)
+    assert_eq!(point, Some(Vec3::new(0.0, 0.0, -6.0)));
+  }
+
+  #[test]
+  fn practice_problem_slide_158() {
+    let ray = Ray {
+      origin: Vec3::new(0.0, 0.0, 0.0),
+      direction: Vec3::new(0.0, 0.5, -1.0),
+    };
+    let sphere = Sphere {
+      center: Vec3::new(0.0, 0.0, -10.0),
+      radius: 4.0,
+    };
+
+    // oops! In this case, the ray does not intersect the sphere.
+    assert_eq!(ray_intersection_time(&ray, &sphere), None);
   }
 }

assignment-1/src/scene_data.rs

@@ -1,42 +1,4 @@
-use std::ops::{Add, Mul};
+use crate::vec3::Vec3;
-
-#[derive(Copy, Clone, Debug, PartialEq, Eq)]
-pub struct Vec3<T = f64> {
-  pub x: T,
-  pub y: T,
-  pub z: T,
-}
-
-impl<T> Vec3<T> {
-  pub fn new(x: T, y: T, z: T) -> Self {
-    Vec3 { x, y, z }
-  }
-}
-
-/// Vector addition
-impl<T> Add<Vec3<T>> for Vec3<T>
-where
-  T: Add<T>,
-{
-  type Output = Vec3<T::Output>;
-
-  fn add(self, rhs: Vec3<T>) -> Self::Output {
-    Vec3::new(self.x + rhs.x, self.y + rhs.y, self.z + rhs.z)
-  }
-}
-
-/// Scalar multiplication
-impl<T, U> Mul<U> for Vec3<T>
-where
-  T: Mul<U, Output = U>,
-  U: Copy,
-{
-  type Output = Vec3<U>;
-
-  fn mul(self, rhs: U) -> Self::Output {
-    Vec3::new(self.x * rhs, self.y * rhs, self.z * rhs)
-  }
-}
 
 pub struct Sphere {
   pub center: Vec3,

assignment-1/src/vec3.rs

@@ -0,0 +1,65 @@
+use std::ops::{Add, Mul};
+
+use num::Float;
+
+#[derive(Copy, Clone, Debug, PartialEq, Eq)]
+pub struct Vec3<T = f64> {
+  pub x: T,
+  pub y: T,
+  pub z: T,
+}
+
+impl<T> Vec3<T> {
+  pub fn new(x: T, y: T, z: T) -> Self {
+    Vec3 { x, y, z }
+  }
+}
+
+impl<T: Float> Vec3<T> {
+  pub fn cross(u: Self, v: Self) -> Self {
+    Vec3::new(
+      u.y * v.z - u.z * v.y,
+      u.z * v.x - u.x * v.z,
+      u.x * v.y - u.y * v.x,
+    )
+  }
+}
+
+/// Vector addition
+impl<T> Add<Vec3<T>> for Vec3<T>
+where
+  T: Add<T>,
+{
+  type Output = Vec3<T::Output>;
+
+  fn add(self, rhs: Vec3<T>) -> Self::Output {
+    Vec3::new(self.x + rhs.x, self.y + rhs.y, self.z + rhs.z)
+  }
+}
+
+/// Scalar multiplication
+impl<T, U> Mul<U> for Vec3<T>
+where
+  T: Mul<U, Output = U>,
+  U: Copy,
+{
+  type Output = Vec3<U>;
+
+  fn mul(self, rhs: U) -> Self::Output {
+    Vec3::new(self.x * rhs, self.y * rhs, self.z * rhs)
+  }
+}
+
+#[cfg(test)]
+mod tests {
+  use super::Vec3;
+
+  #[test]
+  fn test_cross() {
+    let u = Vec3::new(1.0, 0.0, 0.0);
+    let v = Vec3::new(0.0, 1.0, 0.0);
+
+    assert_eq!(Vec3::cross(u, v), Vec3::new(0.0, 0.0, 1.0));
+    assert_eq!(Vec3::cross(v, u), Vec3::new(0.0, 0.0, -1.0));
+  }
+}

assignment-1/src/view.rs

@@ -0,0 +1,12 @@
+use crate::vec3::Vec3;
+
+pub struct Rect {
+  pub upper_left: Vec3,
+  pub upper_right: Vec3,
+  pub lower_left: Vec3,
+  pub lower_right: Vec3,
+}
+
+pub fn compute_viewing_rect() {
+
+}