From 0000045030d3d1d470050c2834537f3629a7a051 Mon Sep 17 00:00:00 2001
From: Michael Zhang <mail@mzhang.io>
Date: Wed, 15 Feb 2023 19:22:17 -0600
Subject: [PATCH] Reimplement dot + cross

---
 assignment-1b/src/scene/data.rs         |  5 ++--
 assignment-1b/src/scene/illumination.rs |  7 +++--
 assignment-1b/src/utils.rs              | 28 +++++++++++++++-----
 participation/2023-02-15.py             | 34 +++++++++++++++++++++++++
 4 files changed, 62 insertions(+), 12 deletions(-)
 create mode 100644 participation/2023-02-15.py

diff --git a/assignment-1b/src/scene/data.rs b/assignment-1b/src/scene/data.rs
index 66fd149..2ae887f 100644
--- a/assignment-1b/src/scene/data.rs
+++ b/assignment-1b/src/scene/data.rs
@@ -5,6 +5,7 @@ use nalgebra::Vector3;
 
 use crate::image::Color;
 use crate::ray::Ray;
+use crate::utils::cross;
 
 use super::cylinder::Cylinder;
 use super::illumination::IntersectionContext;
@@ -134,8 +135,8 @@ impl Scene {
   /// Determine the boundaries of the viewing window in world coordinates
   pub fn compute_viewing_window(&self, distance: f64) -> Rect {
     // Compute viewing directions
-    let u = self.view_dir.cross(&self.up_dir).normalize();
-    let v = u.cross(&self.view_dir).normalize();
+    let u = cross(self.view_dir, self.up_dir).normalize();
+    let v = cross(u, self.view_dir).normalize();
 
     // Compute dimensions of viewing window based on field of view
     let viewing_width = {
diff --git a/assignment-1b/src/scene/illumination.rs b/assignment-1b/src/scene/illumination.rs
index ba1dd00..424fee9 100644
--- a/assignment-1b/src/scene/illumination.rs
+++ b/assignment-1b/src/scene/illumination.rs
@@ -8,7 +8,7 @@ use rayon::prelude::{
   ParallelIterator,
 };
 
-use crate::{image::Color, ray::Ray};
+use crate::{image::Color, ray::Ray, utils::dot};
 
 use super::{
   data::{DepthCueing, Light, LightKind, Object},
@@ -53,12 +53,11 @@ impl Scene {
 
         let diffuse_component = material.k_d
           * material.diffuse_color
-          * normal.dot(&light_direction).max(0.0);
+          * dot(normal, light_direction).max(0.0);
 
         let specular_component = material.k_s
           * material.specular_color
-          * normal
-            .dot(&halfway_direction)
+          * dot(normal, halfway_direction)
             .max(0.0)
             .powf(material.exponent);
 
diff --git a/assignment-1b/src/utils.rs b/assignment-1b/src/utils.rs
index 21f183b..c2ab9f1 100644
--- a/assignment-1b/src/utils.rs
+++ b/assignment-1b/src/utils.rs
@@ -24,6 +24,21 @@ where
     .map(|i| i.into_inner())
 }
 
+/// Dot-product between two 3D vectors.
+#[inline]
+pub fn dot(a: Vector3<f64>, b: Vector3<f64>) -> f64 {
+  a.x * b.x + a.y * b.y + a.z * b.z
+}
+
+/// Cross-product between two 3D vectors.
+#[inline]
+pub fn cross(a: Vector3<f64>, b: Vector3<f64>) -> Vector3<f64> {
+  let x = a.y * b.z - a.z * b.y;
+  let y = a.z * b.x - a.x * b.z;
+  let z = a.x * b.y - a.y * b.x;
+  Vector3::new(x, y, z)
+}
+
 /// Calculate the rotation matrix between the 2 given vectors
 ///
 /// Based on the method given [here][1].
@@ -39,15 +54,15 @@ pub fn compute_rotation_matrix(
     return Ok(Matrix3::identity());
   }
 
-  let cos_t = a.dot(&b);
-  let sin_t = a.cross(&b).norm();
+  let cos_t = dot(a, b);
+  let sin_t = cross(a, b).norm();
 
   let g = Matrix3::new(cos_t, -sin_t, 0.0, sin_t, cos_t, 0.0, 0.0, 0.0, 1.0);
 
   // New basis vectors
   let u = a;
-  let v = (b - a.dot(&b) * a).normalize();
-  let w = b.cross(&a);
+  let v = (b - cos_t * a).normalize();
+  let w = cross(b, a);
 
   // Not sure if this is required to be invertible?
   let f_inverse = Matrix3::from_columns(&[u, v, w]);
@@ -56,8 +71,9 @@ pub fn compute_rotation_matrix(
     None => {
       // So I ran into this case trying to compute the rotation matrix where one
       // of the vector endpoints was (0, 0, 0). I'm pretty sure this case makes
-      // no sense in reality, so going to just error out here and screw
-      // recovering.
+      // no sense in reality, which means if I ever encounter this case, I
+      // probably made a mistake somewhere before. So going to just error
+      // out here and screw recovering.
       //
       // println!("Failed to compute inverse matrix.");
       // println!("- Initial: a = {a}, b = {b}");
diff --git a/participation/2023-02-15.py b/participation/2023-02-15.py
new file mode 100644
index 000000000..7005134
--- /dev/null
+++ b/participation/2023-02-15.py
@@ -0,0 +1,34 @@
+class Point:
+    def __init__(self, x, y, z):
+        self.x = x
+        self.y = y
+        self.z = z
+
+    def __sub__(self, o):
+        return Point(self.x - o.x, self.y - o.y, self.z - o.z)
+
+    def __str__(self):
+        return f"({self.x}, {self.y}, {self.z})"
+
+    def cross(self, o):
+        x = self.y * o.z - self.z * o.y
+        y = self.z * o.x - self.x * o.z
+        z = self.x * o.y - self.y * o.x
+        return Point(x, y, z)
+
+p0 = Point(1, 1, 0)
+p1 = Point(0, 1, 1)
+p2 = Point(1, 0, 1)
+
+e1 = p1 - p0
+print(e1)
+
+e2 = p2 - p0
+print(e2)
+
+n = e1.cross(e2)
+print(n)
+
+# Find A, B, C and D
+D = -(n.x * p0.x + n.y * p0.y + n.z * p0.z)
+print(n.x, n.y, n.z, D)