Flat shading of spheres finished

src/main.rs

@@ -4,36 +4,35 @@ use std::mem;
 extern crate bmp;
 extern crate nalgebra;
 
-use nalgebra::Pnt3;
-use nalgebra::Vec3;
+use nalgebra::*;
 use bmp::Image;
 use bmp::Pixel;
 
 struct Ray {
-  pos: nalgebra::Pnt3<f64>,
-  dir: nalgebra::Vec3<f64>
+  pos: Vec3<f64>,
+  dir: Vec3<f64>
 }
 
 impl Ray {
-  fn new(pos: nalgebra::Pnt3<f64>, dir: nalgebra::Vec3<f64>) -> Ray {
+  fn new(pos: Vec3<f64>, dir: Vec3<f64>) -> Ray {
     Ray {
       pos: pos,
       dir: dir
     }
   }
 
-  fn at(&self, t: f64) -> Pnt3<f64> {
+  fn at(&self, t: f64) -> Vec3<f64> {
     self.pos + t * self.dir
   }
 }
 
 struct OrthoCamera {
-  pos: nalgebra::Pnt3<f64>,
+  pos: Vec3<f64>,
   plane: bmp::Image
 }
 
 impl OrthoCamera {
-  fn new(pos: nalgebra::Pnt3<f64>) -> OrthoCamera {
+  fn new(pos: Vec3<f64>) -> OrthoCamera {
     OrthoCamera {
       pos: pos,
       plane: Image::new(256,256)
@@ -42,59 +41,66 @@ impl OrthoCamera {
 }
 
 struct Sphere {
-  pos: nalgebra::Pnt3<f64>,
+  pos: Vec3<f64>,
   radius: f64
 }
 
 impl Sphere {
-  fn new(pos: nalgebra::Pnt3<f64>, radius: f64) -> Sphere {
+  fn new(pos: Vec3<f64>, radius: f64) -> Sphere {
     Sphere {
       pos: pos,
       radius: radius
     }
   }
 
-  fn intersection(primary_ray: Ray) -> Vec3<f64> {
-    let t0: f64;
-    let t1: f64;
+  // Implemented from
+  // http://kylehalladay.com/blog/tutorial/math/2013/12/24/Ray-Sphere-Intersection.html
+  fn intersection(&self, primary_ray: Ray, t1: &mut f64, t2: &mut f64) -> bool {
+    let l = self.pos - primary_ray.pos;
+    let tc = dot(&l, &primary_ray.dir);
 
-    let center = Vec3::new(pos);
-
-    return center;
-  }
-
-  fn solve_quadratic(a: f64, b: f64, c: f64, x0: &mut f64, x1: &mut f64) -> bool {
-    let discr: f64 = b * b - 4.0 * a * c;
-    if discr < 0.0 {
+    if tc < 0.0 { 
       return false;
-    } else if discr == 0.0 {
-      *x0 = - 0.5 * b / a;
-      *x1 = - 0.5 * b / a;
-    } else {
-      let q: f64 = if b > 0.0 { -0.5 * (b + f64::sqrt(discr)) } else { -0.5 * (b - f64::sqrt(discr)) };
-      *x0 = q / a;
-      *x1 = c / q;
     }
-    if x0 > x1 { mem::swap(x0, x1); }
+
+    let d = f64::sqrt((l.norm() * l.norm()) as f64 - (tc*tc));
+
+    if d > self.radius { return false };
+
+    let t1c = f64::sqrt(f64::powf(self.radius, 2.0) - f64::powf(d, 2.0));
+    *t1 = tc - t1c;
+    *t2 = tc + t1c;
+
     return true;
   }
 }
 
 fn main() {
-  let mut camera = OrthoCamera::new(Pnt3::new(0.0, 0.0, 0.0));
+  let mut camera = OrthoCamera::new(Vec3::new(0.0, 0.0, 0.0));
   let mut spheres = Vec::new();
 
-  spheres.push(Sphere::new(Pnt3::new(0.0, 0.0, 20.0), 5.0));
+  spheres.push(Sphere::new(Vec3::new(100.0, 100.0, 50.0), 25.0));
 
   for (x, y) in camera.plane.coordinates() {
-    camera.plane.set_pixel(x, y, px!(x, y, 200));
+    println!("Camera coords: {}. {}", x, y);
+    for sphere in &spheres {
+      let ray = Ray::new(Vec3::new(x as f64, y as f64, camera.pos.z as f64), Vec3::new(0.0, 0.0, 1.0));
+      let mut t1 = 0.0;
+      let mut t2 = 0.0;
+      let result = sphere.intersection(ray, &mut t1, &mut t2);
+      if result == true {
+        camera.plane.set_pixel(x, y, px!(255, 255, 255));
+      } else {
+        camera.plane.set_pixel(x, y, px!(0, 0, 0));
+      }
+    }
   }
 
   let _ = camera.plane.save("img.bmp");
 
 
   // Testing rays
-  let ray = Ray::new(Pnt3::new(0.0, 0.0, 0.0), Vec3::new(0.0, 0.25, 0.8));
+  let ray = Ray::new(Vec3::new(0.0, 0.0, 0.0), Vec3::new(0.0, 0.25, 0.8));
 
   let result = ray.at(5.0);