Ria-weekend: Added sphere demo

ria-weekend/.gitignore

@@ -1 +1,2 @@
 target/
+*.ppm

ria-weekend/examples/sphere.rs

@@ -0,0 +1,46 @@
+extern crate ria_weekend;
+
+use ria_weekend::{demo::Demo, ray, ray::Ray, vec3::Vec3};
+
+fn main() {
+    let demo = Demo::new("single_sphere_demo");
+    let dimensions = demo.dimensions();
+
+    let mut buf = String::new();
+    // linear interpolation based on y coordinate
+    // top to down
+    let color = |ray: Ray| -> Vec3 {
+        // center at z=-1. xy axis cuts sphere in half
+        if ray_hit_sphere(Vec3::new(0.0, 0.0, -1.0), 0.5, &ray) {
+            // For all rays that hit sphere, return red color
+            // This will result in a sphere that is red in color
+            return Vec3::new(1.0, 0.0, 0.0);
+        }
+        let unit_direction = ray.direction().unit_vector();
+        // For rays that don't hit sphere, It'll paint the gradient as the background
+        // Linear gradient depends on y
+        let t = 0.5 * (unit_direction.y() + 1.0);
+
+        // start color + end color
+        Vec3::new(1.0, 1.0, 1.0) * (1.0 - t) + Vec3::new(0.0, 0.0, 0.0) * t
+    };
+
+    ray::create_ray_demo(&mut buf, dimensions, color);
+
+    demo.save_as_ppm(buf);
+}
+
+fn ray_hit_sphere(center: Vec3, radius: f32, ray: &Ray) -> bool {
+    // dot(A + t*B - C, A + t*B - C) =  R*R
+    // when expanded we get
+    // t * t * dot(B, B) + 2 * t * dot(B, A-C) + dot(A-C, A-C) - R*R = 0
+
+    // A-C
+    let ac = ray.origin() - center;
+    let a = ray.direction().dot(&ray.direction());
+    let b = 2.0 * ac.dot(&ray.direction());
+    let c = ac.dot(&ac) - radius * radius;
+    let discriminant = b * b - 4.0 * a * c;
+
+    discriminant > 0.0
+}