Implement simple intersection detection with sphere

demo.c

@@ -18,8 +18,14 @@ typedef struct {
 	vec3_t orig, dir;
 } ray_t;
 
-static const vec3_t lightblue = { 0.5, 0.7, 1.0 };
+typedef struct {
+	vec3_t centre;
+	double rad;
+} sphere_t;
+
+static const vec3_t lightblue = { 0.4, 0.6, 1.0 };
 static const vec3_t white = { 1.0, 1.0, 1.0 };
+static const vec3_t red = { 1.0, 0.1, 0.2 };
 
 static const vec3_t camera = { 0, 0, 0 };
 static const vec3_t vp_disp = { 0, 0, FOCLEN };
@@ -28,12 +34,35 @@ static const vec3_t vp_v = { 0, -VP_H, 0 };
 static const vec3_t pix_x_step = { VP_W / W, 0, 0 };
 static const vec3_t pix_y_step = { 0, -VP_H / H, 0 };
 
+static const sphere_t obj = {
+	.centre = { 1.0, 0.0, -3.0 },
+	.rad = 1.0,
+};
+
 static pix_t pix[W * H];
 
+static double intersect(sphere_t sphere, ray_t ray)
+{
+	const vec3_t disp = vec3_sub(sphere.centre, ray.orig);
+
+	const double a = vec3_dot(ray.dir, ray.dir);
+	const double b = -2.0 * vec3_dot(ray.dir, disp);
+	const double c = vec3_dot(disp, disp) - sphere.rad * sphere.rad;
+
+	const double discriminant = b * b - 4 * a * c;
+	if (discriminant < 0)
+		return -1.0;
+	else
+		return (-b - sqrt(discriminant)) / (2.0 * a);
+}
+
 static vec3_t raycol(ray_t ray)
 {
-	const vec3_t u = vec3_unit(ray.dir);
-	const double a = (u.y + 1.0) / 2.0;
+	const double t = intersect(obj, ray);
+	if (t > 0.0)
+		return red;
+
+	const double a = (ray.dir.y + 1.0) / 2.0;
 	return vec3_add(vec3_scale(lightblue, a), vec3_scale(white, 1 - a));
 }
 
@@ -64,7 +93,7 @@ int main()
 		for (unsigned x = 0; x < W; ++x) {
 			const ray_t ray = {
 				.orig = camera,
-				.dir = vec3_add(row, vec3_scale(pix_x_step, x)),
+				.dir = vec3_unit(vec3_add(row, vec3_scale(pix_x_step, x))),
 			};
 			const vec3_t col = raycol(ray);
 			setpix(col, pix + (W * y + x));