Define lookat() function for computing view matrices

main.c

@@ -106,10 +106,39 @@ key_callback(GLFWwindow *window, int key, int scancode, int action, int mods)
 	}
 }
 
+static vec3_t sub(vec3_t v, vec3_t u)
+{
+	return (vec3_t) { v.x - u.x, v.y - u.y, v.z - u.z };
+}
+
+static float len(vec3_t v)
+{
+	return sqrtf(v.x * v.x + v.y * v.y + v.z * v.z);
+}
+
+static vec3_t norm(vec3_t v)
+{
+	const float s = len(v);
+	return (vec3_t) { v.x / s, v.y / s, v.z / s };
+}
+
+static float dot(vec3_t v, vec3_t u)
+{
+	return v.x * u.x + v.y * u.y + v.z * u.z;
+}
+
+static vec3_t cross(vec3_t v, vec3_t u)
+{
+	return (vec3_t) {
+		v.y * u.z - v.z * u.y,
+		v.z * u.x - v.x * u.z,
+		v.x * u.y - v.y * u.x,
+	};
+}
+
 static mat4_t mul(mat4_t m, mat4_t n)
 {
-#define ELEM(i, j) \
-	m.x.i *n.j.x + m.y.i *n.j.y + m.z.i *n.j.z + m.w.i *n.j.w
+#define ELEM(i, j) m.x.i *n.j.x + m.y.i *n.j.y + m.z.i *n.j.z + m.w.i *n.j.w
 	return (mat4_t) {
 		{ ELEM(x, x), ELEM(y, x), ELEM(z, x), ELEM(w, x) },
 		{ ELEM(x, y), ELEM(y, y), ELEM(z, y), ELEM(w, y) },
@@ -119,6 +148,22 @@ static mat4_t mul(mat4_t m, mat4_t n)
 #undef MUL_ELEM
 }
 
+static mat4_t lookat(vec3_t cam, vec3_t tgt, vec3_t up)
+{
+	const vec3_t s = sub(tgt, cam);
+
+	const vec3_t s_hat = norm(s);
+	const vec3_t u_hat = norm(cross(up, s_hat));
+	const vec3_t v_hat = cross(s_hat, u_hat);
+
+	return (mat4_t) {
+		{ u_hat.x, v_hat.x, s_hat.x, 0 },
+		{ u_hat.y, v_hat.y, s_hat.y, 0 },
+		{ u_hat.z, v_hat.z, s_hat.z, 0 },
+		{ -dot(u_hat, cam), -dot(v_hat, cam), -dot(s_hat, cam), 1 },
+	};
+}
+
 static mat4_t persp(float aspect, float fov, float ncp, float fcp)
 {
 	const float r = 2 * ncp * tanf(fov / 2);
@@ -155,9 +200,11 @@ int main()
 	gpu_ctx_t gpu;
 	gpu_init(&gpu, &gpu_config);
 
+	const vec3_t cam = { 2, 2, -2 };
+	const vec3_t tgt = { 0, 0, 0 };
 	mvp_t mvp = {
 		.model = SCALE(2),
-		.view = TRANSLATE(0, 0, 4.0),
+		.view = lookat(cam, tgt, (vec3_t) { 0, 1, 0 }),
 		.proj = persp((float)W / H, M_PI / 6, 0.1, 10.0),
 	};