def sample_p(self, p, u1, u2): """Sample at point p.""" # Compute coordinate system for sphere sampling p_center = self.object_to_world(Point(0, 0, 0)) wc = normalize(p_center - p) wc_x, wc_y = coordinate_system(wc) # Sample uniformly on sphere if $\pt{}$ is inside it if (distance_squared(p, p_center) - self.radius * self.radius) < 1e-4: return self.sample(u1, u2) # Sample sphere uniformly inside subtended cone sin_theta_max2 = self.radius * self.radius / distance_squared( p, p_center) cos_theta_max = math.sqrt(max(0.0, 1.0 - sin_theta_max2)) raise Exception("next_line") # r = Ray(p, uniform_sample_cone(u1, u2, cos_theta_max, wcX, wcY, wc), 1e-3) r = Ray(p) intersect, t_hit, ray_epsilon, dg_sphere = self.intersect(r) if not intersect: t_hit = dot(p_center - p, normalize(r.d)) ps = r(t_hit) ns = Normal(normalize(ps - p_center)) if (self.reverse_orientation): ns *= -1.0 return ps, ns
def sample(self, u1, u2): """Sample the shape.""" raise Exception("check_next_line") p = Point(0, 0, 0) + self.radius * 1.0 # uniform_sample_sphere(u1, u2) ns = normalize(self.object_to_world(Normal(p.x, p.y, p.z))) if (self.reverse_orientation): ns *= -1.0 return self.object_to_world(p), ns
def test_transform(self): p = Point(1, 2, 3) p2 = translate(Point(10, 20, 30))(p) self.assertTrue(isinstance(p2, Point)) self.assertEqual(p2, Point(11, 22, 33)) v = Vector(1, 2, 3) v2 = translate(Point(10, 20, 30))(v) self.assertTrue(isinstance(v2, Vector)) self.assertEqual(v2, Vector(1, 2, 3)) self.assertEqual(scale(2, 3, 4)(Point(1, 2, 3)), Point(2, 6, 12)) self.assertEqual(scale(2, 3, 4)(Vector(1, 2, 3)), Vector(2, 6, 12)) self.assertEqual(rotate(90, Vector(0, 1, 0))(Normal(1, 0, 0)), Normal(0, 0, -1))
def test_normal(self): # operator[] n = Normal(1.0, 2.0, 3.0) self.assertEqual(n[0], 1.0) self.assertEqual(n[1], 2.0) self.assertEqual(n[2], 3.0) # face_forward n2 = Normal(1, 0, 0) v = Vector(-0.5, -0.1, 0.2) self.assertEqual(face_forward(n, v), -n) # operator[] for assignments n = Normal(1.0, 2.0, 3.0) for i in range(3): n[i] = 9.0 self.assertEqual(n[i], 9.0)
def __init__(self): """Default constructor for DifferentialGeometry.""" self.p = Point() self.nn = Normal() self.u = 0.0 self.v = 0.0 self.shape = None self.dp_du = Vector() self.dp_dv = Vector() self.dn_du = Normal() self.dn_dv = Normal() self.dp_dx = Vector() self.dp_dy = Vector() self.du_dx = 0.0 self.dv_dx = 0.0 self.du_dy = 0.0 self.dv_dy = 0.0
def __call__(self, elt): """Overload the operator(). Supported operations: * Transform(Point) * Transform(Vector) * Transform(Normal) * Transform(Ray) * Transform(RayDifferential) * Transform(BBox) """ if isinstance(elt, Point): x = elt.x y = elt.y z = elt.z xp = self.m.m[0][0] * x + self.m.m[0][1] * y + self.m.m[0][ 2] * z + self.m.m[0][3] yp = self.m.m[1][0] * x + self.m.m[1][1] * y + self.m.m[1][ 2] * z + self.m.m[1][3] zp = self.m.m[2][0] * x + self.m.m[2][1] * y + self.m.m[2][ 2] * z + self.m.m[2][3] wp = self.m.m[3][0] * x + self.m.m[3][1] * y + self.m.m[3][ 2] * z + self.m.m[3][3] if wp == 1.0: return Point(xp, yp, zp) else: return Point(xp, yp, zp) / wp elif isinstance(elt, Vector): x = elt.x y = elt.y z = elt.z xp = self.m.m[0][0] * x + self.m.m[0][1] * y + self.m.m[0][2] * z yp = self.m.m[1][0] * x + self.m.m[1][1] * y + self.m.m[1][2] * z zp = self.m.m[2][0] * x + self.m.m[2][1] * y + self.m.m[2][2] * z return Vector(xp, yp, zp) elif isinstance(elt, Normal): x = elt.x y = elt.y z = elt.z return Normal( self.m_inv.m[0][0] * x + self.m_inv.m[1][0] * y + self.m_inv.m[2][0] * z, self.m_inv.m[0][1] * x + self.m_inv.m[1][1] * y + self.m_inv.m[2][1] * z, self.m_inv.m[0][2] * x + self.m_inv.m[1][2] * y + self.m_inv.m[2][2] * z) elif isinstance(elt, RayDifferential): ray = RayDifferential.from_ray_differential(elt) ray.o = self(ray.o) ray.d = self(ray.d) ray.rx_origin = self(ray.rx_origin) ray.ry_origin = self(ray.ry_origin) ray.rx_direction = self(ray.rx_direction) ray.ry_direction = self(ray.ry_direction) return ray elif isinstance(elt, Ray): ray = Ray.from_ray(elt) ray.o = self(ray.o) ray.d = self(ray.d) return ray elif isinstance(elt, BBox): ret = BBox(self(Point(elt.p_min.x, elt.p_min.y, elt.p_min.z))) ret = union(ret, self(Point(elt.p_max.x, elt.p_min.y, elt.p_min.z))) ret = union(ret, self(Point(elt.p_min.x, elt.p_max.y, elt.p_min.z))) ret = union(ret, self(Point(elt.p_min.x, elt.p_min.y, elt.p_max.z))) ret = union(ret, self(Point(elt.p_min.x, elt.p_max.y, elt.p_max.z))) ret = union(ret, self(Point(elt.p_max.x, elt.p_max.y, elt.p_min.z))) ret = union(ret, self(Point(elt.p_max.x, elt.p_min.y, elt.p_max.z))) ret = union(ret, self(Point(elt.p_max.x, elt.p_max.y, elt.p_max.z))) return ret