def __init__(self, object_to_world, world_to_object, reverse_orientation, radius, z0, z1, phi_max): """Default constructor for Sphere.""" super(Sphere, self).__init__(object_to_world, world_to_object, reverse_orientation) self.radius = float(radius) self.z_min = clamp(min(z0, z1), -radius, radius) self.z_max = clamp(max(z0, z1), -radius, radius) self.theta_min = math.acos(clamp(self.z_min / radius, -1.0, 1.0)) self.theta_max = math.acos(clamp(self.z_max / radius, -1.0, 1.0)) self.phi_max = math.radians(clamp(phi_max, 0.0, 360.0))
def slerp(t, q1, q2): """Spherical Linear Interpolation between two quaternions.""" cos_theta = dot_quaternions(q1, q2) if cos_theta > 0.9995: return normalize((1.0 - t) * q1 + t * q2) else: theta = math.acos(clamp(cos_theta, -1.0, 1.0)) theta_p = theta * t q_perp = normalize(q2 - q1 * cos_theta) return q1 * math.cos(theta_p) + q_perp * math.sin(theta_p)
def slerp(t, q1, q2): """Spherical Linear Interpolation between two quaternions.""" cos_theta = dot_quaternions(q1, q2) if cos_theta > 0.9995: return normalize((1.0 - t)*q1 + t*q2) else: theta = math.acos(clamp(cos_theta, -1.0, 1.0)) theta_p = theta * t q_perp = normalize(q2 - q1*cos_theta) return q1*math.cos(theta_p) + q_perp*math.sin(theta_p)
def intersect(self, r): """Intersect the ray with the shape.""" # Transform _Ray_ to object space ray = self.world_to_object(r) # Compute quadratic sphere coefficients A = ray.d.x * ray.d.x + ray.d.y * ray.d.y + ray.d.z * ray.d.z B = 2 * (ray.d.x * ray.o.x + ray.d.y * ray.o.y + ray.d.z * ray.o.z) C = ray.o.x*ray.o.x + ray.o.y*ray.o.y + \ ray.o.z*ray.o.z - self.radius*self.radius # Solve quadratic equation for _t_ values found, t0, t1 = quadratic(A, B, C) if not found: return False, float('inf'), 0.0, None # Compute intersection distance along ray if (t0 > ray.maxt or t1 < ray.mint): return False, float('inf'), 0.0, None t_hit = t0 if (t0 < ray.mint): t_hit = t1 if (t_hit > ray.maxt): return False, float('inf'), 0.0, None # Compute sphere hit position and $\phi$ phi_t = ray(t_hit) if (phi_t.x == 0.0 and phi_t.y == 0.0): phi_t.x = 1e-5 * self.radius phi = math.atan2(phi_t.y, phi_t.x) if (phi < 0.0): phi += 2.0 * math.pi # Test sphere intersection against clipping parameters if ((self.z_min > -self.radius and phi_t.z < self.z_min) or \ (self.z_max < self.radius and phi_t.z > self.z_max) or \ phi > self.phi_max): if (t_hit == t1): return False, float('inf'), 0.0, None if (t1 > ray.maxt): return False, float('inf'), 0.0, None t_hit = t1 # Compute sphere hit position and $\phi$ phi_t = ray(t_hit) if (phi_t.x == 0.0 and phi_t.y == 0.0): phi_t.x = 1e-5 * self.radius phi = math.atan2(phi_t.y, phi_t.x) if (phi < 0.0): phi += 2.0 * math.pi if ((self.z_min > -self.radius and phi_t.z < self.z_min) or \ (self.z_max < self.radius and phi_t.z > self.z_max) or \ phi > self.phi_max): return False, float('inf'), 0.0, None # Find parametric representation of sphere hit u = phi / self.phi_max theta = math.acos(clamp(phi_t.z / self.radius, -1.0, 1.0)) v = (theta - self.theta_min) / (self.theta_max - self.theta_min) # Compute sphere $\dpdu$ and $\dpdv$ zradius = math.sqrt(phi_t.x * phi_t.x + phi_t.y * phi_t.y) inv_z_radius = 1.0 / zradius cos_phi = phi_t.x * inv_z_radius sin_phi = phi_t.y * inv_z_radius dpdu = Vector(-self.phi_max * phi_t.y, self.phi_max * phi_t.x, 0) dpdv = (self.theta_max-self.theta_min) * \ Vector(phi_t.z * cos_phi, phi_t.z * sin_phi, -self.radius * math.sin(theta)) # Compute sphere $\dndu$ and $\dndv$ d2Pduu = -self.phi_max * self.phi_max * Vector(phi_t.x, phi_t.y, 0) d2Pduv = (self.theta_max - self.theta_min) * phi_t.z * self.phi_max * \ Vector(-sin_phi, cos_phi, 0.0) d2Pdvv = -(self.theta_max - self.theta_min) * \ (self.theta_max - self.theta_min) * \ Vector(phi_t.x, phi_t.y, phi_t.z) # Compute coefficients for fundamental forms E = dot(dpdu, dpdu) F = dot(dpdu, dpdv) G = dot(dpdv, dpdv) N = normalize(cross(dpdu, dpdv)) e = dot(N, d2Pduu) f = dot(N, d2Pduv) g = dot(N, d2Pdvv) # Compute $\dndu$ and $\dndv$ from fundamental form coefficients invEGF2 = 1.0 / (E * G - F * F) dndu = Normal.from_vector((f*F - e*G) * invEGF2 * dpdu + \ (e*F - f*E) * invEGF2 * dpdv) dndv = Normal.from_vector((g*F - f*G) * invEGF2 * dpdu + \ (f*F - g*E) * invEGF2 * dpdv) # Initialize _DifferentialGeometry_ from parametric information o2w = self.object_to_world dg = DifferentialGeometry.from_intersection(o2w(phi_t), o2w(dpdu), o2w(dpdv), o2w(dndu), o2w(dndv), u, v, self) # Compute _rayEpsilon_ for quadric intersection ray_epsilon = 5e-4 * t_hit return True, t_hit, ray_epsilon, dg
def __init__(self, primitives, refine_immediately): """Default constructor for GridAccel.""" # initialize self.primitives with primitives for grid if refine_immediately: self.primitives = [] for primitive in primitives: primitive.fully_refine(self.primitives) else: self.primitives = list(primitives) # compute bounds and choose grid resolution self.bounds = BBox() for primitive in self.primitives: self.bounds = union(self.bounds, primitive.world_bound()) delta = self.bounds.p_max - self.bounds.p_min # find voxels_per_unit_dist for grid max_axis = self.bounds.maximum_extent() inv_max_width = 1.0 / delta[max_axis] cube_root = 3.0 * pow(len(self.primitives), 1.0 / 3.0) voxels_per_unit_dist = cube_root * inv_max_width self.n_voxels = [] for axis in range(3): self.n_voxels.append( clamp(round_to_int(delta[axis] * voxels_per_unit_dist), 1, 64)) # compute voxel widths and allocate voxels self.width = Vector() self.inv_width = Vector() for axis in range(3): self.width[axis] = delta[axis] / self.n_voxels[axis] if self.width[axis] == 0.0: self.inv_width[axis] = 0.0 else: self.inv_width[axis] = 1.0 / self.width[axis] nv = self.n_voxels[0] * self.n_voxels[1] * self.n_voxels[2] # array of voxels, initialized at None self.voxels = [None] * nv # add primitives to grid voxels for primitive in self.primitives: # find voxel extent of primitive primitive_bound = primitive.world_bound() v_min = [] v_max = [] for axis in range(3): v_min.append(self._pos_to_voxel(primitive_bound.p_min, axis)) v_max.append(self._pos_to_voxel(primitive_bound.p_max, axis)) # add primitive to overlapping voxels for z in range(v_min[2], v_max[2] + 1): for y in range(v_min[1], v_max[1] + 1): for x in range(v_min[0], v_max[0] + 1): index = self._offset(x, y, z) if self.voxels[index] is None: self.voxels[index] = Voxel(primitive) else: self.voxels[index].add_primitive(primitive) # create reader-writer mutex for grid self.rw_lock = DummyRWLock()
def _pos_to_voxel(self, point, axis): """Convert a 1D position into a voxel index.""" v = int((point[axis] - self.bounds.p_min[axis]) * self.inv_width[axis]) return clamp(v, 0, self.n_voxels[axis] - 1)
def test_clamp(self): low = -10.0 high = 10.0 self.assertEqual(clamp(3.4, low, high), 3.4) self.assertEqual(clamp(-100.0, low, high), low) self.assertEqual(clamp(100.0, low, high), high)
def __init__(self, primitives, refine_immediately): """Default constructor for GridAccel.""" # initialize self.primitives with primitives for grid if refine_immediately: self.primitives = [] for primitive in primitives: primitive.fully_refine(self.primitives) else: self.primitives = list(primitives) # compute bounds and choose grid resolution self.bounds = BBox() for primitive in self.primitives: self.bounds = union(self.bounds, primitive.world_bound()) delta = self.bounds.p_max - self.bounds.p_min # find voxels_per_unit_dist for grid max_axis = self.bounds.maximum_extent() inv_max_width = 1.0 / delta[max_axis] cube_root = 3.0 * pow(len(self.primitives), 1.0/3.0) voxels_per_unit_dist = cube_root * inv_max_width self.n_voxels = [] for axis in range(3): self.n_voxels.append(clamp( round_to_int(delta[axis] * voxels_per_unit_dist), 1, 64)) # compute voxel widths and allocate voxels self.width = Vector() self.inv_width = Vector() for axis in range(3): self.width[axis] = delta[axis] / self.n_voxels[axis] if self.width[axis] == 0.0: self.inv_width[axis] = 0.0 else: self.inv_width[axis] = 1.0 / self.width[axis] nv = self.n_voxels[0] * self.n_voxels[1] * self.n_voxels[2] # array of voxels, initialized at None self.voxels = [None] * nv # add primitives to grid voxels for primitive in self.primitives: # find voxel extent of primitive primitive_bound = primitive.world_bound() v_min = [] v_max = [] for axis in range(3): v_min.append(self._pos_to_voxel(primitive_bound.p_min, axis)) v_max.append(self._pos_to_voxel(primitive_bound.p_max, axis)) # add primitive to overlapping voxels for z in range(v_min[2], v_max[2]+1): for y in range(v_min[1], v_max[1]+1): for x in range(v_min[0], v_max[0]+1): index = self._offset(x, y, z) if self.voxels[index] is None: self.voxels[index] = Voxel(primitive) else: self.voxels[index].add_primitive(primitive) # create reader-writer mutex for grid self.rw_lock = DummyRWLock()
def _pos_to_voxel(self, point, axis): """Convert a 1D position into a voxel index.""" v = int((point[axis] - self.bounds.p_min[axis]) * self.inv_width[axis]) return clamp(v, 0, self.n_voxels[axis]-1)
def intersect(self, r): """Intersect the ray with the shape.""" # Transform _Ray_ to object space ray = self.world_to_object(r) # Compute quadratic sphere coefficients A = ray.d.x * ray.d.x + ray.d.y * ray.d.y + ray.d.z * ray.d.z B = 2 * (ray.d.x * ray.o.x + ray.d.y * ray.o.y + ray.d.z * ray.o.z) C = ray.o.x * ray.o.x + ray.o.y * ray.o.y + ray.o.z * ray.o.z - self.radius * self.radius # Solve quadratic equation for _t_ values found, t0, t1 = quadratic(A, B, C) if not found: return False, float("inf"), 0.0, None # Compute intersection distance along ray if t0 > ray.maxt or t1 < ray.mint: return False, float("inf"), 0.0, None t_hit = t0 if t0 < ray.mint: t_hit = t1 if t_hit > ray.maxt: return False, float("inf"), 0.0, None # Compute sphere hit position and $\phi$ phi_t = ray(t_hit) if phi_t.x == 0.0 and phi_t.y == 0.0: phi_t.x = 1e-5 * self.radius phi = math.atan2(phi_t.y, phi_t.x) if phi < 0.0: phi += 2.0 * math.pi # Test sphere intersection against clipping parameters if ( (self.z_min > -self.radius and phi_t.z < self.z_min) or (self.z_max < self.radius and phi_t.z > self.z_max) or phi > self.phi_max ): if t_hit == t1: return False, float("inf"), 0.0, None if t1 > ray.maxt: return False, float("inf"), 0.0, None t_hit = t1 # Compute sphere hit position and $\phi$ phi_t = ray(t_hit) if phi_t.x == 0.0 and phi_t.y == 0.0: phi_t.x = 1e-5 * self.radius phi = math.atan2(phi_t.y, phi_t.x) if phi < 0.0: phi += 2.0 * math.pi if ( (self.z_min > -self.radius and phi_t.z < self.z_min) or (self.z_max < self.radius and phi_t.z > self.z_max) or phi > self.phi_max ): return False, float("inf"), 0.0, None # Find parametric representation of sphere hit u = phi / self.phi_max theta = math.acos(clamp(phi_t.z / self.radius, -1.0, 1.0)) v = (theta - self.theta_min) / (self.theta_max - self.theta_min) # Compute sphere $\dpdu$ and $\dpdv$ zradius = math.sqrt(phi_t.x * phi_t.x + phi_t.y * phi_t.y) inv_z_radius = 1.0 / zradius cos_phi = phi_t.x * inv_z_radius sin_phi = phi_t.y * inv_z_radius dpdu = Vector(-self.phi_max * phi_t.y, self.phi_max * phi_t.x, 0) dpdv = (self.theta_max - self.theta_min) * Vector( phi_t.z * cos_phi, phi_t.z * sin_phi, -self.radius * math.sin(theta) ) # Compute sphere $\dndu$ and $\dndv$ d2Pduu = -self.phi_max * self.phi_max * Vector(phi_t.x, phi_t.y, 0) d2Pduv = (self.theta_max - self.theta_min) * phi_t.z * self.phi_max * Vector(-sin_phi, cos_phi, 0.0) d2Pdvv = ( -(self.theta_max - self.theta_min) * (self.theta_max - self.theta_min) * Vector(phi_t.x, phi_t.y, phi_t.z) ) # Compute coefficients for fundamental forms E = dot(dpdu, dpdu) F = dot(dpdu, dpdv) G = dot(dpdv, dpdv) N = normalize(cross(dpdu, dpdv)) e = dot(N, d2Pduu) f = dot(N, d2Pduv) g = dot(N, d2Pdvv) # Compute $\dndu$ and $\dndv$ from fundamental form coefficients invEGF2 = 1.0 / (E * G - F * F) dndu = Normal.from_vector((f * F - e * G) * invEGF2 * dpdu + (e * F - f * E) * invEGF2 * dpdv) dndv = Normal.from_vector((g * F - f * G) * invEGF2 * dpdu + (f * F - g * E) * invEGF2 * dpdv) # Initialize _DifferentialGeometry_ from parametric information o2w = self.object_to_world dg = DifferentialGeometry.from_intersection(o2w(phi_t), o2w(dpdu), o2w(dpdv), o2w(dndu), o2w(dndv), u, v, self) # Compute _rayEpsilon_ for quadric intersection ray_epsilon = 5e-4 * t_hit return True, t_hit, ray_epsilon, dg