def CalNormal():
for w, h in ti.ndrange(WIDGHT, HEIGTH):
# 基础法向量
base = face_base_normal[deep_index[w, h]]
radius = ti.acos(-base[2])
up = ti.Vector([base[1], -base[0], 0])
q = QuaternionRotationByRadis(res_normal[w, h], up, radius)
res_normal[w,
h][0], res_normal[w,
h][1], res_normal[w,
h][2] = q[0], q[1], q[2]
def ggx_sample(n, wo, roughness):
u = ti.Vector([1.0, 0.0, 0.0])
if abs(n[1]) < 1.0 - eps:
u = n.cross(ti.Vector([0.0, 1.0, 0.0])).normalized()
v = n.cross(u)
r0 = ti.random()
r1 = ti.random()
a = roughness ** 2.0
a2 = a * a
theta = ti.acos(ti.sqrt((1.0 - r0) / ((a2-1.0)*r0 + 1.0)))
phi = 2.0 * math.pi * r1
wm = ti.cos(theta) * n + ti.sin(theta) * ti.cos(phi) * \
u + ti.sin(theta) * ti.sin(phi) * v
wi = reflect(-wo, wm)
return wi
def rotmat2rotvec(rotmat):
m00, m01, m02 = rotmat[0, 0], rotmat[0, 1], rotmat[0, 2]
m10, m11, m12 = rotmat[1, 0], rotmat[1, 1], rotmat[1, 2]
m20, m21, m22 = rotmat[2, 0], rotmat[2, 1], rotmat[2, 2]
tr = m00 + m11 + m22
qw = ti.sqrt(1.0 + tr) / 2.0
qx = (m21 - m12) / (4.0 * qw)
qy = (m02 - m20) / (4.0 * qw)
qz = (m10 - m01) / (4.0 * qw)
angle = ti.acos((tr - 1.0) / 2.0)
axis = (ti.Vector([qx, qy, qz]) *
(ti.sin(angle) / abs(ti.sin(angle)) + 1e-9)).normalized()
return angle * axis
def func():
xi[0] = -yi[None]
xi[1] = ~yi[None]
xi[2] = ti.logical_not(yi[None])
xi[3] = ti.abs(yi[None])
xf[0] = -yf[None]
xf[1] = ti.abs(yf[None])
xf[2] = ti.sqrt(yf[None])
xf[3] = ti.sin(yf[None])
xf[4] = ti.cos(yf[None])
xf[5] = ti.tan(yf[None])
xf[6] = ti.asin(yf[None])
xf[7] = ti.acos(yf[None])
xf[8] = ti.tanh(yf[None])
xf[9] = ti.floor(yf[None])
xf[10] = ti.ceil(yf[None])
xf[11] = ti.exp(yf[None])
xf[12] = ti.log(yf[None])
def intramolecular_forces():
for i in range(0, N):
for j in range(i + 1, N):
kb = intra[i, j][0]
b0 = intra[i, j][1]
if kb != 0:
r = pos[j] - pos[i]
r_norm = r.norm()
U[None] += kb * ((r_norm - b0)**2)
# angle potential
for i in range(0, N_angles):
ri = pos[int(angles[i][0])]
rj = pos[int(angles[i][1])]
rk = pos[int(angles[i][2])]
rij = ri - rj
rkj = rk - rj
theta = ti.acos(rij.dot(rkj) / (rij.norm() * rkj.norm()))
kthetha = angles[i][3]
theta0 = pi * angles[i][4] / 180
U[None] += kthetha * ((theta - theta0)**2)
def test_trigonometric(): grad_test(lambda x: ti.tanh(x), lambda x: np.tanh(x)) grad_test(lambda x: ti.sin(x), lambda x: np.sin(x)) grad_test(lambda x: ti.cos(x), lambda x: np.cos(x)) grad_test(lambda x: ti.acos(x), lambda x: np.arccos(x)) grad_test(lambda x: ti.asin(x), lambda x: np.arcsin(x))
lambda x: x * x * x * x,
lambda x: 0.4 * x * x - 3,
lambda x: (x - 3) * (x - 1),
lambda x: (x - 3) * (x - 1) + x * x,
])
@if_has_autograd
@test_utils.test()
def test_poly(tifunc):
grad_test(tifunc)
@pytest.mark.parametrize('tifunc,npfunc', [
(lambda x: ti.tanh(x), lambda x: np.tanh(x)),
(lambda x: ti.sin(x), lambda x: np.sin(x)),
(lambda x: ti.cos(x), lambda x: np.cos(x)),
(lambda x: ti.acos(x), lambda x: np.arccos(x)),
(lambda x: ti.asin(x), lambda x: np.arcsin(x)),
])
@if_has_autograd
@test_utils.test(exclude=[ti.vulkan])
def test_trigonometric(tifunc, npfunc):
grad_test(tifunc, npfunc)
@pytest.mark.parametrize('tifunc', [
lambda x: 1 / x,
lambda x: (x + 1) / (x - 1),
lambda x: (x + 1) * (x + 2) / ((x - 1) * (x + 3)),
])
@if_has_autograd
@test_utils.test()
def derivative(self, cosx, args):
k, theta0 = args[0], args[1]
return - k * (ti.acos(cosx) - theta0) / ti.sqrt(1 - cosx ** 2)
def __call__(self, cosx, args):
k, theta0 = args[0], args[1]
return 1/2. * k * (ti.acos(cosx) - theta0) ** 2
