def mainImage(iMouse: ti.Vector, iTime: ti.f32, i: ti.i32,
j: ti.i32) -> ti.Vector:
fragCoord = ti.Vector([i, j])
p = -1.0 + 2.0 * fragCoord / iResolution
m = -1.0 + 2.0 * iMouse # iMouse 已经归一化
a1 = ti.atan2(p[1] - m[1], p[0] - m[0])
a2 = ti.atan2(p[1] + m[1], p[0] + m[0])
r1 = ti.sqrt((p - m).dot(p - m))
r2 = ti.sqrt((p + m).dot(p + m))
uv = ti.Vector(
[0.2 * iTime + (r1 - r2) * 0.25,
ti.asin(ti.sin(a1 - a2)) / 3.1416])
w = ti.exp(-15.0 * r1 * r1) + ti.exp(-15.0 * r2 * r2)
w += 0.25 * smoothstep(0.93, 1.0, ti.sin(128.0 * uv[0]))
w += 0.25 * smoothstep(0.93, 1.0, ti.sin(128.0 * uv[1]))
# 可以使用纹理
# vec3 col = texture( iChannel0, 0.125*uv ).zyx;
col = ti.Vector([0.0, 0.0, 0.0])
fragColor = col + w
return fragColor
def test_atan2_f64():
grad_test(lambda x: ti.atan2(0.4, x),
lambda x: np.arctan2(0.4, x),
default_fp=ti.f64)
grad_test(lambda y: ti.atan2(y, 0.4),
lambda y: np.arctan2(y, 0.4),
default_fp=ti.f64)
def computeDstToRefTransform(dst_mean_x, dst_mean_y):
"""
Compute the rotation matrix and translation vectors to move dst p.c. into ref p.c
Beased on https://lucidar.me/en/mathematics/singular-value-decomposition-of-a-2x2-matrix/
"""
a = A[0, 0]
b = A[1, 0]
c = A[0, 1]
d = A[1, 1]
teta = 0.5 * ti.atan2(2 * a * c + 2 * b * d, a * a + b * b - c * c - d * d)
U[0, 0] = ti.cos(teta)
U[1, 0] = -ti.sin(teta)
U[0, 1] = ti.sin(teta)
U[1, 1] = ti.cos(teta)
# We don't need the Sigma matrix for ICP
# s1 = a*a + b*b + c*c + d*d
# s2 = ti.sqrt((a*a + b*b - c*c - d*d) * (a*a + b*b - c*c - d*d) + 4 * (a*c + b*d) * (a*c + b*d))
# sigma1 = ti.sqrt((s1 + s2) * 0.5)
# sigma2 = ti.sqrt((s1 - s2) * 0.5)
# S[0,0] = sigma1
# S[1,0] = 0
# S[0,1] = 0
# S[1,1] = sigma2
phi = 0.5 * ti.atan2(2 * a * b + 2 * c * d, a * a - b * b + c * c - d * d)
s11 = (a * ti.cos(teta) + c * ti.sin(teta)) * ti.cos(phi) + (
b * ti.cos(teta) + d * ti.sin(teta)) * ti.sin(phi)
if s11 != 0:
s11 = s11 / ti.abs(s11)
s22 = (a * ti.sin(teta) - c * ti.cos(teta)) * ti.sin(phi) + (
-b * ti.sin(teta) + d * ti.cos(teta)) * ti.cos(phi)
if s22 != 0:
s22 = s22 / ti.abs(s22)
V[0, 0] = s11 * ti.cos(phi)
V[1, 0] = -s22 * ti.sin(phi)
V[0, 1] = s11 * ti.sin(phi)
V[1, 1] = s22 * ti.cos(phi)
Rot[0, 0] = V[0, 0] * U[0, 0] + V[1, 0] * U[1, 0]
Rot[1, 0] = V[0, 0] * U[0, 1] + V[1, 0] * U[1, 1]
Rot[0, 1] = V[0, 1] * U[0, 0] + V[1, 1] * U[1, 0]
Rot[1, 1] = V[0, 1] * U[0, 1] + V[1, 1] * U[1, 1]
Trans[0] = ref_mean[0] - Rot[0, 0] * dst_mean_x - Rot[1, 0] * dst_mean_y
Trans[1] = ref_mean[1] - Rot[0, 1] * dst_mean_x - Rot[1, 1] * dst_mean_y
def atan(y, x=1):
'''
Return the arc-tangent of the parameters
`atan(y, x)` or `atan(y_over_x)`:
`atan` returns the angle whose trigonometric arctangent is y / x or
y_over_x, depending on which overload is invoked.
In the first overload, the signs of y and x are used to determine
the quadrant that the angle lies in. The values returned by atan in
this case are in the range [−pi, pi]. Results are undefined if x
is zero.
For the second overload, atan returns the angle whose tangent
is y_over_x. Values returned in this case are in the range
[−pi/2, pi/2].
:parameter y:
The numerator of the fraction whose arctangent to return.
:parameter x:
The denominator of the fraction whose arctangent to return.
:return:
The return value is `arctan(x / y)`.
'''
return ti.atan2(y, x)
def paint(t:ti.f32) :
for i, j in pixels:
p = ti.Vector([2*i-Width, 2*j-Height])/min(Width,Height)
#background-color
bcol = ti.Vector([1.0,0.8,0.7-0.07*p[1]]) * (1.0-0.25*p.norm())
#animate
tt = mod(t, 1.5)/1.5
ss = pow(tt, 0.2)*0.5+0.5
ss = 1.0 + ss*0.5*ti.sin(tt*6.2831*3.0+p[1]*0.5)*ti.exp(-4.0*tt)
p *= ti.Vector([0.5, 1.5]) + ss*ti.Vector([0.5, -0.5])
#shape
p[1] -= 0.25
a = ti.atan2(p[0], p[1]) / 3.141593
r = p.norm()
h = abs(a)
d = (13.0*h - 22.0*h*h + 10.0*h*h*h)/(6.0-5.0*h)
#color
s = 0.75 + 0.75*p[0]
s *= 1.0 - 0.4*r
s = 0.3 + 0.7*s
s *= 0.5 + 0.5*pow(1.0-clamp(r/d, 0.0, 1.0), 1.0)
hcol = ti.Vector([1.0, 0.5*r, 0.3])*s
pixels[i,j] = mix(bcol , hcol ,smoothstep(-0.01, 0.01, d-r))
def skewsin(x, t):
"""
skewsin-функция
:param x: радианы
:param t: значение
:return: значение skewsin-функции
"""
return ti.atan2(t * ti.sin(x), (1. - t * ti.cos(x))) / t
def getBoundaryValue(x_index, y_index):
dx = sdf[x_index+1, y_index-1][0] - sdf[x_index-1, y_index-1][0] \
+ sdf[x_index+1, y_index][0] - sdf[x_index-1, y_index][0] \
+ sdf[x_index+1, y_index+1][0] - sdf[x_index-1, y_index+1][0]
dy = sdf[x_index-1, y_index+1][0] - sdf[x_index-1, y_index-1][0] \
+ sdf[x_index, y_index+1][0] - sdf[x_index, y_index-1][0] \
+ sdf[x_index+1, y_index+1][0] - sdf[x_index+1, y_index-1][0]
return ti.abs(ti.atan2(dy, dx) / 3.14159)
def _ΔΦ(i: ti.i32, z: ti.i32) -> ti.f32:
s = 0.0
t = 0.0
for r in range(Rf, Nr):
Δ = (ti.atan2(_J[i, r], _I[i, r]) - _Φ[i, z, r]) % (2 * π)
if (Δ > π):
Δ -= 2 * π
w = ti.sqrt(_I[i, r]**2 + _J[i, r]**2) * _A[i, z, r]
t += w
s += w * Δ
return s / t
def random_point_in_unit_polygon(self, sides, angle):
point = ti.Vector.zero(ti.f32, 2)
central_angle = 2 * math.pi / sides
while True:
point = ti.Vector([ti.random(), ti.random()]) * 2 - 1
point_angle = ti.atan2(point.y, point.x)
theta = (point_angle -
angle) % central_angle # polygon angle is from +X axis
phi = central_angle / 2
dist = ti.sqrt((point**2).sum())
if dist < ti.cos(phi) / ti.cos(phi - theta):
break
return point
def sampleEquiAngular(
u: ti.f32,
maxDistance: ti.f32,
rayOrigin: ti.Vector, # vec3
rayDir: ti.Vector, # vec3
lightPos: ti.Vector # vec3
):
# get coord of closest point to light along(infinite) ray
delta = dot(lightPos - rayOrigin, rayDir)
# get distance this point is from light
D = length(rayOrigin + delta * rayDir - lightPos)
# get angle of endpoints
thetaA = ti.atan2(0.0 - delta, D)
thetaB = ti.atan2(maxDistance - delta, D)
# take sample
t = D * ti.tan(mix(thetaA, thetaB, u))
dist = delta + t
pdf = D / ((thetaB - thetaA) * (D * D + t * t))
return (dist, pdf)
def getDist(p):
diskPos = -1.0 * p
diskDist = sphere(ti.Vector([diskPos[0], diskPos[1], diskPos[2], 5.0]))
diskDist = max(diskDist, diskPos[1] - 0.01)
diskDist = max(diskDist, -1.0 * diskPos[1] - 0.01)
diskDist = max(
diskDist, -1.0 *
sphere(ti.Vector([-1.0 * p[0], -1.0 * p[1], -1.0 * p[2], 1.5]) * 10.0))
if diskDist < 2.0:
c = ti.Vector([
diskPos.norm(), diskPos[1],
ti.atan2(diskPos[2] + 1.0, diskPos[0] + 1.0) * 0.5
])
c *= 10.0
diskDist += noise(c) * 0.4
diskDist += noise(c * 2.5) * 0.2
return diskDist
def friction(t: ti.i32):
# params V, R
# updates Fupdated
for prtcl in range(N):
vx, vy = V[t, prtcl]
v = ti.sqrt(vx * vx + vy * vy)
theta = ti.atan2(vy, vx)
# random doesnt seem to work in tape scope
ffx = friction_coef[None] * v * ti.cos(
theta) # + ti.randn() * temperature
ffy = friction_coef[None] * v * ti.sin(
theta) # + ti.randn() * temperature
Fupdated[t, prtcl][0] += ffx
Fupdated[t, prtcl][0] += ffx
def func():
x[0] = y[None] + z[None]
x[1] = y[None] - z[None]
x[2] = y[None] * z[None]
x[3] = y[None] / z[None]
x[4] = y[None] // z[None]
x[5] = y[None] % z[None]
x[6] = y[None]**z[None]
x[7] = y[None] == z[None]
x[8] = y[None] != z[None]
x[9] = y[None] > z[None]
x[10] = y[None] >= z[None]
x[11] = y[None] < z[None]
x[12] = y[None] <= z[None]
x[13] = ti.atan2(y[None], z[None])
x[14] = ti.min(y[None], z[None])
x[15] = ti.max(y[None], z[None])
def test_constant_matrices():
assert ti.cos(ti.math.pi / 3) == approx(0.5)
assert np.allclose((-ti.Vector([2, 3])).to_numpy(), np.array([-2, -3]))
assert ti.cos(ti.Vector([2,
3])).to_numpy() == approx(np.cos(np.array([2,
3])))
assert ti.max(2, 3) == 3
res = ti.max(4, ti.Vector([3, 4, 5]))
assert np.allclose(res.to_numpy(), np.array([4, 4, 5]))
res = ti.Vector([2, 3]) + ti.Vector([3, 4])
assert np.allclose(res.to_numpy(), np.array([5, 7]))
res = ti.atan2(ti.Vector([2, 3]), ti.Vector([3, 4]))
assert res.to_numpy() == approx(
np.arctan2(np.array([2, 3]), np.array([3, 4])))
res = ti.Matrix([[2, 3], [4, 5]]) @ ti.Vector([2, 3])
assert np.allclose(res.to_numpy(), np.array([13, 23]))
v = ti.Vector([3, 4])
w = ti.Vector([5, -12])
r = ti.Vector([1, 2, 3, 4])
s = ti.Matrix([[1, 2], [3, 4]])
assert v.normalized().to_numpy() == approx(np.array([0.6, 0.8]))
assert v.cross(w) == approx(-12 * 3 - 4 * 5)
w.y = v.x * w[0]
r.x = r.y
r.y = r.z
r.z = r.w
r.w = r.x
assert np.allclose(w.to_numpy(), np.array([5, 15]))
assert ti.select(ti.Vector([1, 0]), ti.Vector([2, 3]),
ti.Vector([4, 5])) == ti.Vector([2, 5])
s[0, 1] = 2
assert s[0, 1] == 2
@ti.kernel
def func(t: ti.i32):
m = ti.Matrix([[2, 3], [4, t]])
print(m @ ti.Vector([2, 3]))
m += ti.Matrix([[3, 4], [5, t]])
print(m @ v)
print(r.x, r.y, r.z, r.w)
s = w.transpose() @ m
print(s)
print(m)
func(5)
def ang(self):
'''Phase angle of the complex'''
return ti.atan2(self.y, self.x)
def test_case_2() -> ti.f32:
x[0] = ti.i32(3)
y[0] = ti.i32(1)
return ti.atan2(x[0], y[0])
def test_case_1() -> ti.f32:
x[0] = ti.i32(2)
return ti.atan2(x[0], 1)
def test_case_0() -> ti.f32:
i = ti.i32(2)
return ti.atan2(i, 1)
def func():
y[0] = x[0] % 3
@ti.kernel
def func2():
ti.atomic_add(y[0], x[0] % 3)
func()
func.grad()
func2()
func2.grad()
@pytest.mark.parametrize('tifunc,npfunc', [
(lambda x: ti.atan2(0.4, x), lambda x: np.arctan2(0.4, x)),
(lambda y: ti.atan2(y, 0.4), lambda y: np.arctan2(y, 0.4)),
])
@if_has_autograd
@test_utils.test()
def test_atan2(tifunc, npfunc):
grad_test(tifunc, npfunc)
@pytest.mark.parametrize('tifunc,npfunc', [
(lambda x: ti.atan2(0.4, x), lambda x: np.arctan2(0.4, x)),
(lambda y: ti.atan2(y, 0.4), lambda y: np.arctan2(y, 0.4)),
])
@if_has_autograd
@test_utils.test(require=ti.extension.data64, default_fp=ti.f64)
def test_atan2_f64(tifunc, npfunc):
def increment_vector_inplace(
array_vector: ti.template(), magnitude: float, dy: float, dx: float):
# increment array_vector (which is/may be row in an [? x 2]) vector field)
theta = ti.atan2(dy, dx)
array_vector[0] += magnitude * ti.cos(theta)
array_vector[1] += magnitude * ti.sin(theta)
def computeNormalAndCurvature():
"""
Compute the normal and the curvature at all points voxels.
Based on the PC limplementation:
https://pointclouds.org/documentation/group__features.html
"""
radius = 50
for i,j in pts:
nb_pts = ti.cast(0, ti.f32)
accu_0 = ti.cast(0, ti.f32)
accu_1 = ti.cast(0, ti.f32)
accu_2 = ti.cast(0, ti.f32)
accu_3 = ti.cast(0, ti.f32)
accu_4 = ti.cast(0, ti.f32)
accu_5 = ti.cast(0, ti.f32)
accu_6 = ti.cast(0, ti.f32)
accu_7 = ti.cast(0, ti.f32)
accu_8 = ti.cast(0, ti.f32)
z = 0
for x in range(i-radius, i+radius):
for y in range(j-radius, j+radius):
if ti.is_active(block1, [x,y]):
accu_0 += x * x
accu_1 += x * y
accu_2 += x * z
accu_3 += y * y
accu_4 += y * z
accu_5 += z * z
accu_6 += x
accu_7 += y
accu_8 += z
nb_pts += 1
accu_0 /= nb_pts
accu_1 /= nb_pts
accu_2 /= nb_pts
accu_3 /= nb_pts
accu_4 /= nb_pts
accu_5 /= nb_pts
accu_6 /= nb_pts
accu_7 /= nb_pts
accu_8 /= nb_pts
cov_mat_0 = accu_0 - accu_6 * accu_6
cov_mat_1 = accu_1 - accu_6 * accu_7
cov_mat_2 = accu_2 - accu_6 * accu_8
cov_mat_4 = accu_3 - accu_7 * accu_7
cov_mat_5 = accu_4 - accu_7 * accu_8
cov_mat_8 = accu_5 - accu_8 * accu_8
cov_mat_3 = cov_mat_1
cov_mat_6 = cov_mat_2
cov_mat_7 = cov_mat_5
# Compute eigen value and eigen vector
# Make sure in [-1, 1]
scale = ti.max(1.0, ti.abs(cov_mat_0))
scale = ti.max(scale, ti.abs(cov_mat_1))
scale = ti.max(scale, ti.abs(cov_mat_2))
scale = ti.max(scale, ti.abs(cov_mat_3))
scale = ti.max(scale, ti.abs(cov_mat_4))
scale = ti.max(scale, ti.abs(cov_mat_5))
scale = ti.max(scale, ti.abs(cov_mat_6))
scale = ti.max(scale, ti.abs(cov_mat_7))
scale = ti.max(scale, ti.abs(cov_mat_8))
if scale > 1.0:
cov_mat_0 /= scale
cov_mat_1 /= scale
cov_mat_2 /= scale
cov_mat_3 /= scale
cov_mat_4 /= scale
cov_mat_5 /= scale
cov_mat_6 /= scale
cov_mat_7 /= scale
cov_mat_8 /= scale
# Compute roots
eigen_val_0 = ti.cast(0, ti.f32)
eigen_val_1 = ti.cast(0, ti.f32)
eigen_val_2 = ti.cast(0, ti.f32)
c0 = cov_mat_0 * cov_mat_4 * cov_mat_8 \
+ 2 * cov_mat_3 * cov_mat_6 * cov_mat_7 \
- cov_mat_0 * cov_mat_7 * cov_mat_7 \
- cov_mat_4 * cov_mat_6 * cov_mat_6 \
- cov_mat_8 * cov_mat_3 * cov_mat_3
c1 = cov_mat_0 * cov_mat_4 \
- cov_mat_3 * cov_mat_3 \
+ cov_mat_0 * cov_mat_8 \
- cov_mat_6 * cov_mat_6 \
+ cov_mat_4 * cov_mat_8 \
- cov_mat_7 * cov_mat_7
c2 = cov_mat_0 + cov_mat_4 + cov_mat_8
if ti.abs(c0) < 0.00001:
eigen_val_0 = 0
d = c2 * c2 - 4.0 * c1
if d < 0.0: # no real roots ! THIS SHOULD NOT HAPPEN!
d = 0.0
sd = ti.sqrt(d)
eigen_val_2 = 0.5 * (c2 + sd)
eigen_val_1 = 0.5 * (c2 - sd)
else:
s_inv3 = ti.cast(1.0 / 3.0, ti.f32)
s_sqrt3 = ti.sqrt(3.0)
c2_over_3 = c2 * s_inv3
a_over_3 = (c1 - c2 * c2_over_3) * s_inv3
if a_over_3 > 0:
a_over_3 = 0
half_b = 0.5 * (c0 + c2_over_3 * (2 * c2_over_3 * c2_over_3 - c1))
q = half_b * half_b + a_over_3 * a_over_3 * a_over_3
if q > 0:
q = 0
rho = ti.sqrt(-a_over_3)
theta = ti.atan2(ti.sqrt(-q), half_b) * s_inv3
cos_theta = ti.cos(theta)
sin_theta = ti.sin(theta)
eigen_val_0 = c2_over_3 + 2 * rho * cos_theta
eigen_val_1 = c2_over_3 - rho * (cos_theta + s_sqrt3 * sin_theta)
eigen_val_2 = c2_over_3 - rho * (cos_theta - s_sqrt3 * sin_theta)
temp_swap = ti.cast(0, ti.f32)
# Sort in increasing order.
if eigen_val_0 >= eigen_val_1:
temp_swap = eigen_val_1
eigen_val_1 = eigen_val_0
eigen_val_0 = temp_swap
if eigen_val_1 >= eigen_val_2:
temp_swap = eigen_val_2
eigen_val_2 = eigen_val_1
eigen_val_1 = temp_swap
if eigen_val_0 >= eigen_val_1:
temp_swap = eigen_val_1
eigen_val_1 = eigen_val_0
eigen_val_0 = temp_swap
if eigen_val_0 <= 0:
eigen_val_0 = 0
d = c2 * c2 - 4.0 * c1
if d < 0.0: # no real roots ! THIS SHOULD NOT HAPPEN!
d = 0.0
sd = ti.sqrt(d)
eigen_val_2 = 0.5 * (c2 + sd)
eigen_val_1 = 0.5 * (c2 - sd)
# end of compute roots
eigen_value = eigen_val_1 * scale # eigen value for 2D SDF
# eigen value for 3D SDF
#eigen_value = eigen_val_0 * scale
#print("eigen_val_0 ", eigen_val_0)
#print("eigen_val_1 ", eigen_val_1)
#print("eigen_val_2 ", eigen_val_2)
# TODO
#scaledMat.diagonal ().array () -= eigenvalues (0)
#eigenvector = detail::getLargest3x3Eigenvector<Vector> (scaledMat).vector;
# Compute normal vector (TODO)
#visual_norm[i,j][0] = eigen_val_0 #eigen_vector[0]
#visual_norm[i,j][1] = eigen_val_1 #eigen_vector[1]
#visual_norm[i,j][2] = eigen_val_2 #eigen_vector[2]
# Compute the curvature surface change
eig_sum = cov_mat_0 + cov_mat_1 + cov_mat_2
visual_curv[i,j][0] = 0
if eig_sum != 0:
visual_curv[i,j][0] = eigen_val_1 # true curvature is: ti.abs(eigen_value / eig_sum)
def unspherical(dir):
p = ti.atan2(dir.y, dir.x) / ti.tau
return dir.z, p % 1
def complex_power(z, power: ti.i32):
r = ti.sqrt(z[0]**2 + z[1]**2)
theta = ti.atan2(z[1], z[0])
return ti.Vector(
[r**power * ti.cos(power * theta), r**power * ti.sin(power * theta)])
def dir2tex(dir):
dir = dir.normalized()
s = ti.atan2(dir.z, dir.x) / ti.pi * 0.5 + 0.5
t = ti.atan2(dir.y, dir.xz.norm()) / ti.pi + 0.5
return V(s, t)
def foo():
y[None] = x[None]**2
z[None] = ti.atan2(y[None], 0.3)
def test_atan2(): grad_test(lambda x: ti.atan2(0.4, x), lambda x: np.arctan2(0.4, x)) grad_test(lambda y: ti.atan2(y, 0.4), lambda y: np.arctan2(y, 0.4))
def test_atan2_f64():
ti.set_default_fp(ti.f64)
grad_test(lambda x: ti.atan2(0.4, x), lambda x: np.arctan2(0.4, x))
grad_test(lambda y: ti.atan2(y, 0.4), lambda y: np.arctan2(y, 0.4))