def quat_to_euler(q):
name = _ek.detail.array_name('Array', q.Type, [3], q.IsScalar)
module = _modules.get(q.__module__)
Array3f = getattr(module, name)
sinp = 2 * _ek.fmsub(q.w, q.y, q.z * q.x)
gimbal_lock = _ek.abs(sinp) > (1.0 - 5e-8)
# roll (x-axis rotation)
q_y_2 = _ek.sqr(q.y)
sinr_cosp = 2 * _ek.fmadd(q.w, q.x, q.y * q.z)
cosr_cosp = _ek.fnmadd(2, _ek.fmadd(q.x, q.x, q_y_2), 1)
roll = _ek.select(gimbal_lock, 2 * _ek.atan2(q.x, q.w),
_ek.atan2(sinr_cosp, cosr_cosp))
# pitch (y-axis rotation)
pitch = _ek.select(gimbal_lock, _ek.copysign(0.5 * _ek.Pi, sinp),
_ek.asin(sinp))
# yaw (z-axis rotation)
siny_cosp = 2 * _ek.fmadd(q.w, q.z, q.x * q.y)
cosy_cosp = _ek.fnmadd(2, _ek.fmadd(q.z, q.z, q_y_2), 1)
yaw = _ek.select(gimbal_lock, 0, _ek.atan2(siny_cosp, cosy_cosp))
return Array3f(roll, pitch, yaw)
def sph_convert(v):
x2 = ek.pow(v.x, 2)
y2 = ek.pow(v.y, 2)
z2 = ek.pow(v.z, 2)
r = ek.sqrt(x2 + y2 + z2)
phi = ek.atan2(v.y, v.x)
theta = ek.atan2(ek.sqrt(x2 + y2), v.z)
return r, theta, phi
def forward(ctx, arg1, arg2):
ctx.in1 = ek.FloatD(arg1)
ctx.in2 = ek.FloatD(arg2)
ek.set_requires_gradient(ctx.in1, arg1.requires_grad)
ek.set_requires_gradient(ctx.in2, arg2.requires_grad)
ctx.out = ek.atan2(ctx.in1, ctx.in2)
out_torch = ctx.out.torch()
ek.cuda_malloc_trim()
return out_torch
def atan2_(a0, a1):
if not a0.IsFloat:
raise Exception("atan2(): requires floating point operands!")
ar, sr = _check2(a0, a1)
if not a0.IsSpecial:
for i in range(sr):
ar[i] = _ek.atan2(a0[i], a1[i])
else:
raise Exception("atan2(): unsupported array type!")
return ar
def quat_to_euler(q):
q_y_2 = _ek.sqr(q.y)
sinr_cosp = 2 * _ek.fmadd(q.w, q.x, q.y * q.z)
cosr_cosp = _ek.fnmadd(2, _ek.fmadd(q.x, q.x, q_y_2), 1)
roll = _ek.atan2(sinr_cosp, cosr_cosp)
# pitch (y-axis rotation)
sinp = 2 * _ek.fmsub(q.w, q.y, q.z * q.x)
if (_ek.abs(sinp) >= 1.0):
pitch = _ek.copysign(0.5 * _ek.Pi, sinp)
else:
pitch = _ek.asin(sinp)
# yaw (z-axis rotation)
siny_cosp = 2 * _ek.fmadd(q.w, q.z, q.x * q.y)
cosy_cosp = _ek.fnmadd(2, _ek.fmadd(q.z, q.z, q_y_2), 1)
yaw = _ek.atan2(siny_cosp, cosy_cosp)
name = _ek.detail.array_name('Array', q.Type, [3], q.IsScalar)
module = _modules.get(q.__module__)
Array3f = getattr(module, name)
return Array3f(roll, pitch, yaw)
def test32_atan2(m):
x = ek.linspace(m.Float, -.8, .8, 10)
y = m.Float(ek.arange(m.Int, 10) & 1) * 1 - .5
ek.enable_grad(x, y)
z = ek.atan2(y, x)
ek.backward(z)
assert ek.allclose(
z,
m.Float(-2.58299, 2.46468, -2.29744, 2.06075, -1.74674, 1.39486,
-1.08084, 0.844154, -0.676915, 0.558599))
assert ek.allclose(
ek.grad(x),
m.Float(0.561798, -0.784732, 1.11724, -1.55709, 1.93873, -1.93873,
1.55709, -1.11724, 0.784732, -0.561798))
assert ek.allclose(
ek.grad(y),
m.Float(-0.898876, -0.976555, -0.993103, -0.83045, -0.344663, 0.344663,
0.83045, 0.993103, 0.976555, 0.898876))
def map_backward(self, p):
from mitsuba.core import Vector2f
return Vector2f(ek.atan2(y=p.y, x=p.x), -p.z)
def cartesian2spherical(w):
# Convert: Cartesian coordinates -> Spherical
theta = elevation(w) #ek.acos(w.z)
phi = ek.atan2(w.y, w.x)
return theta, phi
