def matrix_to_quat(m):
if not _ek.is_matrix_v(m):
raise Exception('Unsupported type!')
name = _ek.detail.array_name('Quaternion', m.Type, [4], m.IsScalar)
module = _modules.get(m.__module__)
Quat4f = getattr(module, name)
o = 1.0
t0 = o + m[0, 0] - m[1, 1] - m[2, 2]
q0 = Quat4f(t0, m[1, 0] + m[0, 1], m[0, 2] + m[2, 0], m[2, 1] - m[1, 2])
t1 = o - m[0, 0] + m[1, 1] - m[2, 2]
q1 = Quat4f(m[1, 0] + m[0, 1], t1, m[2, 1] + m[1, 2], m[0, 2] - m[2, 0])
t2 = o - m[0, 0] - m[1, 1] + m[2, 2]
q2 = Quat4f(m[0, 2] + m[2, 0], m[2, 1] + m[1, 2], t2, m[1, 0] - m[0, 1])
t3 = o + m[0, 0] + m[1, 1] + m[2, 2]
q3 = Quat4f(m[2, 1] - m[1, 2], m[0, 2] - m[2, 0], m[1, 0] - m[0, 1], t3)
mask0 = m[0, 0] > m[1, 1]
t01 = _ek.select(mask0, t0, t1)
q01 = _ek.select(mask0, q0, q1)
mask1 = m[0, 0] < -m[1, 1]
t23 = _ek.select(mask1, t2, t3)
q23 = _ek.select(mask1, q2, q3)
mask2 = m[2, 2] < 0.0
t0123 = _ek.select(mask2, t01, t23)
q0123 = _ek.select(mask2, q01, q23)
return q0123 * (_ek.rsqrt(t0123) * 0.5)
def trace(a):
if not _ek.is_matrix_v(a):
raise Exception('Unsupported type!')
result = a[0, 0]
for i in range(1, a.Size):
result += a[i, i]
return result
def frob(a):
if not _ek.is_matrix_v(a):
raise Exception('Unsupported type!')
result = _ek.sqr(a[0])
for i in range(1, a.Size):
value = a[i]
result = _ek.fmadd(value, value, result)
return _ek.hsum(result)
def transpose(a):
if not _ek.is_matrix_v(a):
raise Exception("Unsupported target type!")
result = type(a)()
for i in range(a.Size):
for j in range(a.Size):
result[j, i] = a[i, j]
return result
def transform_compose(s, q, t):
if not _ek.is_matrix_v(s) or not _ek.is_quaternion_v(q):
raise Exception('Unsupported type!')
name = _ek.detail.array_name('Matrix', q.Type, (4, 4), q.IsScalar)
module = _modules.get(q.__module__)
Matrix4f = getattr(module, name)
result = Matrix4f(quat_to_matrix(q, 3) @ s)
result[3] = [t[0], t[1], t[2], 1.0]
return result
def diag(a):
if _ek.is_matrix_v(a):
result = a.Value()
for i in range(a.Size):
result[i] = a[i, i]
return result
elif _ek.is_static_array_v(a):
name = _ek.detail.array_name('Matrix', a.Type, (a.Size, *a.Shape),
a.IsScalar)
module = _modules.get(a.__module__)
cls = getattr(module, name)
result = _ek.zero(cls)
for i in range(a.Size):
result[i, i] = a[i]
return result
else:
raise Exception('Unsupported type!')
def transform_decompose(a, it=10):
if not _ek.is_matrix_v(a):
raise Exception('Unsupported type!')
name = _ek.detail.array_name('Array', a.Type, [3], a.IsScalar)
module = _modules.get(a.__module__)
Array3f = getattr(module, name)
name = _ek.detail.array_name('Matrix', a.Type, (3, 3), a.IsScalar)
Matrix3f = getattr(module, name)
Q, P = polar_decomp(Matrix3f(a), it)
sign_q = det(Q)
Q = _ek.mulsign(Q, sign_q)
P = _ek.mulsign(P, sign_q)
return P, matrix_to_quat(Q), Array3f(a[3][0], a[3][1], a[3][2])
def det(m):
if not _ek.is_matrix_v(m):
raise Exception("Unsupported target type!")
if m.Size == 1:
return m[0, 0]
elif m.Size == 2:
return _ek.fmsub(m[0, 0], m[1, 1], m[0, 1] * m[1, 0])
elif m.Size == 3:
return _ek.dot(m[0], _ek.cross(m[1], m[2]))
elif m.Size == 4:
col0, col1, col2, col3 = m
col1 = _ek.shuffle((2, 3, 0, 1), col1)
col3 = _ek.shuffle((2, 3, 0, 1), col3)
temp = _ek.shuffle((1, 0, 3, 2), col2 * col3)
row0 = col1 * temp
temp = _ek.shuffle((2, 3, 0, 1), temp)
row0 = _ek.fmsub(col1, temp, row0)
temp = _ek.shuffle((1, 0, 3, 2), col1 * col2)
row0 = _ek.fmadd(col3, temp, row0)
temp = _ek.shuffle((2, 3, 0, 1), temp)
row0 = _ek.fnmadd(col3, temp, row0)
col1 = _ek.shuffle((2, 3, 0, 1), col1)
col2 = _ek.shuffle((2, 3, 0, 1), col2)
temp = _ek.shuffle((1, 0, 3, 2), col1 * col3)
row0 = _ek.fmadd(col2, temp, row0)
temp = _ek.shuffle((2, 3, 0, 1), temp)
row0 = _ek.fnmadd(col2, temp, row0)
return _ek.dot(col0, row0)
else:
raise Exception('Unsupported array size!')
def inverse_transpose(m):
if not _ek.is_matrix_v(m):
raise Exception("Unsupported target type!")
t = type(m)
if m.Size == 1:
return t(_ek.rcp(m[0, 0]))
elif m.Size == 2:
inv_det = _ek.rcp(_ek.fmsub(m[0, 0], m[1, 1], m[0, 1] * m[1, 0]))
return t(m[1, 1] * inv_det, -m[1, 0] * inv_det, -m[0, 1] * inv_det,
m[0, 0] * inv_det)
elif m.Size == 3:
col0, col1, col2 = m
row0 = _ek.cross(col1, col2)
row1 = _ek.cross(col2, col0)
row2 = _ek.cross(col0, col1)
inv_det = _ek.rcp(_ek.dot(col0, row0))
return t(row0 * inv_det, row1 * inv_det, row2 * inv_det)
elif m.Size == 4:
col0, col1, col2, col3 = m
col1 = _ek.shuffle((2, 3, 0, 1), col1)
col3 = _ek.shuffle((2, 3, 0, 1), col3)
temp = _ek.shuffle((1, 0, 3, 2), col2 * col3)
row0 = col1 * temp
row1 = col0 * temp
temp = _ek.shuffle((2, 3, 0, 1), temp)
row0 = _ek.fmsub(col1, temp, row0)
row1 = _ek.shuffle((2, 3, 0, 1), _ek.fmsub(col0, temp, row1))
temp = _ek.shuffle((1, 0, 3, 2), col1 * col2)
row0 = _ek.fmadd(col3, temp, row0)
row3 = col0 * temp
temp = _ek.shuffle((2, 3, 0, 1), temp)
row0 = _ek.fnmadd(col3, temp, row0)
row3 = _ek.shuffle((2, 3, 0, 1), _ek.fmsub(col0, temp, row3))
temp = _ek.shuffle((1, 0, 3, 2),
_ek.shuffle((2, 3, 0, 1), col1) * col3)
col2 = _ek.shuffle((2, 3, 0, 1), col2)
row0 = _ek.fmadd(col2, temp, row0)
row2 = col0 * temp
temp = _ek.shuffle((2, 3, 0, 1), temp)
row0 = _ek.fnmadd(col2, temp, row0)
row2 = _ek.shuffle((2, 3, 0, 1), _ek.fmsub(col0, temp, row2))
temp = _ek.shuffle((1, 0, 3, 2), col0 * col1)
row2 = _ek.fmadd(col3, temp, row2)
row3 = _ek.fmsub(col2, temp, row3)
temp = _ek.shuffle((2, 3, 0, 1), temp)
row2 = _ek.fmsub(col3, temp, row2)
row3 = _ek.fnmadd(col2, temp, row3)
temp = _ek.shuffle((1, 0, 3, 2), col0 * col3)
row1 = _ek.fnmadd(col2, temp, row1)
row2 = _ek.fmadd(col1, temp, row2)
temp = _ek.shuffle((2, 3, 0, 1), temp)
row1 = _ek.fmadd(col2, temp, row1)
row2 = _ek.fnmadd(col1, temp, row2)
temp = _ek.shuffle((1, 0, 3, 2), col0 * col2)
row1 = _ek.fmadd(col3, temp, row1)
row3 = _ek.fnmadd(col1, temp, row3)
temp = _ek.shuffle((2, 3, 0, 1), temp)
row1 = _ek.fnmadd(col3, temp, row1)
row3 = _ek.fmadd(col1, temp, row3)
inv_det = _ek.rcp(_ek.dot(col0, row0))
return t(row0 * inv_det, row1 * inv_det, row2 * inv_det,
row3 * inv_det)
else:
raise Exception('Unsupported array size!')