/
transformation.pyx
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transformation.pyx
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#cython: cdivision=True
'''
Transformation
==============
This module contain a Matrix class, used for our Graphics calculation. We are
supporting:
- rotation, translation, scaling matrix
- multiply matrix
- create clip matrix (with or without perspective)
- transform 3d touch on a matrix
'''
__all__ = ('Matrix', )
cdef extern from "math.h":
double sqrt(double x) nogil
double sin(double x) nogil
double cos(double x) nogil
double fabs(double x) nogil
cdef extern from "string.h":
void *memcpy(void *dest, void *src, int n)
void *memset(void *s, int c, int n)
cdef double _EPS = 8.8817841970012523e-16
cdef class Matrix:
'''
Optimized matrix class for OpenGL::
>>> from kivy.graphics.transformation import Matrix
>>> m = Matrix()
>>> print m
[[ 1.000000 0.000000 0.000000 0.000000 ]
[ 0.000000 1.000000 0.000000 0.000000 ]
[ 0.000000 0.000000 1.000000 0.000000 ]
[ 0.000000 0.000000 0.000000 1.000000 ]]
[ 0 1 2 3]
[ 4 5 6 7]
[ 8 9 10 11]
[ 12 13 14 15]
'''
def __cinit__(self):
memset(self.mat, 0, sizeof(matrix_t))
def __init__(self):
self.identity()
cpdef Matrix rotate(Matrix self, double angle, double x, double y, double z):
'''Rotate the matrix with the angle, around the axis (x, y, z)
'''
cdef double d, c, s, co, ox, oy, oz, f1, f2, f3, f4, f5, f6, f7, f8, f9
with nogil:
d = sqrt(x * x + y * y + z * z)
if (d != 1.0):
x /= d
y /= d
z /= d
c = cos(angle)
s = sin(angle)
co = 1.0 - c
ox = x * co
oy = y * co
oz = z * co
f1 = x * ox + c
f5 = y * oy + c
f9 = z * oz + c
d = z * s
f2 = x * oy - d
f4 = y * ox + d
d = y * s
f3 = x * oz + d
f7 = z * ox - d
d = x * s
f6 = y * oz - d
f8 = z * oy + d
ox = self.mat[0]
oy = self.mat[1]
oz = self.mat[2]
self.mat[0] = ox * f1 + oy * f2 + oz * f3
self.mat[1] = ox * f4 + oy * f5 + oz * f6
self.mat[2] = ox * f7 + oy * f8 + oz * f9
ox = self.mat[4]
oy = self.mat[5]
oz = self.mat[6]
self.mat[4] = ox * f1 + oy * f2 + oz * f3
self.mat[5] = ox * f4 + oy * f5 + oz * f6
self.mat[6] = ox * f7 + oy * f8 + oz * f9
ox = self.mat[ 8]
oy = self.mat[ 9]
oz = self.mat[10]
self.mat[ 8] = ox * f1 + oy * f2 + oz * f3
self.mat[ 9] = ox * f4 + oy * f5 + oz * f6
self.mat[10] = ox * f7 + oy * f8 + oz * f9
return self
cpdef Matrix scale(Matrix self, double x, double y, double z):
'''Scale the matrix current Matrix (inplace).
'''
with nogil:
self.mat[ 0] *= x;
self.mat[ 5] *= y;
self.mat[10] *= z;
return self
cpdef Matrix translate(Matrix self, double x, double y, double z):
'''Translate the matrix
'''
with nogil:
self.mat[12] += x
self.mat[13] += y
self.mat[14] += z
return self
cpdef Matrix view_clip(Matrix self, double left, double right, double bottom, double top,
double near, double far, int perspective):
'''Create a clip matrix (inplace)
'''
cdef double t
if left >= right or bottom >= top or near >= far:
raise ValueError('invalid frustrum')
if perspective:
raise Exception('not tested')
'''
# original code
if near <= _EPS:
raise ValueError('invalid frustrum: near <= 0')
'''
with nogil:
if perspective:
t = 2.0 * near
self.mat[0] = -t/(right-left)
self.mat[4] = 0.0
self.mat[8] = (right+left)/(right-left)
self.mat[12] = 0.0
self.mat[1] = 0.0
self.mat[5] = -t/(top-bottom)
self.mat[9] = (top+bottom)/(top-bottom)
self.mat[13] = 0.0
self.mat[2] = 0.0
self.mat[6] = 0.0
self.mat[10] = -(far+near)/(far-near)
self.mat[14] = t*far/(far-near)
self.mat[3] = 0.0
self.mat[7] = 0.0
self.mat[11] = -1.0
self.mat[15] = 0.0
else:
#(0, 4, 8, 12, 1, 5, 9, 13, 2, 6, 10, 14, 3, 7, 11, 15)
self.mat[0] = 2.0/(right-left)
self.mat[4] = 0.0
self.mat[8] = 0.0
self.mat[12] = (right+left)/(left-right)
self.mat[1] = 0.0
self.mat[5] = 2.0/(top-bottom)
self.mat[9] = 0.0
self.mat[13] = (top+bottom)/(bottom-top)
self.mat[2] = 0.0
self.mat[6] = 0.0
self.mat[10] = 2.0/(far-near)
self.mat[14] = (far+near)/(near-far)
self.mat[3] = 0.0
self.mat[7] = 0.0
self.mat[11] = 0.0
self.mat[15] = 1.0
return self
cpdef tuple transform_point(Matrix self, double x, double y, double z):
cdef double tx, ty, tz
with nogil:
tx = x * self.mat[0] + y * self.mat[4] + z * self.mat[ 8] + self.mat[12];
ty = x * self.mat[1] + y * self.mat[5] + z * self.mat[ 9] + self.mat[13];
tz = x * self.mat[2] + y * self.mat[6] + z * self.mat[10] + self.mat[14];
return (tx, ty, tz)
cpdef Matrix identity(self):
'''Reset matrix to identity matrix (inplace)
'''
cdef double *m = self.mat
with nogil:
m[0] = m[5] = m[10] = m[15] = 1
m[1] = m[2] = m[3] = m[4] = m[6] = m[7] = \
m[8] = m[9] = m[11] = m[12] = m[13] = m[14] = 0
return self
cpdef Matrix inverse(self):
'''Return the inverted matrix
'''
cdef Matrix mr = Matrix()
cdef double *m = self.mat, *r = mr.mat
cdef double det
with nogil:
det = m[0] * (m[5] * m[10] - m[9] * m[6]) \
- m[4] * (m[1] * m[10] - m[9] * m[2]) \
+ m[8] * (m[1] * m[ 6] - m[5] * m[2])
if det == 0:
return
with nogil:
det = 1.0 / det
r[ 0] = det * (m[5] * m[10] - m[9] * m[6])
r[ 4] = - det * (m[4] * m[10] - m[8] * m[6])
r[ 8] = det * (m[4] * m[ 9] - m[8] * m[5])
r[ 1] = - det * (m[1] * m[10] - m[9] * m[2])
r[ 5] = det * (m[0] * m[10] - m[8] * m[2])
r[ 9] = - det * (m[0] * m[ 9] - m[8] * m[1])
r[ 2] = det * (m[1] * m[ 6] - m[5] * m[2])
r[ 6] = - det * (m[0] * m[ 6] - m[4] * m[2])
r[10] = det * (m[0] * m[ 5] - m[4] * m[1])
r[ 3] = 0
r[ 7] = 0
r[11] = 0
r[15] = 1
r[12] = -(m[12] * r[0] + m[13] * r[4] + m[14] * r[ 8])
r[13] = -(m[12] * r[1] + m[13] * r[5] + m[14] * r[ 9])
r[14] = -(m[12] * r[2] + m[13] * r[6] + m[14] * r[10])
return mr
cpdef Matrix multiply(Matrix mb, Matrix ma):
'''Multiply the given matrix with self (from the left).
I.e., we premultiply the given matrix to the current matrix and return
the result (not inplace)::
m.multiply(n) -> n * m
'''
cdef Matrix mr = Matrix()
cdef double *a = ma.mat, *b = mb.mat, *r = mr.mat
with nogil:
r[ 0] = a[ 0] * b[0] + a[ 1] * b[4] + a[ 2] * b[ 8]
r[ 4] = a[ 4] * b[0] + a[ 5] * b[4] + a[ 6] * b[ 8]
r[ 8] = a[ 8] * b[0] + a[ 9] * b[4] + a[10] * b[ 8]
r[12] = a[12] * b[0] + a[13] * b[4] + a[14] * b[ 8] + b[12]
r[ 1] = a[ 0] * b[1] + a[ 1] * b[5] + a[ 2] * b[ 9]
r[ 5] = a[ 4] * b[1] + a[ 5] * b[5] + a[ 6] * b[ 9]
r[ 9] = a[ 8] * b[1] + a[ 9] * b[5] + a[10] * b[ 9]
r[13] = a[12] * b[1] + a[13] * b[5] + a[14] * b[ 9] + b[13]
r[ 2] = a[ 0] * b[2] + a[ 1] * b[6] + a[ 2] * b[10]
r[ 6] = a[ 4] * b[2] + a[ 5] * b[6] + a[ 6] * b[10]
r[10] = a[ 8] * b[2] + a[ 9] * b[6] + a[10] * b[10]
r[14] = a[12] * b[2] + a[13] * b[6] + a[14] * b[10] + b[14]
r[ 3] = 0
r[ 7] = 0
r[11] = 0
r[15] = 1
return mr
def __str__(self):
cdef double *m = self.mat
return '[[ %f %f %f %f ]\n[ %f %f %f %f ]\n' \
'[ %f %f %f %f ]\n[ %f %f %f %f ]]' % (
m[0], m[1], m[2], m[3],
m[4], m[5], m[6], m[7],
m[8], m[9], m[10], m[11],
m[12], m[13], m[14], m[15])