/usr/share/pyshared/VisionEgg/ThreeDeeMath.py is in python-visionegg 1.2.1-1.
This file is owned by root:root, with mode 0o644.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 | # The Vision Egg: ThreeDeeMath
#
# Copyright (C) 2001-2003 Andrew Straw.
# Copyright (C) 2008 California Institute of Technology
#
# URL: <http://www.visionegg.org/>
#
# Distributed under the terms of the GNU Lesser General Public License
# (LGPL). See LICENSE.TXT that came with this file.
"""
Vertex and matrix operations - simulate OpenGL transforms.
"""
import math
import numpy
import numpy.oldnumeric as Numeric, numpy.oldnumeric.mlab as MLab
def make_homogeneous_coord_rows(v):
"""Convert vertex (or row-wise vertices) into homogeneous coordinates."""
v = Numeric.array(v,typecode=Numeric.Float) # copy
if len(v.shape) == 1:
v = v[Numeric.NewAxis,:] # make a rank-2 array
if v.shape[1] == 3:
ws = Numeric.ones((v.shape[0],1),typecode=Numeric.Float)
v = Numeric.concatenate( (v,ws), axis=1 )
return v
def normalize_homogeneous_rows(v):
v = Numeric.asarray(v)
homog = make_homogeneous_coord_rows(v)
r = (homog/homog[:,3,Numeric.NewAxis])[:,:3]
if len(homog.shape) > len(v.shape):
r = Numeric.reshape(r,(3,))
return r
class TransformMatrix:
def __init__(self,matrix=None):
if matrix is None:
self.matrix = MLab.eye(4,typecode=Numeric.Float)
else:
self.matrix = matrix
def __make_normalized_vert3(self, x, y, z ):
mag = math.sqrt( x**2 + y**2 + z**2 )
return Numeric.array((x,y,z))/mag
def rotate(self, angle_degrees, axis_x, axis_y, axis_z ):
"""Follows the right hand rule.
I visualize the right hand rule most easily as follows:
Naturally, using your right hand, wrap it around the axis of
rotation. Your fingers now point in the direction of rotation.
"""
angleRadians = angle_degrees / 180.0 * math.pi
u = self.__make_normalized_vert3(axis_x, axis_y, axis_z )
u=-u #follow right hand rule
S = Numeric.zeros( (3,3), Numeric.Float )
S[0,1] = -u[2]
S[0,2] = u[1]
S[1,0] = u[2]
S[1,2] = -u[0]
S[2,0] = -u[1]
S[2,1] = u[0]
U = Numeric.outerproduct(u,u)
R = U + math.cos(angleRadians)*(MLab.eye(3)-U) + math.sin(angleRadians)*S
R = Numeric.concatenate( (R,Numeric.zeros( (3,1), Numeric.Float)), axis=1)
R = Numeric.concatenate( (R,Numeric.zeros( (1,4), Numeric.Float)), axis=0)
R[3,3] = 1.0
self.matrix = numpy.dot(R,self.matrix)
def translate(self, x, y, z):
T = MLab.eye(4,typecode=Numeric.Float)
T[3,0] = x
T[3,1] = y
T[3,2] = z
self.matrix = numpy.dot(T,self.matrix)
def scale(self, x, y, z):
T = MLab.eye(4,typecode=Numeric.Float)
T[0,0] = x
T[1,1] = y
T[2,2] = z
self.matrix = numpy.dot(T,self.matrix)
def get_matrix(self):
return self.matrix
def transform_vertices(self,verts):
v = Numeric.asarray(verts)
homog = make_homogeneous_coord_rows(v)
r = numpy.dot(homog,self.matrix)
if len(homog.shape) > len(v.shape):
r = Numeric.reshape(r,(4,))
return r
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