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Wed, Nov 13, 20:03

ttree_matrix_stack.py
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# Author: Andrew Jewett (jewett.aij@gmail.com)
# http://www.chem.ucsb.edu/~sheagroup
# License: 3-clause BSD License (See LICENSE.TXT)
# Copyright (c) 2012, Regents of the University of California
# All rights reserved.
from collections import deque
from array import array
from ttree_lex import *
#import sys
def MultMat(dest, A, B):
""" Multiply two matrices together. Store result in "dest".
"""
I = len(A)
J = len(B[0])
K = len(B) # or len(A[0])
for i in range(0,I):
for j in range(0,J):
dest[i][j] = 0.0
for k in range(0,K):
dest[i][j] += A[i][k] * B[k][j]
def MatToStr(M):
strs = []
for i in range(0, len(M)):
for j in range(0, len(M[i])):
strs.append(str(M[i][j])+' ')
strs.append('\n')
return(''.join(strs))
def LinTransform(dest, M, x):
""" Multiply matrix M by 1-dimensioal array (vector) "x" (from the right).
Store result in 1-dimensional array "dest".
In this function, wetreat "x" and "dest" as a column vectors.
(Not row vectors.)
"""
I = len(A)
J = len(x)
for i in range(0,I):
dest[i] = 0.0
for j in range(0,J):
dest[i] += M[i][j] * x[j]
def AffineTransform(dest, M, x):
""" This function performs an affine transformation on vector "x".
Multiply 3-dimensional vector "x" by first three columns of 3x4
matrix M. Add to this the final column of M. Store result in "dest":
dest[0] = M[0][0]*x[0] + M[0][1]*x[1] + M[0][2]*x[2] + M[0][3]
dest[1] = M[1][0]*x[0] + M[1][1]*x[1] + M[1][2]*x[2] + M[1][3]
dest[2] = M[2][0]*x[0] + M[2][1]*x[1] + M[2][2]*x[2] + M[2][3]
"""
D = len(M)
#assert(len(M[0]) == D+1)
for i in range(0,D):
dest[i] = 0.0
for j in range(0,D):
dest[i] += M[i][j] * x[j]
dest[i] += M[i][D] #(translation offset stored in final column)
def AffineCompose(dest, M2, M1):
"""
Multiplication for pairs of 3x4 matrices is technically undefined.
However what we want to do is compose two affine transformations: M1 and M2
3x4 matrices are used to define rotations/translations
x' = M[0][0]*x + M[0][1]*y + M[0][2]*z + M[0][3]
y' = M[1][0]*x + M[1][1]*y + M[1][2]*z + M[1][3]
z' = M[2][0]*x + M[2][1]*y + M[2][2]*z + M[2][3]
We want to create a new 3x4 matrix representing an affine transformation
(M2 M1), defined so that when (M2 M1) is applied to vector x, the result is
M2 (M1 x). In other words:
first, affine transformation M1 is applied to to x
then, affine transformation M2 is applied to (M1 x)
"""
D = len(M1)
#assert(len(M1[0]) == D+1)
#assert(len(M2[0]) == D+1)
for i in range(0, D):
dest[i][D] = 0.0
for j in range(0, D+1):
dest[i][j] = 0.0
for k in range(0, D):
dest[i][j] += M2[i][k] * M1[k][j]
dest[i][D] += M2[i][D]
def CopyMat(dest, source):
for i in range(0, len(source)):
for j in range(0, len(source[i])):
dest[i][j] = source[i][j]
class AffineStack(object):
"""
This class defines a matrix stack used to define compositions of affine
transformations of 3 dimensional coordinates (rotation and translation).
Affine transformations are represented using 3x4 matrices.
(Coordinates of atoms are thought of as column vectors: [[x],[y],[z]],
although they are represented internally in the more ordinary way [x,y,z].
To aplly an affine transformation to a vector, multiply the vector
by the matrix, from the left-hand side, as explained in the comments for:
AffineTransform(dest, M, x)
Note: The last column of the 3x4 matrix stores a translational offset.
This bears similarity with the original OpenGL matrix stack
http://content.gpwiki.org/index.php/OpenGL:Tutorials:Theory
(OpenGL uses 4x4 matrices. We don't need the final row of these matrices,
because in OpenGL, these rows are used for perspective transformations.)
http://en.wikipedia.org/wiki/Homogeneous_coordinates#Use_in_computer_graphics
"""
def __init__(self):
self.stack = None
self.M = None
self._tmp = None
self.Clear()
def Clear(self):
self.stack = deque([])
self.M = [[1.0, 0.0, 0.0, 0.0],
[0.0, 1.0, 0.0, 0.0],
[0.0, 0.0, 1.0, 0.0]] # (identity, initially)
self._tmp = [[1.0, 0.0, 0.0, 0.0],
[0.0, 1.0, 0.0, 0.0],
[0.0, 0.0, 1.0, 0.0]]
def PushRight(self, M):
#Push a copy of matrix self.M onto the stack
# We make no distinction between "right" and "left" here.
# All transformations are pushed onto the stack in the same way.
# (The "right" and "left" refer to whether the matrix is multiplied
# on the right of left hand side. Because not all matrices need be
# invertible, we require that matrices be popped from the stack
# in the reverse order they were pushed. This prevents the ability
# to push and pop matrices to either end of the stack in an arbitrary
# order (like append(), appendleft(), pop(), popleft()).)
self.stack.append([[self.M[i][j] for j in range(0,len(self.M[i]))]
for i in range(0,len(self.M))])
# The "Right" and "Left" refer to whether the new matrix is multiplied
# on the right or left side of the culmulatie matrix product.
AffineCompose(self._tmp, self.M, M) # Afterwards, self._tmp = self.M * M
#sys.stderr.write('DEBUG: PushLeft()\n' +
# MatToStr(self._tmp) + '\n = \n' +
# MatToStr(M) + '\n * \n' +
# MatToStr(self.M) + '\n')
CopyMat(self.M, self._tmp) # Copy self._tmp into self.M
def PushLeft(self, M):
#Push a copy of matrix self.M onto the stack
# We make no distinction between right and left here.
# All transformations are pushed onto the stack in the same way.
# (The "right" and "left" refer to whether the matrix is multiplied
# on the right of left hand side. Because not all matrices need be
# invertible, we require that matrices be popped from the stack
# in the reverse order they were pushed. This prevents the ability
# to push and pop matrices to either end of the stack in an arbitrary
# order (like append(), appendleft(), pop(), popleft()).)
self.stack.append([[self.M[i][j] for j in range(0,len(self.M[i]))]
for i in range(0,len(self.M))])
# The "Right" and "Left" refer to whether the new matrix is multiplied
# on the right or left side of the culmulatie matrix product.
AffineCompose(self._tmp, M, self.M) # Afterwards, self._tmp = M * self.M
#sys.stderr.write('DEBUG: PushLeft()\n' +
# MatToStr(self._tmp) + '\n = \n' +
# MatToStr(M) + '\n * \n' +
# MatToStr(self.M) + '\n')
CopyMat(self.M, self._tmp) # Copy self.tmp into self.M
def Pop(self):
CopyMat(self.M, self.stack.pop())
# (No need to return a matrix,"self.M",after popping.
# The caller can directly access self.M later.)
#return self.M
def PopRight(self):
self.Pop()
def PopLeft(self):
self.Pop()
def PushCommandsRight(self,
text, # text containing affine transformation commands
# The next two arguments are optional:
src_loc = OSrcLoc(), # for debugging
xcm = None): # position of center of object
"""Generate affine transformation matrices from simple text commands
(such as \"rotcm(90,0,0,1)\" and \"move(0,5.0,0)".
Chains of "rotcm", "movecm", "rot", and "move" commands
can also be strung together:
\"rotcm(90,0,0,1).move(0,5.0,0)\"
Commands ending in \"cm\" are carried out relative to center-of-mass
(average position) of the object, and consequently require
an additional argument (\"xcm\").
"""
self.PushRight(AffineStack.CommandsToMatrix(text, src_loc, xcm))
def PushCommandsLeft(self,
text, # text containing affine transformation commands
# The next two arguments are optional:
src_loc = OSrcLoc(), # for debugging
xcm = None): # position of center of object
self.PushLeft(AffineStack.CommandsToMatrix(text, src_loc, xcm))
def __len__(self):
return 1 + len(self.stack)
@staticmethod
def CommandsToMatrix(text, # text containing affine transformation commands
src_loc = OSrcLoc(), # for debugging
xcm = None): # position of center of object
Mdest=[[1.0, 0.0, 0.0, 0.0], [0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 1.0, 0.0]]
M =[[1.0, 0.0, 0.0, 0.0], [0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 1.0, 0.0]]
Mtmp =[[1.0, 0.0, 0.0, 0.0], [0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 1.0, 0.0]]
transform_commands = text.split(').')
for transform_str in transform_commands:
if transform_str.find('move(') == 0:
i_paren_close = transform_str.find(')')
if i_paren_close == -1:
i_paren_close = len(transform_str)
args = transform_str[5:i_paren_close].split(',')
if (len(args) != 3):
raise InputError('Error near '+ErrorLeader(src_loc.infile, src_loc.lineno)+':\n'
' Invalid command: \"'+transform_str+'\"\n'
' This command requires 3 numerical arguments.')
M = [[1.0, 0.0, 0.0, float(args[0])],
[0.0, 1.0, 0.0, float(args[1])],
[0.0, 0.0, 1.0, float(args[2])]]
AffineCompose(Mtmp, M, Mdest)
CopyMat(Mdest, Mtmp)
#if transform_str.find('movecm(') == 0:
# # assert(xcm != None)
# i_paren_close = transform_str.find(')')
# if i_paren_close == -1:
# i_paren_close = len(transform_str)
# args = transform_str[8:i_paren_close].split(',')
# if (len(args) != 3):
# raise InputError('Error near '+ErrorLeader(src_loc.infile, src_loc.lineno)+':\n'
# ' Invalid command: \"'+transform_str+'\"\n'
# ' This command requires 3 numerical arguments.')
# M = [[1.0, 0.0, 0.0, float(args[0])-(xcm[0])],
# [0.0, 1.0, 0.0, float(args[1])-(xcm[1])],
# [0.0, 0.0, 1.0, float(args[2])-(xcm[2])]]
# AffineCompose(Mtmp, M, Mdest)
# CopyMat(Mdest, Mtmp)
elif transform_str.find('rot(') == 0:
i_paren_close = transform_str.find(')')
if i_paren_close == -1:
i_paren_close = len(transform_str)
args = transform_str[4:i_paren_close].split(',')
center_v = None
if (len(args) == 7):
center_v = [float(args[4]), float(args[5]), float(args[6])]
elif (len(args) != 4):
raise InputError('Error near '+ErrorLeader(src_loc.infile, src_loc.lineno)+':\n'
' Invalid command: \"'+transform_str+'\"\n'
' This command requires either 4 or 7 numerical arguments. Either:\n'
' rot(angle, axisX, axisY, axiZ) or \n'
' rot(angle, axisX, axisY, axiZ, centerX, centerY, centerZ)')
M[0][3] = 0.0 #RotMatAXYZ() only modifies 3x3 submatrix of M
M[1][3] = 0.0 #The remaining final column must be zeroed by hand
M[2][3] = 0.0
RotMatAXYZ(M,
float(args[0])*math.pi/180.0,
float(args[1]),
float(args[2]),
float(args[3]))
if (center_v == None):
AffineCompose(Mtmp, M, Mdest)
CopyMat(Mdest, Mtmp)
else:
# Move "center_v" to the origin
moveCentToOrig = [[1.0, 0.0, 0.0, -center_v[0]],
[0.0, 1.0, 0.0, -center_v[1]],
[0.0, 0.0, 1.0, -center_v[2]]]
AffineCompose(Mtmp, moveCentToOrig, Mdest)
CopyMat(Mdest, Mtmp)
# Rotate the coordinates (relative to the origin)
AffineCompose(Mtmp, M, Mdest) # M is the rotation matrix
CopyMat(Mdest, Mtmp)
# Move the origin back to center_v
moveCentBack = [[1.0, 0.0, 0.0, center_v[0]],
[0.0, 1.0, 0.0, center_v[1]],
[0.0, 0.0, 1.0, center_v[2]]]
AffineCompose(Mtmp, moveCentBack, Mdest)
CopyMat(Mdest, Mtmp)
# # elif transform_str.find('rotcm(') == 0:
# # assert(xcm != None)
# # i_paren_close = transform_str.find(')')
# # if i_paren_close == -1:
# # i_paren_close = len(transform_str)
# # args = transform_str[6:i_paren_close].split(',')
# # if (len(args) != 4):
# # raise InputError('Error near '+ErrorLeader(src_loc.infile, src_loc.lineno)+':\n'
# # ' Invalid command: \"'+transform_str+'\"\n'
# # ' This command requires 4 numerical arguments.')
# #
# # moveCMtoOrig = [[1.0, 0.0, 0.0, -xcm[0]],
# # [0.0, 1.0, 0.0, -xcm[1]],
# # [0.0, 0.0, 1.0, -xcm[2]]]
# # AffineCompose(Mtmp, moveCMtoOrig, Mdest)
# # CopyMat(Mdest, Mtmp)
# # M[0][3] = 0.0#RotMatAXYZ() only modifies 3x3 submatrix of M
# # M[1][3] = 0.0#The remaining final column must be zeroed by hand
# # M[2][3] = 0.0
# # RotMatAXYZ(M,
# # float(args[0])*math.pi/180.0,
# # float(args[1]),
# # float(args[2]),
# # float(args[3]))
# # AffineCompose(Mtmp, M, Mdest)
# # CopyMat(Mdest, Mtmp)
# # moveCmBack = [[1.0, 0.0, 0.0, xcm[0]],
# # [0.0, 1.0, 0.0, xcm[1]],
# # [0.0, 0.0, 1.0, xcm[2]]]
# # AffineCompose(Mtmp, moveCmBack, Mdest)
# # CopyMat(Mdest, Mtmp)
elif transform_str.find('rotvv(') == 0:
i_paren_close = transform_str.find(')')
if i_paren_close == -1:
i_paren_close = len(transform_str)
args = transform_str[6:i_paren_close].split(',')
center_v = None
if (len(args) == 9):
center_v = [float(args[6]), float(args[7]), float(args[8])]
elif (len(args) != 6):
raise InputError('Error near '+ErrorLeader(src_loc.infile, src_loc.lineno)+':\n'
' Invalid command: \"'+transform_str+'\"\n'
' This command requires either 6 or 9 numerical arguments. Either:\n'
' rotvv(Xold,Yold,Zold,Xnew,Ynew,Znew) or \n'
' rotvv(Xold,Yold,Zold,Xnew,Ynew,Znew,centerX,centerY,centerZ)')
M[0][3] = 0.0 #RotMatXYZXYZ() only modifies 3x3 submatrix of M
M[1][3] = 0.0 #The remaining final column must be zeroed by hand
M[2][3] = 0.0
RotMatXYZXYZ(M,
float(args[0]),
float(args[1]),
float(args[2]),
float(args[3]),
float(args[4]),
float(args[5]))
if (center_v == None):
AffineCompose(Mtmp, M, Mdest)
CopyMat(Mdest, Mtmp)
else:
# Move "center_v" to the origin
moveCentToOrig = [[1.0, 0.0, 0.0, -center_v[0]],
[0.0, 1.0, 0.0, -center_v[1]],
[0.0, 0.0, 1.0, -center_v[2]]]
AffineCompose(Mtmp, moveCentToOrig, Mdest)
CopyMat(Mdest, Mtmp)
# Rotate the coordinates (relative to the origin)
AffineCompose(Mtmp, M, Mdest) # M is the rotation matrix
CopyMat(Mdest, Mtmp)
# Move the origin back to center_v
moveCentBack = [[1.0, 0.0, 0.0, center_v[0]],
[0.0, 1.0, 0.0, center_v[1]],
[0.0, 0.0, 1.0, center_v[2]]]
AffineCompose(Mtmp, moveCentBack, Mdest)
CopyMat(Mdest, Mtmp)
elif transform_str.find('scale(') == 0:
i_paren_close = transform_str.find(')')
if i_paren_close == -1:
i_paren_close = len(transform_str)
args = transform_str[6:i_paren_close].split(',')
if (len(args) == 1):
scale_v = [float(args[0]), float(args[0]), float(args[0])]
center_v = [0.0, 0.0, 0.0]
elif (len(args) == 3):
scale_v = [float(args[0]), float(args[1]), float(args[2])]
center_v = [0.0, 0.0, 0.0]
elif (len(args) == 4):
scale_v = [float(args[0]), float(args[0]), float(args[0])]
center_v = [float(args[1]), float(args[2]), float(args[3])]
elif (len(args) == 6):
scale_v = [float(args[0]), float(args[1]), float(args[2])]
center_v = [float(args[3]), float(args[4]), float(args[5])]
else:
raise InputError('Error near '+ErrorLeader(src_loc.infile, src_loc.lineno)+':\n'
' Invalid command: \"'+transform_str+'\"\n'
' This command requires either 1, 3, 4, or 6 numerical arguments. Either:\n'
' scale(ratio), or \n'
' scale(ratioX, ratioY, ratioZ),\n'
' scale(ratio, centerX, centerY, centerZ), or\n'
' scale(ratioX, ratioY, ratioZ, centerX, centerY, centerZ)')
ScaleMat(M, scale_v)
# Now worry about translation:
for d in range(0, 3):
M[d][3] = center_v[d] * (1.0 - scale_v[d])
AffineCompose(Mtmp, M, Mdest)
CopyMat(Mdest, Mtmp)
# # elif transform_str.find('scalecm(') == 0:
# # assert(xcm != None)
# # i_paren_close = transform_str.find(')')
# # if i_paren_close == -1:
# # i_paren_close = len(transform_str)
# # args = transform_str[8:i_paren_close].split(',')
# #
# # moveCMtoOrig = [[1.0, 0.0, 0.0, -xcm[0]],
# # [0.0, 1.0, 0.0, -xcm[1]],
# # [0.0, 0.0, 1.0, -xcm[2]]]
# # AffineCompose(Mtmp, moveCMtoOrig, Mdest)
# # CopyMat(Mdest, Mtmp)
# #
# # M[0][3] = 0.0 #ScaleMat() only modifies 3x3 submatrix of M
# # M[1][3] = 0.0 #The remaining final column must be zeroed by hand
# # M[2][3] = 0.0
# # if (len(args) == 1):
# # ScaleMat(M, args[0])
# # elif (len(args) == 3):
# # ScaleMat(M, args)
# # else:
# # raise InputError('Error near '+ErrorLeader(src_loc.infile, src_loc.lineno)+':\n'
# # ' Invalid command: \"'+transform_str+'\"\n'
# # ' This command requires either 1 or 3 numerical arguments.')
# #
# # AffineCompose(Mtmp, M, Mdest)
# # CopyMat(Mdest, Mtmp)
# # moveCmBack = [[1.0, 0.0, 0.0, xcm[0]],
# # [0.0, 1.0, 0.0, xcm[1]],
# # [0.0, 0.0, 1.0, xcm[2]]]
# # AffineCompose(Mtmp, moveCmBack, Mdest)
# # CopyMat(Mdest, Mtmp)
else:
raise InputError('Error near '+ErrorLeader(src_loc.infile, src_loc.lineno)+':\n'
' Unknown transformation command: \"'+transform_str+'\"\n')
return Mdest
class MultiAffineStack(object):
def __init__(self, which_stack=None):
self.tot_stack = None
self.stack_lookup = None
self.stack_keys = None
self.stacks = None
self.M = None
self.error_if_substack_empty = False
self.Clear()
def Clear(self):
self.tot_stack = AffineStack()
self.stack_lookup = {}
self.stack_keys = deque([])
self.stacks = deque([])
self.M = self.tot_stack.M
self.error_if_substack_empty = False
def _Update(self):
self.tot_stack.Clear()
self.M = self.tot_stack.M
assert(len(self.stacks) > 0)
for stack in self.stacks:
self.tot_stack.PushRight(stack.M)
def PushStack(self, which_stack):
stack = AffineStack()
self.stack_keys.append(which_stack)
self.stack_lookup[which_stack] = stack
self.stacks.append(stack)
self.tot_stack.PushRight(stack.M)
def PopStack(self):
assert(len(self.stacks) > 0)
self.tot_stack.PopRight()
which_stack = self.stack_keys.pop()
del self.stack_lookup[which_stack]
self.stacks.pop()
def Push(self, M, which_stack=None, right_not_left = True):
if len(self.stacks) == 0:
self.PushStack(which_stack)
if which_stack == None:
stack = self.stacks[-1]
if right_not_left:
stack.PushRight(M) # This should copy the matrix M into stack.M
else:
stack.PushLeft(M)
else:
stack = self.stack_lookup[which_stack]
if right_not_left:
stack.PushRight(M)
else:
stack.PushLeft(M)
if stack == self.stacks[-1]:
self.tot_stack.PopRight() #Replace the last matrix on self.tot_stack
# Note: Always use tot_stack.PopRight (even if right_not_left=False)
self.tot_stack.PushRight(stack.M) # with the the updated version.
# Note: We could call self._Update(M) here, but that is slower.
else:
self._Update()
def PushRight(self, M, which_stack=None):
self.Push(M, which_stack, right_not_left=True)
def PushLeft(self, M, which_stack=None):
self.Push(M, which_stack, right_not_left=False)
def PushCommandsRight(self,
text, # text containing affine transformation commands
# The next two arguments are optional:
src_loc = OSrcLoc(), # for debugging
xcm = None,
which_stack=None): # position of center of object
"""Generate affine transformation matrices from simple text commands
(such as \"rotcm(90,0,0,1)\" and \"move(0,5.0,0)".
Chains of "rotcm", "movecm", "rot", and "move" commands
can also be strung together:
\"rotcm(90,0,0,1).move(0,5.0,0)\"
Commands ending in \"cm\" are carried out relative to center-of-mass
(average position) of the object, and consequently require
an additional argument (\"xcm\").
"""
self.PushRight(AffineStack.CommandsToMatrix(text, src_loc, xcm),
which_stack)
def PushCommandsLeft(self,
text, # text containing affine transformation commands
# The next two arguments are optional:
src_loc = OSrcLoc(), # for debugging
xcm = None, # position of center of object
which_stack = None):
self.PushLeft(AffineStack.CommandsToMatrix(text, src_loc, xcm),
which_stack)
def Pop(self, which_stack=None, right_not_left=True):
#empty_stack_error = False
if which_stack == None:
stack = self.stacks[-1]
if len(stack) >= 1:
if right_not_left:
stack.PopRight()
else:
stack.PopLeft()
# Note: We could call self._Update(M) here, but that is slower
self.tot_stack.PopRight() #Replace the last matrix on self.tot_stack
# Note: Always use tot_stack.PopRight (even if right_not_left=False)
self.tot_stack.PushRight(stack.M) # with the the updated version.
else:
assert(False)
# OPTIONAL CODE BELOW AUTOMATICALLY INVOKES self.PopStack() WHEN
# THE stacks[-1].stack IS EMPTY. PROBABLY DOES NOT WORK. IGNORE
# if (not self.error_if_substack_empty):
# if right_not_left:
# assert(len(self.stacks) > 0)
# self.PopStack()
# else:
# assert(False)
# else:
# empty_stack_error = True
else:
stack = self.stack_lookup[which_stack]
if len(stack) > 1:
if right_not_left:
stack.PopRight()
else:
stack.PopLeft()
self._Update()
else:
assert(False)
#empty_stack_error = True
def PopRight(self, which_stack=None):
self.Pop(which_stack, right_not_left=True)
def PopLeft(self, which_stack=None):
self.Pop(which_stack, right_not_left=True)
import math
def ScaleMat(dest, scale):
for i in range(0, len(dest)):
for j in range(0, len(dest[i])):
dest[i][j] = 0.0
if ((type(scale) is float) or (type(scale) is int)):
for i in range(0, len(dest)):
dest[i][i] = scale
else:
for i in range(0, len(dest)):
dest[i][i] = scale[i]
def RotMatAXYZ(dest, angle, axis_x, axis_y, axis_z):
r = math.sqrt(axis_x*axis_x + axis_y*axis_y + axis_z*axis_z)
X = 1.0
Y = 0.0
Z = 0.0
if r > 0.0: # check for non-sensical input
X = axis_x / r
Y = axis_y / r
Z = axis_z / r
else:
angle = 0.0
#angle *= math.pi/180.0 # "angle" is assumed to be in degrees
# on second thought, let the caller worry about angle units.
c = math.cos(angle)
s = math.sin(angle)
dest[0][0] = X*X*(1-c) + c
dest[1][1] = Y*Y*(1-c) + c
dest[2][2] = Z*Z*(1-c) + c
dest[0][1] = X*Y*(1-c) - Z*s
dest[0][2] = X*Z*(1-c) + Y*s
dest[1][0] = Y*X*(1-c) + Z*s
dest[2][0] = Z*X*(1-c) - Y*s
dest[1][2] = Y*Z*(1-c) - X*s
dest[2][1] = Z*Y*(1-c) + X*s
# formula from these sources:
# http://inside.mines.edu/~gmurray/ArbitraryAxisRotation/
# also check
# http://www.manpagez.com/man/3/glRotate/
# some pdb test commands:
# from lttree_matrixstack import *
# r = [[1.0,0.0,0.0], [0.0,1.0,0.0], [0.0,0.0,1.0]]
# RotMatAXYZ(r, 90.0, 0.0, 0.0, 1.0)
def CrossProd(dest, A, B):
dest[0] = (A[1]*B[2] - B[1]*A[2])
dest[1] = (A[2]*B[0] - B[2]*A[0])
dest[2] = (A[0]*B[1] - B[0]*A[1])
def DotProd(A, B):
c = 0.0
for d in range(0, len(A)):
c += A[d]*B[d]
return c
def Length(A):
L = 0.0
for x in A:
L += x*x
return math.sqrt(L)
def Normalize(dest, source):
assert(len(dest) == len(source))
L = Length(source)
for d in range(0, len(source)):
dest[d] = source[d] / L
def RotMatXYZXYZ(dest,
xold, yold, zold,
xnew, ynew, znew):
A = [xold, yold, zold]
B = [xnew, ynew, znew]
axis = [0.0, 0.0, 0.0]
CrossProd(axis, A, B)
La = Length(A)
Lb = Length(B)
Lc = Length(axis)
sinAng = Lc / (La*Lb)
cosAng = DotProd(A,B) / (La*Lb)
if Lc > 0.0:
Normalize(axis, axis)
angle = math.atan2(sinAng, cosAng)
else:
axis = [1.0, 0.0, 0.0]
angle = 0.0
RotMatAXYZ(dest, angle, axis[0], axis[1], axis[2])

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