126126 c = sy*sin(alpha);
127127 d = sy*cos(alpha);
128128
129+ The affine transformation can be accomplished for row vectors with a
130+ single matrix multiplication
131+ X_new = X_old * M
132+ where
133+ M = [ a b 0
134+ c d 0
135+ tx ty 1]
136+ and each X is the row vector [x, y, 1]. Hence M is
137+ the transpose of the matrix representation given in
138+ http://en.wikipedia.org/wiki/Affine_transformation,
139+ which is for the more usual column-vector representation
140+ of the position.)
141+
142+
143+
129144From a user perspective, the most important Tranformation methods are
130145
131146All transformations
233248and attributes to Bbox and/or putting them elsewhere in this module.
234249"""
235250from __future__import division
236-
237251import math
238- from _transforms import Value ,Point ,Interval ,Bbox ,Affine
239- from _transforms import IDENTITY ,LOG10 ,POLAR ,Func ,FuncXY
240- from _transforms import SeparableTransformation ,NonseparableTransformation
241- from matplotlib .numerix import array ,Float
242- from matplotlib .numerix .linear_algebra import inverse
252+ import numpy as npy
253+
254+ from matplotlib ._transforms import Value ,Point ,Interval ,Bbox ,Affine
255+ from matplotlib ._transforms import IDENTITY ,LOG10 ,POLAR ,Func ,FuncXY
256+ from matplotlib ._transforms import SeparableTransformation
257+ from matplotlib ._transforms import NonseparableTransformation
243258
244259def nonsingular (vmin ,vmax ,expander = 0.001 ,tiny = 1e-15 ,increasing = True ):
245260'''
@@ -249,7 +264,8 @@ def nonsingular(vmin, vmax, expander=0.001, tiny=1e-15, increasing=True):
249264 the maximum absolute value.
250265
251266 If they are too close, each will be moved by the 'expander'.
252- If 'increasing' is True and vmin > vmax, they will be swapped.
267+ If 'increasing' is True and vmin > vmax, they will be swapped,
268+ regardless of whether they are too close.
253269 '''
254270swapped = False
255271if vmax < vmin :
@@ -372,19 +388,13 @@ def lbwh_to_bbox(l,b,w,h):
372388
373389def invert_vec6 (v ):
374390"""
375- v is a,b,c,d,tx,ty vec6 repr of a matrix
376- [ a b 0
377- c d 0
378- tx ty 1]
379-
391+ v is a,b,c,d,tx,ty vec6 repr of an affine transformation.
380392 Return the inverse of v as a vec6
381393 """
382- M = array ([ [a ,b ,0 ], [c ,d ,0 ], [tx ,ty ,1 ]],typecode = Float )
383- Mi = inverse (M )
384- a ,b = M [0 ,0 :2 ]
385- c ,d = M [1 ,0 :2 ]
386- tx ,ty = M [2 ,0 :2 ]
387- return a ,b ,c ,d ,tx ,ty
394+ a ,b ,c ,d ,tx ,ty = v
395+ M = npy .array ([ [a ,b ,0 ], [c ,d ,0 ], [tx ,ty ,1 ]],dtype = npy .float64 )
396+ Mi = npy .linalg .inv (M )
397+ return Mi [:,:2 ].ravel ()
388398
389399def multiply_affines (v1 ,v2 ):
390400"""