pgfplots

git-svn-id: svn://tug.org/texlive/trunk@29531 c570f23f-e606-0410-a88d-b1316a301751

1 files changed, 347 insertions, 114 deletions

diff --git a/Master/texmf-dist/tex/generic/pgfplots/libs/tikzlibrarypgfplots.patchplots.code.tex b/Master/texmf-dist/tex/generic/pgfplots/libs/tikzlibrarypgfplots.patchplots.code.tex
index 933f48854d2..9e885f380ba 100644
--- a/Master/texmf-dist/tex/generic/pgfplots/libs/tikzlibrarypgfplots.patchplots.code.tex
+++ b/Master/texmf-dist/tex/generic/pgfplots/libs/tikzlibrarypgfplots.patchplots.code.tex
@@ -64,10 +64,8 @@
 % segmment, <right> the function value at the right end, and <middle>
 % the function value in the middle of the spline segment.
 \pgfplotsdeclarepatchclass{quadratic spline}{%
-	allow matrix=0,
-	uses view depth=0,
-	get dimension=1,
-	supports global path=1,
+	get dimension=\def\pgfplotsretval{1},
+	supports global path=\def\pgfplotsretval{1},
 	new=\def\pgfplotspatchclass@qspline@no{A},
 	set next vertex={%
 		% EXPECTED ORDERING: first 2 corners, then 1 mid nodes
@@ -148,7 +146,7 @@
 		\pgfplotsplothandlermesh@setlastpoint{\expandafter\pgfplotspointpatchvertex\PC\endvertex}%
 		\endgroup
 	},
-	triangulate class=line,
+	triangulate class=\def\pgfplotsretval{line},
 	triangulate={%
 		\let\pgfplotsplothandlermesh@patchclass@=\pgfplotsplothandlermesh@patchclass
 		\def\pgfplotsplothandlermesh@patchclass{line}%
@@ -185,14 +183,12 @@
 		%
 	},%
 	get pdf shading type=0,
-	get num vertices=3,
+	get num vertices=\def\pgfplotsretval{3},
 }%
 
 \pgfplotsdeclarepatchclass{cubic spline}{%
-	allow matrix=0,
-	uses view depth=0,
-	get dimension=1,
-	supports global path=1,
+	get dimension=\def\pgfplotsretval{1},
+	supports global path=\def\pgfplotsretval{1},
 	new=\def\pgfplotspatchclass@cspline@no{A},
 	set next vertex={%
 		% EXPECTED ORDERING: first 2 corners, then 1 mid nodes
@@ -256,7 +252,7 @@
 			{\pgfplotspatchclass@cspline@B}%
 		\pgfplotsplothandlermesh@setlastpoint{\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@cspline@B\endvertex}%
 	},
-	triangulate class=line,
+	triangulate class=\def\pgfplotsretval{line},
 	triangulate={%
 		\let\pgfplotsplothandlermesh@patchclass@=\pgfplotsplothandlermesh@patchclass
 		\def\pgfplotsplothandlermesh@patchclass{line}%
@@ -347,7 +343,7 @@
 		#1%
 	},
 	get pdf shading type=0,
-	get num vertices=4,
+	get num vertices=\def\pgfplotsretval{4},
 }%
 
 \def\pgfplotspathcubicfrominterpolation#1#2#3#4{%
@@ -407,8 +403,7 @@
 % A 3-point interpolatory patch which draws quadratic polynomial
 % splines (functions f(x), x 1d).
 \pgfplotsdeclarepatchclass{triangle quadr}{%
-	allow matrix=0,
-	uses view depth=1,
+	uses view depth=\def\pgfplotsretval{1},% used by the shader: we reorder corners.
 	new=\def\pgfplotspatchclass@qtri@no{A}\let\pgfplotspatchclass@qtrie@AB\relax,
 	set next vertex={%
 		% EXPECTED ORDERING: first 3 corners, then 3 mid nodes.
@@ -474,6 +469,11 @@
 		\expandafter\pgfplotspatchvertex\pgfplotspatchclass@qtri@E\endvertex #1%
 		\expandafter\pgfplotspatchvertex\pgfplotspatchclass@qtri@F\endvertex #1%
 	},
+	foreach cdata vertex={%
+		\expandafter\pgfplotspatchvertex\pgfplotspatchclass@qtri@A\endvertex #1%
+		\expandafter\pgfplotspatchvertex\pgfplotspatchclass@qtri@B\endvertex #1%
+		\expandafter\pgfplotspatchvertex\pgfplotspatchclass@qtri@C\endvertex #1%
+	},
 	fill path={%
 		\begingroup
 		% Draw the patch boundary using three bezier curves.
@@ -811,7 +811,8 @@
 		%
 	},%
 	get pdf shading type=6,
-	get num vertices=6,
+	get num vertices=\def\pgfplotsretval{6},
+	get num cdata vertices=\def\pgfplotsretval{3},
 }%
 
 
@@ -902,7 +903,7 @@
 
 % bilinear is the same as 'rectangle', but it uses a different shader.
 \pgfplotsdeclarepatchclass{bilinear}{%
-	allow matrix=1,
+	allow matrix=\def\pgfplotsretval{1},
 	new=\def\pgfplotspatchclass@rect@no{0},
 	set next vertex={%
 		\ifcase\pgfplotspatchclass@rect@no\relax
@@ -1004,29 +1005,12 @@
 		\pgfplotscoordmath{meta}{parsenumber}{0.25}%
 		\let\pgfplots@loc@scale=\pgfmathresult
 		%
-		\pgf@xa=0pt
-		\pgf@ya=0pt
-		\pgf@yb=0pt
-		\pgfplotscoordmath{meta}{zero}%
-		\def\pgfplots@loc@accum@mean{%
-			\advance\pgf@xa by\pgfplotspatchvertexx\relax
-			\advance\pgf@ya by\pgfplotspatchvertexy\relax
-			\pgfplotscoordmath{meta}{op}{add}{{\pgfmathresult}{\pgfplotspatchvertexmeta}}%
-			\ifx\pgfplotspatchvertexdepth\pgfutil@empty
-			\else
-				\advance\pgf@yb by\pgfplotspatchvertexdepth pt\relax
-			\fi
-		}%
-		\expandafter\pgfplotspatchvertex\pgfplotspatchclass@rect@A\endvertex \pgfplots@loc@accum@mean%
-		\expandafter\pgfplotspatchvertex\pgfplotspatchclass@rect@B\endvertex \pgfplots@loc@accum@mean%
-		\expandafter\pgfplotspatchvertex\pgfplotspatchclass@rect@C\endvertex \pgfplots@loc@accum@mean%
-		\expandafter\pgfplotspatchvertex\pgfplotspatchclass@rect@D\endvertex \pgfplots@loc@accum@mean%
-		%
-		\divide\pgf@xa by4
-		\divide\pgf@ya by4
-		\divide\pgf@yb by4
-		\pgfplotscoordmath{meta}{op}{multiply}{{\pgfmathresult}{\pgfplots@loc@scale}}%
-		\edef\pgfplotspatchclass@rect@M{{\the\pgf@xa}{\the\pgf@ya}{\pgfmathresult}\ifx\pgfplotspatchvertexdepth\pgfutil@empty\else \pgf@sys@tonumber\pgf@yb\fi:}%
+		\pgfplotspatchvertexaccumstart
+		\expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@rect@A\endvertex\times{0.25}%
+		\expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@rect@B\endvertex\times{0.25}%
+		\expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@rect@C\endvertex\times{0.25}%
+		\expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@rect@D\endvertex\times{0.25}%
+		\pgfplotspatchvertexfinish\pgfplotspatchclass@rect@M
 		%
 		\let\pgfplotsplothandlermesh@patchclass@=\pgfplotsplothandlermesh@patchclass
 		\def\pgfplotsplothandlermesh@patchclass{triangle}%
@@ -1062,7 +1046,7 @@
 	serialize except vertices=\let\pgfplotsretval\pgfutil@empty,%
 	deserialize except vertices=,
 	get pdf shading type=6,
-	get num vertices=4,
+	get num vertices=\def\pgfplotsretval{4},
 }%
 
 \pgfplotsdeclarepatchclass{rectangle}{%
@@ -1202,7 +1186,7 @@
 	serialize except vertices=\let\pgfplotsretval\pgfutil@empty,%
 	deserialize except vertices=,
 	get pdf shading type=4,
-	get num vertices=\pgfkeysvalueof{/pgfplots/vertex count},
+	get num vertices=\def\pgfplotsretval{\pgfkeysvalueof{/pgfplots/vertex count}},
 }%
 \def\pgfplotspatchclass@poly@checkcount{%
 	\ifnum\pgfkeysvalueof{/pgfplots/vertex count}>0
@@ -1271,7 +1255,6 @@
 %   i*(1 - xi^2) (1 - eta^2)
 % here, a,b,...,i are the 9 nodes.
 \pgfplotsdeclarepatchclass{biquadratic}{%
-	allow matrix=0,
 	new=\def\pgfplotspatchclass@biquad@no{A}\let\pgfplotspatchclass@biquade@AB\relax,
 	set next vertex={%
 		% defines \pgfplotspatchclass@biquad@A ... \pgfplotspatchclass@biquad@I (9 points)
@@ -1325,6 +1308,12 @@
 		\expandafter\pgfplotspatchvertex\pgfplotspatchclass@biquad@H\endvertex #1%
 		\expandafter\pgfplotspatchvertex\pgfplotspatchclass@biquad@I\endvertex #1%
 	},
+	foreach cdata vertex={%
+		\expandafter\pgfplotspatchvertex\pgfplotspatchclass@biquad@A\endvertex #1%
+		\expandafter\pgfplotspatchvertex\pgfplotspatchclass@biquad@B\endvertex #1%
+		\expandafter\pgfplotspatchvertex\pgfplotspatchclass@biquad@C\endvertex #1%
+		\expandafter\pgfplotspatchvertex\pgfplotspatchclass@biquad@D\endvertex #1%
+	},
 	fill path={%
 		\begingroup
 		% Visualize the patch boundary using four bezier curves.
@@ -1407,36 +1396,235 @@
 	%-------------------------------------------------- 
 	stream to shader={%
 		\begingroup
+		%
+		% An early version of this shader used Coons patch shadings
+		% (which provides coordinates only for the 9 boundary
+		% vertices, not for the inner vertices). That is a little bit
+		% simpler than what you see in the following lines of code: a
+		% transformation to a tensor bezier shading.
+		%
+		% What we need is to map the 3x3 data from lagrangrian
+		% (interpolation) representation to 4x4 cubic bezier - and
+		% handle the four INNER nodes correctly.
+		%
+		% The algorithm to convert from 1d curves with 3 point langrange to 4 point
+		% bezier is well-known and relatively simple. Fortunately, the
+		% extension to 3x3 -> 4x4 can be boiled down to a successive
+		% application of the 1d algorithm - applied to horizontal and
+		% vertical lines in the data matrizes.
+		%
+		% NOTE: the algorithm in the following lines results in
+		% EXACTLY THE SAME four cubic boundary curves as the approach
+		% in 'fill path'. The only difference is that it also does the
+		% right thing for the inner node.
+		%
+		% STEP 1: ensure that the patch's coordinates are streamed in
+		% a sequence which is compatible with the DEPTH of the
+		% corners.
+		%
+		% we use
+		% \pgfplotspatchclass@rect@to@coonspatch@findshadingsequence@for@depth
+		% which works for bilinear, biquadratic, and bicubic 
 		\pgfplotspatchclass@rect@to@coonspatch@findshadingsequence@for@depth
 			{pgfplotspatchclass@biquad@}{\Pcur}{\Pnextseq}%
 		%
-		\let\Pstartidx\Pcur%
-		\pgfutil@namelet{Pstart}{pgfplotspatchclass@biquad@\Pcur}%
+		% STEP 2:
+		% now, translate the result into our matrix form.
+		% This means to (a) identify the FIRST point which needs to be
+		% streamed (it is stored in \Pcur as 'A', 'B', 'C', or 'D')
+		% and (b) keep in mind that we have to take care of the
+		% sequence in which points are streamed ("forward" means to
+		% rotate the matrix elements and "backward" means to transpose
+		% the "forward" result).
 		%
-		% create a tensor cubic bezier patch.
+		% This can be seen as conversion from the "linearized"
+		% numbering to matrix indexing - while respecting the "start
+		% point".
 		%
-		% Again, the outer boundary involves a map from 3 point lagrange
-		% representation to 4 point cubic bezier.
+		% INPUT:
 		%
-		% The main complication arises to support the INNER node (\pgfplotspatchclass@biquad@I) .
-		% We need the four inner bezier control points to get it
-		% correctly.
+		% D G C
+		% H I F
+		% A E B
 		%
-		% this here handles only the OUTER shaper. It is the same as
-		% for 'fill path'.
-		% See 'fill path' for docs.
+		\if A\Pcur
+			% Ah - the point "A" needs to be streamed as first.
+			%
+			% Well, this is simple: take the matrix as-is!
+			% simply copy 1:1
+			%
+			% i.e. convert 
+			% D G C
+			% H I F
+			% A E B
+			%
+			% to
+			%
+			% AC BC CC 
+			% AB BB CB 
+			% AA BA CA 
+			\let\P@AA=\pgfplotspatchclass@biquad@A
+			\let\P@BA=\pgfplotspatchclass@biquad@E
+			\let\P@CA=\pgfplotspatchclass@biquad@B
+			\let\P@AB=\pgfplotspatchclass@biquad@H
+			\let\P@BB=\pgfplotspatchclass@biquad@I
+			\let\P@CB=\pgfplotspatchclass@biquad@F
+			\let\P@AC=\pgfplotspatchclass@biquad@D
+			\let\P@BC=\pgfplotspatchclass@biquad@G
+			\let\P@CC=\pgfplotspatchclass@biquad@C
+		\fi
+		\if B\Pcur
+			% the "B" point needs to be streamed as first.
+			%
+			% i.e. reorder 
+			% D G C
+			% H I F
+			% A E B
+			%
+			% to 
+			% A H D     AC BC CC 
+			% E I G =:  AB BB CB 
+			% B F C     AA BA CA 
+			%
+			\let\P@AA=\pgfplotspatchclass@biquad@B
+			\let\P@BA=\pgfplotspatchclass@biquad@F
+			\let\P@CA=\pgfplotspatchclass@biquad@C
+			\let\P@AB=\pgfplotspatchclass@biquad@E
+			\let\P@BB=\pgfplotspatchclass@biquad@I
+			\let\P@CB=\pgfplotspatchclass@biquad@G
+			\let\P@AC=\pgfplotspatchclass@biquad@A
+			\let\P@BC=\pgfplotspatchclass@biquad@H
+			\let\P@CC=\pgfplotspatchclass@biquad@D
+		\fi
+		\if C\Pcur
+			% the "C" point needs to be streamed as first.
+			%
+			% i.e. reorder 
+			% D G C
+			% H I F
+			% A E B
+			%
+			% to 
+			% B E A     AC BC CC 
+			% F I H =:  AB BB CB 
+			% C G D     AA BA CA 
+			%
+			\let\P@AA=\pgfplotspatchclass@biquad@C
+			\let\P@BA=\pgfplotspatchclass@biquad@G
+			\let\P@CA=\pgfplotspatchclass@biquad@D
+			\let\P@AB=\pgfplotspatchclass@biquad@F
+			\let\P@BB=\pgfplotspatchclass@biquad@I
+			\let\P@CB=\pgfplotspatchclass@biquad@H
+			\let\P@AC=\pgfplotspatchclass@biquad@B
+			\let\P@BC=\pgfplotspatchclass@biquad@E
+			\let\P@CC=\pgfplotspatchclass@biquad@A
+		\fi
+		\if D\Pcur
+			% the "D" point needs to be streamed as first.
+			%
+			% i.e. reorder 
+			% D G C
+			% H I F
+			% A E B
+			%
+			% to 
+			% C F B     AC BC CC 
+			% G I E =:  AB BB CB 
+			% D H A     AA BA CA 
+			%
+			\let\P@AA=\pgfplotspatchclass@biquad@D
+			\let\P@BA=\pgfplotspatchclass@biquad@H
+			\let\P@CA=\pgfplotspatchclass@biquad@A
+			\let\P@AB=\pgfplotspatchclass@biquad@G
+			\let\P@BB=\pgfplotspatchclass@biquad@I
+			\let\P@CB=\pgfplotspatchclass@biquad@E
+			\let\P@AC=\pgfplotspatchclass@biquad@C
+			\let\P@BC=\pgfplotspatchclass@biquad@F
+			\let\P@CC=\pgfplotspatchclass@biquad@B
+		\fi
+		\ifx\Pnextseq\pgfutil@empty
+		\else
+			% reverse the ordering. This means to transpose the
+			% matrix:
+			\pgfplotspatchclass@biquad@transpose
+		\fi
+		%
+		%
+		% Step: convert to tensor bezier representation.
+		%
+		% Converting a 2d tensor product lagrangian interpoland to a
+		% 2d tensor product bezier interpoland can be achieved by
+		% means of 1d algorithms along LINES in the matrix.
+		%
+		% The underlying proof for this is related to the tensor
+		% product form: the U and V coordinates are orthogonal to each
+		% other, so we can redistribute all intermediate results. (I
+		% do not have the real proof, so this hand-waving argument has
+		% to be enough). I verified its results experimentally.
+		%
+		% Note that the underlying 1d operation is the same as for
+		% 'patch type=quadratic spline' . We only need to apply it to all
+		% lines in U direction and afterwards to all lines in V
+		% direction.
 		% 
-		\pgfplotspatchclass@biquad@coonsedge
+		\def\pgfplotspatchvertexaddXY@expanded##1\times{%
+			\edef\pgfplots@loc@TMPa{##1}%
+			\expandafter\pgfplotspatchvertexaddXY\pgfplots@loc@TMPa\times
+		}%
 		%
-		\pgfplotspatchclass@biquad@coonsedge
+		% this macro operates on \pgfplots@line{[ABC]} and defines
+		% \pgfplots@line{[ABCD]} (i.e. one dimension more!)
+		\def\pgfplots@apply@to@line{%
+			\pgfplotspatchvertexaccumstart
+			\pgfplotspatchvertexaddXY@expanded\pgfplots@line{B}\times{1.333333}%
+			\pgfplotspatchvertexaddXY@expanded\pgfplots@line{C}\times{-0.333333}%
+			\pgfplotspatchvertexfinish\pgfplots@controlpoint@A
+			%
+			\pgfplotspatchvertexaccumstart
+			\pgfplotspatchvertexaddXY@expanded\pgfplots@line{A}\times{-0.333333}%
+			\pgfplotspatchvertexaddXY@expanded\pgfplots@line{B}\times{1.333333}%
+			\pgfplotspatchvertexfinish\pgfplots@controlpoint@B
+			%
+			% ... we output 4 points (cubic!).
+			% A= left endpoint (untouched)
+			% B= first control
+			% C= second control
+			% D= right endpoint (untouched, is formerly called 'C')
+			\edef\pgfplots@loc@TMPa{\pgfplots@line{C}}%
+			\expandafter\expandafter\expandafter\let\pgfplots@line{B}=\pgfplots@controlpoint@A
+			\expandafter\expandafter\expandafter\let\pgfplots@line{C}=\pgfplots@controlpoint@B
+			\expandafter\expandafter\expandafter\let\pgfplots@line{D}=\pgfplots@loc@TMPa
+		}%
 		%
-		\pgfplotspatchclass@biquad@coonsedge
+		\def\pgfplots@line##1{\csname P@##1A\endcsname}%
+		\pgfplots@apply@to@line
 		%
-		\pgfplotspatchclass@biquad@coonsedge
+		\def\pgfplots@line##1{\csname P@##1B\endcsname}%
+		\pgfplots@apply@to@line
 		%
-		% FIXME:
-		% \pgfplotspatchclass@biquad@innercontrolpoints
+		\def\pgfplots@line##1{\csname P@##1C\endcsname}%
+		\pgfplots@apply@to@line
+		%
+		% Now, we have a 3x4 matrix.
+		%
+		%
+		\def\pgfplots@line##1{\csname P@A##1\endcsname}%
+		\pgfplots@apply@to@line
 		%
+		\def\pgfplots@line##1{\csname P@B##1\endcsname}%
+		\pgfplots@apply@to@line
+		%
+		\def\pgfplots@line##1{\csname P@C##1\endcsname}%
+		\pgfplots@apply@to@line
+		%
+		\def\pgfplots@line##1{\csname P@D##1\endcsname}%
+		\pgfplots@apply@to@line
+		%
+		% OK. The tensor product representation is READY.
+		%
+		% in particular, we have a 4x4 matrix right now:
+		%
+		\pgfplotsplothandlermesh@shade@cubic@tensor
 		\endgroup
 	},%
 	triangulate={%
@@ -1749,10 +1937,22 @@
 		#1%
 		%
 	},%
-	get pdf shading type=6,
-	get num vertices=9,
+	get pdf shading type*={%
+		\if1\b@pgfplotsplothandlermesh@enable@fixed@biquadratic
+			\def\pgfplotsretval{7}%
+		\else
+			\def\pgfplotsretval{6}%
+		\fi
+	},%
+	get num vertices=\def\pgfplotsretval{9},
+	get num cdata vertices=\def\pgfplotsretval{4},
 }%
 
+% set this to 0 to revert to an older implementation (which was buggy,
+% though)
+\def\b@pgfplotsplothandlermesh@enable@fixed@biquadratic{1}%
+
+
 % see docs in 'biquadratic::stream to shader' for details.
 % PRECONDITION: to be used inside of 'stream to shader'.
 \def\pgfplotspatchclass@biquad@coonsedge{%
@@ -1881,7 +2081,6 @@
 % Direct interface to coons patches (pdf shading type 6).
 % See manual and/or pdf reference
 \pgfplotsdeclarepatchclass{coons}{%
-	allow matrix=0,
 	new=\def\pgfplotspatchclass@coons@no{A},
 	set next vertex={%
 		% defines \pgfplotspatchclass@coons@A ... \pgfplotspatchclass@coons@L (12 points)
@@ -1934,14 +2133,13 @@
 	serialize except vertices=\let\pgfplotsretval\pgfutil@empty,%
 	deserialize except vertices=,
 	get pdf shading type=6,
-	get num vertices=12,
-	get num cdata vertices=4,
+	get num vertices=\def\pgfplotsretval{12},
+	get num cdata vertices=\def\pgfplotsretval{4},
 }%
 
 % Direct interface to tensor product bezier patches (pdf shading type 7).
 % See manual and/or pdf reference
 \pgfplotsdeclarepatchclass{tensor bezier}{%
-	allow matrix=0,
 	new=\def\pgfplotspatchclass@tensor@no{A},
 	set next vertex={%
 		% defines \pgfplotspatchclass@tensor@A ... \pgfplotspatchclass@tensor@P (16 points)
@@ -1998,8 +2196,8 @@
 	serialize except vertices=\let\pgfplotsretval\pgfutil@empty,%
 	deserialize except vertices=,
 	get pdf shading type=7,
-	get num vertices=16,
-	get num cdata vertices=4,
+	get num vertices=\def\pgfplotsretval{16},
+	get num cdata vertices=\def\pgfplotsretval{4},
 }%
 
 % A bicubic patch with 16 points.
@@ -2012,7 +2210,6 @@
 % AA BA CA DA
 %
 \pgfplotsdeclarepatchclass{bicubic}{%
-	allow matrix=0,
 	new=\def\pgfplotspatchclass@bicubic@row{A}\def\pgfplotspatchclass@bicubic@col{A},
 	set next vertex={%
 		% defines \pgfplotspatchclass@bicubic@AA ... \pgfplotspatchclass@bicubic@DD (16 points)
@@ -2125,22 +2322,22 @@
 			{\pgfplotspatchclass@bicubic@AA}
 			{\pgfplotspatchclass@bicubic@BA}
 			{\pgfplotspatchclass@bicubic@CA}
-			{\pgfplotspatchclass@bicubic@DA}
+			{\pgfplotspatchclass@bicubic@DA}%
 		\pgfplotspathcubicfrominterpolation
 			{\pgfplotspatchclass@bicubic@DA}
 			{\pgfplotspatchclass@bicubic@DB}
 			{\pgfplotspatchclass@bicubic@DC}
-			{\pgfplotspatchclass@bicubic@DD}
+			{\pgfplotspatchclass@bicubic@DD}%
 		\pgfplotspathcubicfrominterpolation
 			{\pgfplotspatchclass@bicubic@DD}
 			{\pgfplotspatchclass@bicubic@CD}
 			{\pgfplotspatchclass@bicubic@BD}
-			{\pgfplotspatchclass@bicubic@AD}
+			{\pgfplotspatchclass@bicubic@AD}%
 		\pgfplotspathcubicfrominterpolation
 			{\pgfplotspatchclass@bicubic@AD}
 			{\pgfplotspatchclass@bicubic@AC}
 			{\pgfplotspatchclass@bicubic@AB}
-			{\pgfplotspatchclass@bicubic@AA}
+			{\pgfplotspatchclass@bicubic@AA}%
 		\pgfpathclose
 	},
 	stream to shader={%
@@ -2368,46 +2565,7 @@
 		%
 		% OK. The tensor product representation is READY.
 		%
-		% Stream it to the shader. Note that the shader has a
-		% DIFFERENT ordering; it expects points in the cyclic ordering
-		%
-		% AA BA CA DA   DB DC DD  CD BD AD   AC AB    BB CB CC BC
-		%
-		% note furthermore that only the corners have "point meta" in
-		% this shading :-(
-		%
-		\expandafter\pgfplotspatchvertex\P@AA\endvertex
-			\let\pgfplots@current@point@meta=\pgfplotspatchvertexmeta
-			\pgfplotsaxisvisphasetransformpointmeta
-		\pgfplotslibrarysurfstreamcoord{\pgfqpoint\pgfplotspatchvertexx\pgfplotspatchvertexy}{\pgfplotspointmetatransformed}%
-		\pgfplotslibrarysurfstreamcoord{\expandafter\pgfplotspointpatchvertex\P@BA\endvertex}{\pgfplotspointmetatransformed}%
-		\pgfplotslibrarysurfstreamcoord{\expandafter\pgfplotspointpatchvertex\P@CA\endvertex}{\pgfplotspointmetatransformed}%
-		\expandafter\pgfplotspatchvertex\P@DA\endvertex
-			\let\pgfplots@current@point@meta=\pgfplotspatchvertexmeta
-			\pgfplotsaxisvisphasetransformpointmeta
-		\pgfplotslibrarysurfstreamcoord{\pgfqpoint\pgfplotspatchvertexx\pgfplotspatchvertexy}{\pgfplotspointmetatransformed}%
-		%
-		\pgfplotslibrarysurfstreamcoord{\expandafter\pgfplotspointpatchvertex\P@DB\endvertex}{\pgfplotspointmetatransformed}%
-		\pgfplotslibrarysurfstreamcoord{\expandafter\pgfplotspointpatchvertex\P@DC\endvertex}{\pgfplotspointmetatransformed}%
-		\expandafter\pgfplotspatchvertex\P@DD\endvertex
-			\let\pgfplots@current@point@meta=\pgfplotspatchvertexmeta
-			\pgfplotsaxisvisphasetransformpointmeta
-		\pgfplotslibrarysurfstreamcoord{\pgfqpoint\pgfplotspatchvertexx\pgfplotspatchvertexy}{\pgfplotspointmetatransformed}%
-		%
-		\pgfplotslibrarysurfstreamcoord{\expandafter\pgfplotspointpatchvertex\P@CD\endvertex}{\pgfplotspointmetatransformed}%
-		\pgfplotslibrarysurfstreamcoord{\expandafter\pgfplotspointpatchvertex\P@BD\endvertex}{\pgfplotspointmetatransformed}%
-		\expandafter\pgfplotspatchvertex\P@AD\endvertex
-			\let\pgfplots@current@point@meta=\pgfplotspatchvertexmeta
-			\pgfplotsaxisvisphasetransformpointmeta
-		\pgfplotslibrarysurfstreamcoord{\pgfqpoint\pgfplotspatchvertexx\pgfplotspatchvertexy}{\pgfplotspointmetatransformed}%
-		%
-		\pgfplotslibrarysurfstreamcoord{\expandafter\pgfplotspointpatchvertex\P@AC\endvertex}{\pgfplotspointmetatransformed}%
-		\pgfplotslibrarysurfstreamcoord{\expandafter\pgfplotspointpatchvertex\P@AB\endvertex}{\pgfplotspointmetatransformed}%
-		%
-		\pgfplotslibrarysurfstreamcoord{\expandafter\pgfplotspointpatchvertex\P@BB\endvertex}{\pgfplotspointmetatransformed}%
-		\pgfplotslibrarysurfstreamcoord{\expandafter\pgfplotspointpatchvertex\P@CB\endvertex}{\pgfplotspointmetatransformed}%
-		\pgfplotslibrarysurfstreamcoord{\expandafter\pgfplotspointpatchvertex\P@CC\endvertex}{\pgfplotspointmetatransformed}%
-		\pgfplotslibrarysurfstreamcoord{\expandafter\pgfplotspointpatchvertex\P@BC\endvertex}{\pgfplotspointmetatransformed}%
+		\pgfplotsplothandlermesh@shade@cubic@tensor
 		\endgroup
 	},
 	triangulate={%
@@ -2462,8 +2620,8 @@
 	serialize except vertices=\let\pgfplotsretval\pgfutil@empty,%
 	deserialize except vertices=,
 	get pdf shading type=7,
-	get num vertices=16,
-	get num cdata vertices=4,
+	get num vertices=\def\pgfplotsretval{16},
+	get num cdata vertices=\def\pgfplotsretval{4},
 }%
 
 % Transpose a bicubic matrix (4x4).
@@ -2486,4 +2644,79 @@
 	\pgfplotsutil@swap\P@BD\P@DB
 	\pgfplotsutil@swap\P@DC\P@CD
 }
+
+% Transpose a bicubic matrix (4x4).
+%
+% Reorder 
+% AC BC CC 
+% AB BB CB 
+% AA BA CA 
+% to 
+% CA CB CC 
+% BA BB BC 
+% AA AB AC 
+\def\pgfplotspatchclass@biquad@transpose{%
+	\pgfplotsutil@swap\P@AB\P@BA
+	\pgfplotsutil@swap\P@CA\P@AC
+	\pgfplotsutil@swap\P@CB\P@BC
+}
+
+% Expects that a 4x4 matrix in tensor bezier representation where 
+% A = left end point
+% B = first control point
+% C = second control point
+% D = right end point
+%
+% and the coordinates are stored in \csname P@[ABCD][ABCD]\endcsname
+% 
+% Streaming starts with \P@AA and is applied rowwise.
+\def\pgfplotsplothandlermesh@shade@cubic@tensor{%
+	% Stream it to the shader. Note that the shader has a
+	% DIFFERENT ordering; it expects points in the cyclic ordering
+	%
+	% AA BA CA DA   DB DC DD  CD BD AD   AC AB    BB CB CC BC
+	%
+	% note furthermore that only the corners have "point meta" in
+	% this shading :-(
+	%
+	\expandafter\pgfplotspatchvertex\P@AA\endvertex
+		\let\pgfplots@current@point@meta=\pgfplotspatchvertexmeta
+		\pgfplotsaxisvisphasetransformpointmeta
+	\pgfplotslibrarysurfstreamcoord{\pgfqpoint\pgfplotspatchvertexx\pgfplotspatchvertexy}{\pgfplotspointmetatransformed}%
+	\pgfplotslibrarysurfstreamcoord{\expandafter\pgfplotspointpatchvertex\P@BA\endvertex}{\pgfplotspointmetatransformed}%
+	\pgfplotslibrarysurfstreamcoord{\expandafter\pgfplotspointpatchvertex\P@CA\endvertex}{\pgfplotspointmetatransformed}%
+	\expandafter\pgfplotspatchvertex\P@DA\endvertex
+		\let\pgfplots@current@point@meta=\pgfplotspatchvertexmeta
+		\pgfplotsaxisvisphasetransformpointmeta
+	\pgfplotslibrarysurfstreamcoord{\pgfqpoint\pgfplotspatchvertexx\pgfplotspatchvertexy}{\pgfplotspointmetatransformed}%
+	%
+	\pgfplotslibrarysurfstreamcoord{\expandafter\pgfplotspointpatchvertex\P@DB\endvertex}{\pgfplotspointmetatransformed}%
+	\pgfplotslibrarysurfstreamcoord{\expandafter\pgfplotspointpatchvertex\P@DC\endvertex}{\pgfplotspointmetatransformed}%
+	\expandafter\pgfplotspatchvertex\P@DD\endvertex
+		\let\pgfplots@current@point@meta=\pgfplotspatchvertexmeta
+		\pgfplotsaxisvisphasetransformpointmeta
+	\pgfplotslibrarysurfstreamcoord{\pgfqpoint\pgfplotspatchvertexx\pgfplotspatchvertexy}{\pgfplotspointmetatransformed}%
+	%
+	\pgfplotslibrarysurfstreamcoord{\expandafter\pgfplotspointpatchvertex\P@CD\endvertex}{\pgfplotspointmetatransformed}%
+	\pgfplotslibrarysurfstreamcoord{\expandafter\pgfplotspointpatchvertex\P@BD\endvertex}{\pgfplotspointmetatransformed}%
+	\expandafter\pgfplotspatchvertex\P@AD\endvertex
+		\let\pgfplots@current@point@meta=\pgfplotspatchvertexmeta
+		\pgfplotsaxisvisphasetransformpointmeta
+	\pgfplotslibrarysurfstreamcoord{\pgfqpoint\pgfplotspatchvertexx\pgfplotspatchvertexy}{\pgfplotspointmetatransformed}%
+	%
+	\pgfplotslibrarysurfstreamcoord{\expandafter\pgfplotspointpatchvertex\P@AC\endvertex}{\pgfplotspointmetatransformed}%
+	\pgfplotslibrarysurfstreamcoord{\expandafter\pgfplotspointpatchvertex\P@AB\endvertex}{\pgfplotspointmetatransformed}%
+	%
+	%
+	\pgfplotspatchclass{\pgfplotspatchclassname}{get pdf shading type}%
+	\if 7\pgfplotsretval
+		\pgfplotslibrarysurfstreamcoord{\expandafter\pgfplotspointpatchvertex\P@BB\endvertex}{\pgfplotspointmetatransformed}%
+		\pgfplotslibrarysurfstreamcoord{\expandafter\pgfplotspointpatchvertex\P@CB\endvertex}{\pgfplotspointmetatransformed}%
+		\pgfplotslibrarysurfstreamcoord{\expandafter\pgfplotspointpatchvertex\P@CC\endvertex}{\pgfplotspointmetatransformed}%
+		\pgfplotslibrarysurfstreamcoord{\expandafter\pgfplotspointpatchvertex\P@BC\endvertex}{\pgfplotspointmetatransformed}%
+	\else
+		% assume 'get pdf shading type=6' - it does not contain the
+		% inner vertices.
+	\fi
+}
 \endinput