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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 new file mode 100644 index 00000000000..4076e37281c --- /dev/null +++ b/Master/texmf-dist/tex/generic/pgfplots/libs/tikzlibrarypgfplots.patchplots.code.tex @@ -0,0 +1,1783 @@ +%-------------------------------------------- +% +% Package pgfplots, library for higher order patch plots. +% It contains advanced patch plots like quadratic triangles, +% biquadratic quadrilaterals, coons patches and others. +% The basic implementation for patches supports already line, triangle +% and rectangle (=2 triangles) patches. +% +% Copyright 2007/2008/2009 by Christian Feuersänger. +% +% This program is free software: you can redistribute it and/or modify +% it under the terms of the GNU General Public License as published by +% the Free Software Foundation, either version 3 of the License, or +% (at your option) any later version. +% +% This program is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. +% +% You should have received a copy of the GNU General Public License +% along with this program. If not, see <http://www.gnu.org/licenses/>. +% +%-------------------------------------------- + + % NOTES: + % In general, a Bezier spline C:[0,1] -> \R of order n fulfills + % C'(0) = n ( P_1 - P_0 ), + % C'(1) = n ( P_n - P_{n-1} ). + % For n=3 and given P_0 and P_3, I can directly compute P_1 and P_2 once I know + % the derivatives at t=0 and t=1. + % + % + % +%-------------------------------------------------- +% 4-point Lagrange interpolation on {0,1/3,2/3,1}: +% C(x) = +% a * (1/3 - x)/(1/3) * (2/3-x)/(2/3) * (1-x) + +% b * (0 - x)/(0 - 1/3) * (2/3-x)/(2/3-1/3) * (1-x)/(1-1/3) + +% c * (0 - x)/(0 - 2/3) * (1/3-x)/(1/3-2/3) * (1-x)/(1-2/3) + +% d * (0 - x)/(0 - 1) * (1/3-x)/(1/3-1) * (2/3-x) /(2/3-1) +% +% +% Derivative: +% +% (-9*c + 2*d + 72*c*x - 18*d*x - 81*c*x^2 + 27*d*x^2 + +% a*(-11 + 36*x - 27*x^2) + 9*b*(2 - 10*x + 9*x^2))/2 +% +% bezier control points are +% P1 = (-5*a)/6 + 3*b - (3*c)/2 + d/3 +% = -0.833333 a + 3. b - 1.5 c + 0.333333 d +% +% P2 = 0.333333 (0.5 (2. a - 9. b + 18. c - 11. d) + 3. d) +% = 0.333333 a - 1.5 b + 3. c - 0.833333 d +%-------------------------------------------------- + + + +\pgfplotsdeclarepatchclass{quadratic spline}{% + allow matrix=0, + uses view depth=0, + new=\def\pgfplotspatchclass@qspline@no{A}, + set next vertex={% + % EXPECTED ORDERING: first 2 corners, then 1 mid nodes + % (interpolatory). + % defines \pgfplotspatchclass@qspline@A ... \pgfplotspatchclass@qspline@C (3 points) + \expandafter\edef\csname pgfplotspatchclass@qspline@\pgfplotspatchclass@qspline@no\endcsname{#1}% + \if C\pgfplotspatchclass@qspline@no + \def\pgfplotspatchclass@qspline@no{A}% + \pgfplotspatchready + \else + \expandafter\let\expandafter\pgfplotspatchclass@qspline@no\csname pgfpptchindexnext@\pgfplotspatchclass@qspline@no\endcsname + \fi + }, + first vertex=\expandafter\pgfplotspatchvertex\pgfplotspatchclass@qspline@A\endvertex, + foreach vertex={% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@qspline@A\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@qspline@B\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@qspline@C\endvertex #1% + }, + fill path={% + \begingroup + % Draw the patch boundary using a bezier curves. + % + % Since I have lagrange points to describe the patch (i.e. + % points the patch passes through), I have to convert the + % lagrange representation to bezier. + % + % Furthermore, I convert to *cubic* bezier since pdf only + % supports cubic curves. + % + % See the docs for 'biquadratic::fill path' for more details, + % in does the same. + \def\pgfplots@edge{% + \ifx\pgfplotspatchclass@qspline@A\PA + \pgfpathmoveto{\expandafter\pgfplotspointpatchvertex\PA\endvertex}% + \fi + \pgfpathcurveto {% + \pgfpointadd + {\pgfqpointscale{1.333333}{\expandafter\pgfplotspointpatchvertex\PB\endvertex}}% + {\pgfqpointscale{-0.333333}{\expandafter\pgfplotspointpatchvertex\PC\endvertex}}% + }{% + \pgfpointadd + {\pgfqpointscale{1.333333}{\expandafter\pgfplotspointpatchvertex\PB\endvertex}}% + {\pgfqpointscale{-0.333333}{\expandafter\pgfplotspointpatchvertex\PA\endvertex}}% + }{% + \expandafter\pgfplotspointpatchvertex\PC\endvertex + }% + }% + \let\PA=\pgfplotspatchclass@qspline@A + \let\PB=\pgfplotspatchclass@qspline@C + \let\PC=\pgfplotspatchclass@qspline@B + \pgfplots@edge + \endgroup + }, + triangulate class=line, + triangulate={% + \let\pgfplotsplothandlermesh@patchclass@=\pgfplotsplothandlermesh@patchclass + \def\pgfplotsplothandlermesh@patchclass{line}% + \pgfplotspatchclass{\pgfplotsplothandlermesh@patchclass}{new}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qspline@A}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qspline@C}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qspline@C}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qspline@B}% + \let\pgfplotsplothandlermesh@patchclass=\pgfplotsplothandlermesh@patchclass@ + },% + recursive refine@={% + \pgfplotspatchclass{\pgfplotspatchclassname}{new}% + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qspline@A\times{0.375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qspline@B\times{-0.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qspline@C\times{0.75}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@qspline@AC + % + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qspline@A}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qspline@C}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qspline@AC}% + #1% + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qspline@A\times{-0.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qspline@B\times{0.375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qspline@C\times{0.75}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@qspline@CB + % + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qspline@C}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qspline@B}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qspline@CB}% + #1% + % + },% + get pdf shading type=0, + get num vertices=3, +}% + +\pgfplotsdeclarepatchclass{cubic spline}{% + allow matrix=0, + uses view depth=0, + new=\def\pgfplotspatchclass@cspline@no{A}, + set next vertex={% + % EXPECTED ORDERING: first 2 corners, then 1 mid nodes + % (interpolatory). + % defines \pgfplotspatchclass@cspline@A ... \pgfplotspatchclass@cspline@D (4 points) + \expandafter\edef\csname pgfplotspatchclass@cspline@\pgfplotspatchclass@cspline@no\endcsname{#1}% + \if D\pgfplotspatchclass@cspline@no + \def\pgfplotspatchclass@cspline@no{A}% + \pgfplotspatchready + \else + \expandafter\let\expandafter\pgfplotspatchclass@cspline@no\csname pgfpptchindexnext@\pgfplotspatchclass@cspline@no\endcsname + \fi + }, + first vertex=\expandafter\pgfplotspatchvertex\pgfplotspatchclass@cspline@A\endvertex, + foreach vertex={% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@cspline@A\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@cspline@B\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@cspline@C\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@cspline@D\endvertex #1% + }, + fill path={% + % Draw the patch boundary using a bezier curve. + \pgfpathmoveto{\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@cspline@A\endvertex}% + % switch basis from lagrange to bezier (see formular on top of + % this file) + \pgfpathcurveto {% + \begingroup + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexaddXY\pgfplotspatchclass@cspline@A\times{-0.833333}% + \expandafter\pgfplotspatchvertexaddXY\pgfplotspatchclass@cspline@C\times{3}% + \expandafter\pgfplotspatchvertexaddXY\pgfplotspatchclass@cspline@D\times{-1.5}% + \expandafter\pgfplotspatchvertexaddXY\pgfplotspatchclass@cspline@B\times{0.3333333}% + \pgfplotspatchvertexfinish\pgfplots@loc@TMPa + \expandafter\pgfplotspointpatchvertex\pgfplots@loc@TMPa\endvertex + \endgroup + }{% + \begingroup + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexaddXY\pgfplotspatchclass@cspline@A\times{0.333333}% + \expandafter\pgfplotspatchvertexaddXY\pgfplotspatchclass@cspline@C\times{-1.5}% + \expandafter\pgfplotspatchvertexaddXY\pgfplotspatchclass@cspline@D\times{3}% + \expandafter\pgfplotspatchvertexaddXY\pgfplotspatchclass@cspline@B\times{-0.833333}% + \pgfplotspatchvertexfinish\pgfplots@loc@TMPa + \expandafter\pgfplotspointpatchvertex\pgfplots@loc@TMPa\endvertex + \endgroup + }{% + \expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@cspline@B\endvertex + }% + }, + triangulate class=line, + triangulate={% + \let\pgfplotsplothandlermesh@patchclass@=\pgfplotsplothandlermesh@patchclass + \def\pgfplotsplothandlermesh@patchclass{line}% + \pgfplotspatchclass{\pgfplotsplothandlermesh@patchclass}{new}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@cspline@A}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@cspline@C}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@cspline@C}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@cspline@D}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@cspline@D}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@cspline@B}% + \let\pgfplotsplothandlermesh@patchclass=\pgfplotsplothandlermesh@patchclass@ + },% + recursive refine@={% + % The 4-point lagrangian interpolation formular is shown on + % the top of this page. What I do here is simply to evaluate + % C(i*1/9) for i =0,...,9: + % 0 + % 0.493827 A +0.740741 C -0.296296 D +0.0617284 B + % 0.17284 A +1.03704 C -0.259259 D +0.0493827 B + % 1/3 + % -0.0617284 A +0.740741 C +0.37037 D -0.0493827 B + % -0.0493827 A +0.37037 C +0.740741 D -0.0617284 B + % 2/3 + % 0.0493827 A -0.259259 C +1.03704 D +0.17284 B + % 0.0617284 A -0.296296 C +0.740741 D +0.493827 B + % 1 + \pgfplotspatchclass{\pgfplotspatchclassname}{new}% + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@cspline@A\times{0.493827}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@cspline@B\times{0.0617284}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@cspline@C\times{0.740741}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@cspline@D\times{-0.296296}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@cspline@AA + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@cspline@A\times{0.17284}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@cspline@B\times{0.0493827}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@cspline@C\times{1.03704}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@cspline@D\times{-0.259259}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@cspline@AB + % + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@cspline@A}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@cspline@C}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@cspline@AA}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@cspline@AB}% + #1% + % + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@cspline@A\times{-0.0617284}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@cspline@B\times{-0.0493827}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@cspline@C\times{0.740741}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@cspline@D\times{0.37037}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@cspline@AA + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@cspline@A\times{-0.0493827}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@cspline@B\times{-0.0617284}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@cspline@C\times{0.37037}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@cspline@D\times{0.740741}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@cspline@AB + % + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@cspline@C}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@cspline@D}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@cspline@AA}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@cspline@AB}% + #1% + % + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@cspline@A\times{0.0493827}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@cspline@B\times{0.17284}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@cspline@C\times{-0.259259}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@cspline@D\times{+1.03704}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@cspline@AA + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@cspline@A\times{0.0617284}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@cspline@B\times{0.493827}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@cspline@C\times{-0.296296}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@cspline@D\times{0.740741}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@cspline@AB + % + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@cspline@D}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@cspline@B}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@cspline@AA}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@cspline@AB}% + #1% + }, + get pdf shading type=0, + get num vertices=4, +}% + +% make a linearized sequence around the edge of the quad.triangle. +% note the ordering: first 3 corners, then 3 mid nodes: +\def\pgfplots@qtri@next@A{D}% +\def\pgfplots@qtri@next@B{E}% +\def\pgfplots@qtri@next@C{F}% +\def\pgfplots@qtri@next@D{B}% +\def\pgfplots@qtri@next@E{C}% +\def\pgfplots@qtri@next@F{A}% + +\def\pgfplots@qtri@rnext@A{F}% +\def\pgfplots@qtri@rnext@B{D}% +\def\pgfplots@qtri@rnext@C{E}% +\def\pgfplots@qtri@rnext@D{A}% +\def\pgfplots@qtri@rnext@E{B}% +\def\pgfplots@qtri@rnext@F{C}% + +\def\pgfplotspatchclass@qtri@recursiverefine@newnames{% + \let\pgfplotspatchclass@qtri@A@=\pgfplotspatchclass@qtri@A% + \let\pgfplotspatchclass@qtri@B@=\pgfplotspatchclass@qtri@B% + \let\pgfplotspatchclass@qtri@C@=\pgfplotspatchclass@qtri@C% + \let\pgfplotspatchclass@qtri@D@=\pgfplotspatchclass@qtri@D% + \let\pgfplotspatchclass@qtri@E@=\pgfplotspatchclass@qtri@E% + \let\pgfplotspatchclass@qtri@F@=\pgfplotspatchclass@qtri@F% +}% + + +% 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, + new=\def\pgfplotspatchclass@qtri@no{A}\let\pgfplotspatchclass@qtrie@AB\relax, + set next vertex={% + % EXPECTED ORDERING: first 3 corners, then 3 mid nodes. + % defines \pgfplotspatchclass@qtri@A ... \pgfplotspatchclass@qtri@F (6 points) + \expandafter\edef\csname pgfplotspatchclass@qtri@\pgfplotspatchclass@qtri@no\endcsname{#1}% + \if F\pgfplotspatchclass@qtri@no + \def\pgfplotspatchclass@qtri@no{A}% + \pgfplotspatchready + \else + \expandafter\let\expandafter\pgfplotspatchclass@qtri@no\csname pgfpptchindexnext@\pgfplotspatchclass@qtri@no\endcsname + \fi + }, + first vertex=\expandafter\pgfplotspatchvertex\pgfplotspatchclass@qtri@A\endvertex, + foreach vertex={% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@qtri@A\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@qtri@B\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@qtri@C\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@qtri@D\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@qtri@E\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@qtri@F\endvertex #1% + }, + fill path={% + \begingroup + % Draw the patch boundary using three bezier curves. + % + % Since I have lagrange points to describe the patch (i.e. + % points the patch passes through), I have to convert the + % lagrange representation to bezier. + % + % Furthermore, I convert to *cubic* bezier since pdf only + % supports cubic curves. + % + % See the docs for 'biquadratic::fill path' for more details, + % in does the same. + \def\pgfplots@edge{% + \ifx\pgfplotspatchclass@qtri@A\PA + \pgfpathmoveto{\expandafter\pgfplotspointpatchvertex\PA\endvertex}% + \fi + \pgfpathcurveto {% + \pgfpointadd + {\pgfqpointscale{1.333333}{\expandafter\pgfplotspointpatchvertex\PB\endvertex}}% + {\pgfqpointscale{-0.333333}{\expandafter\pgfplotspointpatchvertex\PC\endvertex}}% + }{% + \pgfpointadd + {\pgfqpointscale{1.333333}{\expandafter\pgfplotspointpatchvertex\PB\endvertex}}% + {\pgfqpointscale{-0.333333}{\expandafter\pgfplotspointpatchvertex\PA\endvertex}}% + }{% + \expandafter\pgfplotspointpatchvertex\PC\endvertex + }% + }% + \let\PA=\pgfplotspatchclass@qtri@A + \let\PB=\pgfplotspatchclass@qtri@D + \let\PC=\pgfplotspatchclass@qtri@B + \pgfplots@edge + % + \let\PA=\pgfplotspatchclass@qtri@B + \let\PB=\pgfplotspatchclass@qtri@E + \let\PC=\pgfplotspatchclass@qtri@C + \pgfplots@edge + % + \let\PA=\pgfplotspatchclass@qtri@C + \let\PB=\pgfplotspatchclass@qtri@F + \let\PC=\pgfplotspatchclass@qtri@A + \pgfplots@edge + \endgroup + \pgfpathclose + }, + %-------------------------------------------------- + % stroke path={% + % \ifx\pgfplotspatchclass@qtrie@AB\relax + % \pgfpathmoveto{\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@qtri@A\endvertex}% + % \pgfpathlineto{\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@qtri@B\endvertex}% + % \pgfpathlineto{\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@qtri@C\endvertex}% + % \pgfpathclose + % \else + % \if1\pgfplotspatchclass@qtrie@AB + % \pgfpathmoveto{\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@qtri@A\endvertex}% + % \pgfpathlineto{\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@qtri@B\endvertex}% + % \fi + % \if1\pgfplotspatchclass@qtrie@BC + % \pgfpathmoveto{\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@qtri@B\endvertex}% + % \pgfpathlineto{\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@qtri@C\endvertex}% + % \fi + % \if1\pgfplotspatchclass@qtrie@CA + % \pgfpathmoveto{\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@qtri@C\endvertex}% + % \pgfpathlineto{\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@qtri@A\endvertex}% + % \fi + % \fi + % }, + %-------------------------------------------------- + stream to shader={% + % create a degenerate coons patch: + \begingroup +%\message{EDGE INIT^^J}% + % this defines \Pcur and \Pnextseq : + \pgfplotspatchclass@tri@to@coonspatch@findshadingsequence@for@depth + % + \pgfutil@namelet{Pstart}{pgfplotspatchclass@qtri@\Pcur}% + % + % see the docus for "fill path" about these 1.33333 and -0.33333 factors + \def\pgfplots@coonsedge{% +%\message{EDGE \Pcur^^J}% + \expandafter\let\expandafter\PA\csname pgfplotspatchclass@qtri@\Pcur\endcsname + \edef\Pcur{\csname pgfplots@qtri@\Pnextseq next@\Pcur\endcsname}% +%\message{---> \Pcur^^J}% + \expandafter\let\expandafter\PB\csname pgfplotspatchclass@qtri@\Pcur\endcsname + \edef\Pcur{\csname pgfplots@qtri@\Pnextseq next@\Pcur\endcsname}% +%\message{---> \Pcur^^J}% + \expandafter\let\expandafter\PC\csname pgfplotspatchclass@qtri@\Pcur\endcsname + \ifx\PA\Pstart + \expandafter\pgfplotspatchvertex\PA\endvertex + \let\pgfplots@current@point@meta=\pgfplotspatchvertexmeta + \pgfplotsaxisvisphasetransformpointmeta + \pgfplotslibrarysurfstreamcoord{\pgfqpoint\pgfplotspatchvertexx\pgfplotspatchvertexy}{\pgfplotspointmetatransformed}% + % degenerate: the "edge" \PA -- \PA collabses into one + % point. + % Per construction, the "edge" is the FOREGROUND. +%\message{STREAMING COLLAPSED EDGE AT START POINT^^J}% + \pgfplotslibrarysurfstreamcoord{\pgfqpoint\pgfplotspatchvertexx\pgfplotspatchvertexy}{\pgfplotspointmetatransformed}% + \pgfplotslibrarysurfstreamcoord{\pgfqpoint\pgfplotspatchvertexx\pgfplotspatchvertexy}{\pgfplotspointmetatransformed}% + \pgfplotslibrarysurfstreamcoord{\pgfqpoint\pgfplotspatchvertexx\pgfplotspatchvertexy}{\pgfplotspointmetatransformed}% + \fi + \pgfplotslibrarysurfstreamcoord{% + \pgfpointadd + {\pgfqpointscale{1.333333}{\expandafter\pgfplotspointpatchvertex\PB\endvertex}}% + {\pgfqpointscale{-0.333333}{\expandafter\pgfplotspointpatchvertex\PC\endvertex}}% + }{}% + \pgfplotslibrarysurfstreamcoord{% + \pgfpointadd + {\pgfqpointscale{1.333333}{\expandafter\pgfplotspointpatchvertex\PB\endvertex}}% + {\pgfqpointscale{-0.333333}{\expandafter\pgfplotspointpatchvertex\PA\endvertex}}% + }{}% + \ifx\PC\Pstart + \else + \expandafter\pgfplotspatchvertex\PC\endvertex + \let\pgfplots@current@point@meta=\pgfplotspatchvertexmeta + \pgfplotsaxisvisphasetransformpointmeta + \pgfplotslibrarysurfstreamcoord{\pgfqpoint\pgfplotspatchvertexx\pgfplotspatchvertexy}{\pgfplotspointmetatransformed}% + \fi + }% + \pgfplots@coonsedge + % + \pgfplots@coonsedge + % + \pgfplots@coonsedge + % + % + \endgroup + },% + triangulate={% + \let\pgfplotsplothandlermesh@patchclass@=\pgfplotsplothandlermesh@patchclass + \def\pgfplotsplothandlermesh@patchclass{triangle}% + \pgfplotspatchclass{\pgfplotsplothandlermesh@patchclass}{new}% + \pgfplotspatchclass{\pgfplotsplothandlermesh@patchclass}{set edge visible}01% + \pgfplotspatchclass{\pgfplotsplothandlermesh@patchclass}{set edge visible}11% + \pgfplotspatchclass{\pgfplotsplothandlermesh@patchclass}{set edge visible}20% + % Ok. Now create 4 triangles. The ordering is not arbitrary + % (unless z buffer=sort is in effect). Let's assume that the + % AB edge is BACKGROUND and the CD edge is FOREGROUND. Then + % this sequence here should have approximately the same depth + % ordering: + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@F}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@A}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@D}% + % + \pgfplotspatchclass{\pgfplotsplothandlermesh@patchclass}{set edge visible}00% + \pgfplotspatchclass{\pgfplotsplothandlermesh@patchclass}{set edge visible}10% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@F}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@D}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@E}% + % + \pgfplotspatchclass{\pgfplotsplothandlermesh@patchclass}{set edge visible}01% + \pgfplotspatchclass{\pgfplotsplothandlermesh@patchclass}{set edge visible}11% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@D}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@B}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@E}% + % + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@E}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@C}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@F}% + \let\pgfplotsplothandlermesh@patchclass=\pgfplotsplothandlermesh@patchclass@ + },% + set edge visible={% + \ifcase#1 + \edef\pgfplotspatchclass@qtrie@AB{#2}% + \or + \edef\pgfplotspatchclass@qtrie@BC{#2}% + \or + \edef\pgfplotspatchclass@qtrie@CA{#2}% + \fi + }, + serialize except vertices={% + \ifx\pgfplotspatchclass@qtrie@AB\relax + \let\pgfplotsretval\pgfutil@empty% + \else + \edef\pgfplotsretval{% + \noexpand\def\noexpand\pgfplotspatchclass@qtrie@AB{\pgfplotspatchclass@qtrie@AB}% + \noexpand\def\noexpand\pgfplotspatchclass@qtrie@BC{\pgfplotspatchclass@qtrie@BC}% + \noexpand\def\noexpand\pgfplotspatchclass@qtrie@CA{\pgfplotspatchclass@qtrie@CA}% + }% + \fi + },% + deserialize except vertices=% + \let\pgfplotspatchclass@qtrie@AB\relax + #1, + recursive refine@={% + \pgfplotspatchclass@qtri@recursiverefine@newnames + % + \pgfplotspatchclass{\pgfplotspatchclassname}{new}% + %-------------------------------------------------- + % \pgfplotspatchclass{\pgfplotspatchclassname}{set edge visible}01% + % \pgfplotspatchclass{\pgfplotspatchclassname}{set edge visible}11% + % \pgfplotspatchclass{\pgfplotspatchclassname}{set edge visible}20% + %-------------------------------------------------- + % The ordering is not arbitrary + % (unless z buffer=sort is in effect). Let's assume that the + % AB edge is BACKGROUND and the CD edge is FOREGROUND. Then + % this sequence here should have approximately the same depth + % ordering: + % + % I used the reference triangle and shape functions as listed in + % http://www.colorado.edu/engineering/CAS/courses.d/IFEM.d/ + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@A\times{0.375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@B\times{-0.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@D\times{0.75}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@qtri@AD + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@B\times{-.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@C\times{-.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@D\times{0.5}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@E\times{0.25}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@F\times{0.5}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@qtri@DF + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@A\times{0.375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@C\times{-0.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@F\times{0.75}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@qtri@AF + % + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@F@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@A@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@D@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@AF}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@AD}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@DF}% + % + #1\pgfplotspatchclass@qtri@recursiverefine@newnames + % + % + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@B\times{-.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@C\times{-.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@D\times{0.5}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@E\times{0.25}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@F\times{0.5}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@qtri@DF + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@A\times{-.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@C\times{-.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@D\times{0.5}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@E\times{0.5}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@F\times{0.25}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@qtri@DE + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@A\times{-.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@B\times{-.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@D\times{0.25}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@E\times{0.5}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@F\times{0.5}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@qtri@EF + % + % + %-------------------------------------------------- + % \pgfplotspatchclass{\pgfplotspatchclassname}{set edge visible}00% + % \pgfplotspatchclass{\pgfplotspatchclassname}{set edge visible}10% + %-------------------------------------------------- + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@F@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@D@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@E@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@DF}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@DE}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@EF}% + % % + % %-------------------------------------------------- + % % \pgfplotspatchclass{\pgfplotspatchclassname}{set edge visible}01% + % % \pgfplotspatchclass{\pgfplotspatchclassname}{set edge visible}11% + % %-------------------------------------------------- + #1\pgfplotspatchclass@qtri@recursiverefine@newnames + % + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@A\times{-0.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@B\times{0.375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@D\times{0.75}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@qtri@DB + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@A\times{-.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@C\times{-.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@D\times{0.5}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@E\times{0.5}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@F\times{0.25}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@qtri@DE + % + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@B\times{0.375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@C\times{-0.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@E\times{0.75}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@qtri@BE + % + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@D@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@B@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@E@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@DB}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@BE}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@DE}% + % + #1\pgfplotspatchclass@qtri@recursiverefine@newnames + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@B\times{-0.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@C\times{0.375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@E\times{0.75}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@qtri@EC + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@A\times{-.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@B\times{-.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@D\times{0.25}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@E\times{0.5}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@F\times{0.5}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@qtri@EF + % + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@A\times{-0.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@C\times{0.375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@qtri@F\times{0.75}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@qtri@CF + % + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@E@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@C@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@F@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@EC}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@CF}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@qtri@EF}% + % + #1% + % + },% + get pdf shading type=6, + get num vertices=6, +}% + + +% see +% \pgfplotspatchclass@rect@to@coonspatch@findshadingsequence@for@depth +% and its documentation. +% +% POSTCONDITION: +% \Pcur and \Pnextseq are defined. +\def\pgfplotspatchclass@tri@to@coonspatch@findshadingsequence@for@depth{% + \def\Pcur{A}% + \def\Pnextseq{}% + % + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@qtri@A\endvertex + \ifx\pgfplotspatchvertexdepth\pgfutil@empty + \else + % ah. We have view depth. Use it! + % The idea here is as follows. + % According to pdf standard, the COONS Shading is + % generated in the unit cube and then mapped to the + % shading. If u,v in [0,1] are the coordinates in the unit + % cube, pixel values for v=1 overwrite values for v=0. + % If pixel values have the same v, u=1 overwrites u=0. + % In other words, the loop is + % for v= 0 to Nv + % for u = 0 to Nu + % shade pixel for (u,v) + % + % BB-------CC <--v=1 + % | | + % | | + % | | + % AA-------DD <--v=0 + % | | + % u=0 u=1 + % + % + % IDEA: re-order the sequence of vertices such that z + % buffering is obtained. + % + % APPROACH: + % the edge BB--CC collapses into just one point, namely + % the FOREGROUND point (i.e. it is drawn on top of + % everything else). + % + % The AA point is the second nearest foreground point. + % The sequence is chosen such that AA,BB is the first + % edge. + % + % What is to do (besides determining the vertices for AA + % and BB)? Well, make sure, that we can arrange them in + % the desired order. This involves a periodic "next vertex" + % algorithm which might either go forward + % or backward. + % + % sort according to depth. + % To do so, prepare macros \PA,\PB,\PC for use in + % \pgfplotsutilsortthree. FORMAT: + % \PA={<sortkey>pt <originalindex>} + \edef\PA{\pgfplotspatchvertexdepth pt A}% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@qtri@B\endvertex + \edef\PB{\pgfplotspatchvertexdepth pt B}% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@qtri@C\endvertex + \edef\PC{\pgfplotspatchvertexdepth pt C}% + \pgfplotsutilsortthree\PA\PB\PC + \def\toCHAR##1pt ##2{##2}% get original index + % + \edef\Pcur{\expandafter\toCHAR\PB}%% + \edef\Pnext{\csname pgfplots@qtri@next@\Pcur\endcsname}% + \edef\Pnext{\csname pgfplots@qtri@next@\Pnext\endcsname}% + \if\Pnext\PA + % ok, next(next(AA)) = BB. + % that means we have to advance forward. + \def\Pnextseq{}% + \else + % well, since we have a triangle, there only remains + % the backwards direction. + \def\Pnextseq{r}% + \fi +%\message{FOREGROUND VERTEX = \PA.^^J}% +%\message{SECOND NEAREST VERTEX = \PB.^^J}% + \fi +} +\def\pgfplotspatchclass@tri@to@coonspatch@findshadingsequence@for@depth@no@op{% + \def\Pcur{A}% + \def\Pnextseq{}% +} + +% bilinear is the same as 'rectangle', but it uses a different shader. +\pgfplotsdeclarepatchclass{bilinear}{% + allow matrix=1, + new=\def\pgfplotspatchclass@rect@no{0}, + set next vertex={% + \ifcase\pgfplotspatchclass@rect@no\relax + \edef\pgfplotspatchclass@rect@A{#1}% + \def\pgfplotspatchclass@rect@no{1}% + \or + \edef\pgfplotspatchclass@rect@B{#1}% + \def\pgfplotspatchclass@rect@no{2}% + \or + \edef\pgfplotspatchclass@rect@C{#1}% + \def\pgfplotspatchclass@rect@no{3}% + \or + \edef\pgfplotspatchclass@rect@D{#1}% + \def\pgfplotspatchclass@rect@no{0}% + \pgfplotspatchready% + \fi + }, + first vertex=\expandafter\pgfplotspatchvertex\pgfplotspatchclass@rect@A\endvertex, + foreach vertex={% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@rect@A\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@rect@B\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@rect@C\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@rect@D\endvertex #1% + }, + stream to shader={% + % create a coons patch: + \begingroup + \pgfplotspatchclass@rect@to@coonspatch@findshadingsequence@for@depth + {pgfplotspatchclass@rect@}{\Pcur}{\Pnextseq}% + % + \pgfutil@namelet{Pstart}{pgfplotspatchclass@rect@\Pcur}% + \def\pgfplots@coonsedge{% +%\message{EDGE \Pcur^^J}% + \expandafter\let\expandafter\PA\csname pgfplotspatchclass@rect@\Pcur\endcsname + \edef\Pcur{\csname pgfplots@rect@\Pnextseq next@\Pcur\endcsname}% +%\message{---> \Pcur^^J}% + \expandafter\let\expandafter\PB\csname pgfplotspatchclass@rect@\Pcur\endcsname + \ifx\PA\Pstart + \expandafter\pgfplotspatchvertex\PA\endvertex + \let\pgfplots@current@point@meta=\pgfplotspatchvertexmeta + \pgfplotsaxisvisphasetransformpointmeta + \pgfplotslibrarysurfstreamcoord{\pgfqpoint\pgfplotspatchvertexx\pgfplotspatchvertexy}{\pgfplotspointmetatransformed}% + \fi + % + % CONTROL POINT A+1/3(B-A) + \pgfplotslibrarysurfstreamcoord{% + \pgfpointadd + {\pgfqpointscale{0.6666666}{\expandafter\pgfplotspointpatchvertex\PA\endvertex}}% + {\pgfqpointscale{0.3333333}{\expandafter\pgfplotspointpatchvertex\PB\endvertex}}% + }{}% + % CONTROL POINT A+2/3(B-A) + \pgfplotslibrarysurfstreamcoord{% + \pgfpointadd + {\pgfqpointscale{0.3333333}{\expandafter\pgfplotspointpatchvertex\PA\endvertex}}% + {\pgfqpointscale{0.6666666}{\expandafter\pgfplotspointpatchvertex\PB\endvertex}}% + }{}% + \ifx\PB\Pstart + \else + \expandafter\pgfplotspatchvertex\PB\endvertex + \let\pgfplots@current@point@meta=\pgfplotspatchvertexmeta + \pgfplotsaxisvisphasetransformpointmeta + \pgfplotslibrarysurfstreamcoord{\pgfqpoint\pgfplotspatchvertexx\pgfplotspatchvertexy}{\pgfplotspointmetatransformed}% + \fi + }% + % + \pgfplots@coonsedge + % + \pgfplots@coonsedge + % + \pgfplots@coonsedge + % + \pgfplots@coonsedge + % + \endgroup + },% + fill path={% + \pgfpathmoveto{\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@rect@A\endvertex}% + \pgfpathlineto{\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@rect@B\endvertex}% + \pgfpathlineto{\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@rect@C\endvertex}% + \pgfpathlineto{\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@rect@D\endvertex}% + \pgfpathclose + }, + triangulate={% + \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}% + % + \let\pgfplotsplothandlermesh@patchclass@=\pgfplotsplothandlermesh@patchclass + \def\pgfplotsplothandlermesh@patchclass{triangle}% + \pgfplotspatchclass{\pgfplotsplothandlermesh@patchclass}{new}% + \pgfplotspatchclass{\pgfplotsplothandlermesh@patchclass}{set edge visible}01% + \pgfplotspatchclass{\pgfplotsplothandlermesh@patchclass}{set edge visible}10% + \pgfplotspatchclass{\pgfplotsplothandlermesh@patchclass}{set edge visible}20% + % Ok. Now create 4 triangles. The ordering is not arbitrary + % (unless z buffer=sort is in effect). Let's assume that the + % AB edge is BACKGROUND and the CD edge is FOREGROUND. Then + % this sequence here should have approximately the same depth + % ordering: + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@rect@A}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@rect@B}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@rect@M}% + % + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@rect@B}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@rect@C}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@rect@M}% + % + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@rect@D}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@rect@A}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@rect@M}% + % + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@rect@C}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@rect@D}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@rect@M}% + \let\pgfplotsplothandlermesh@patchclass=\pgfplotsplothandlermesh@patchclass@ + },% + recursive refine@={% + \pgfplotspatchclass@rect@refine@{#1}% + },% + serialize except vertices=\let\pgfplotsretval\pgfutil@empty,% + deserialize except vertices=, + get pdf shading type=6, + get num vertices=4, +}% + +\pgfplotsdeclarepatchclass{rectangle}{% + recursive refine@={% + \pgfplotspatchclass@rect@refine@{#1}% + },% +} +\def\pgfplotspatchclass@rect@refine@#1{% + \pgfplotspatchclass@rect@recursiverefine@newnames + % + \pgfplotspatchclass{\pgfplotspatchclassname}{new}% + %-------------------------------------------------- + % \pgfplotspatchclass{\pgfplotspatchclassname}{set edge visible}01% + % \pgfplotspatchclass{\pgfplotspatchclassname}{set edge visible}11% + % \pgfplotspatchclass{\pgfplotspatchclassname}{set edge visible}20% + %-------------------------------------------------- + % The ordering is not arbitrary + % (unless z buffer=sort is in effect). Let's assume that the + % AB edge is BACKGROUND and the CD edge is FOREGROUND. Then + % this sequence here should have approximately the same depth + % ordering: + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@rect@A\times{0.25}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@rect@B\times{0.25}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@rect@C\times{0.25}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@rect@D\times{0.25}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@rect@M + % + \expandafter\pgfplotspatchclass@rect@refine@@\expandafter{\pgfplotspatchclass@rect@M}{#1}% +} +\def\pgfplotspatchclass@rect@refine@@#1#2{% + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@rect@A\times{0.5}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@rect@B\times{0.5}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@rect@AB + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@rect@A\times{0.5}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@rect@D\times{0.5}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@rect@DA + % + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@rect@A@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@rect@AB}% + \pgfplotsplothandlermesh@setnextvertex{#1}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@rect@DA}% + #2\pgfplotspatchclass@rect@recursiverefine@newnames + % + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@rect@A\times{0.5}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@rect@B\times{0.5}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@rect@AB + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@rect@B\times{0.5}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@rect@C\times{0.5}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@rect@BC + % + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@rect@AB}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@rect@B@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@rect@BC}% + \pgfplotsplothandlermesh@setnextvertex{#1}% + #2\pgfplotspatchclass@rect@recursiverefine@newnames + % + % + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@rect@C\times{0.5}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@rect@D\times{0.5}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@rect@CD + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@rect@B\times{0.5}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@rect@C\times{0.5}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@rect@BC + % + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@rect@BC}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@rect@C@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@rect@CD}% + \pgfplotsplothandlermesh@setnextvertex{#1}% + #2\pgfplotspatchclass@rect@recursiverefine@newnames + % + % + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@rect@C\times{0.5}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@rect@D\times{0.5}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@rect@CD + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@rect@D\times{0.5}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@rect@A\times{0.5}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@rect@DA + % + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@rect@CD}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@rect@D@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@rect@DA}% + \pgfplotsplothandlermesh@setnextvertex{#1}% + #2\pgfplotspatchclass@rect@recursiverefine@newnames + % +}% + +\def\pgfplotspatchclass@rect@recursiverefine@newnames{% + \let\pgfplotspatchclass@rect@A@=\pgfplotspatchclass@rect@A% + \let\pgfplotspatchclass@rect@B@=\pgfplotspatchclass@rect@B% + \let\pgfplotspatchclass@rect@C@=\pgfplotspatchclass@rect@C% + \let\pgfplotspatchclass@rect@D@=\pgfplotspatchclass@rect@D% +}% + +\def\pgfplots@biquad@next@A{E} +\def\pgfplots@biquad@next@B{F} +\def\pgfplots@biquad@next@C{G} +\def\pgfplots@biquad@next@D{H} +\def\pgfplots@biquad@next@E{B} +\def\pgfplots@biquad@next@F{C} +\def\pgfplots@biquad@next@G{D} +\def\pgfplots@biquad@next@H{A} + + +\def\pgfplots@biquad@rnext@A{H} +\def\pgfplots@biquad@rnext@B{E} +\def\pgfplots@biquad@rnext@C{F} +\def\pgfplots@biquad@rnext@D{G} +\def\pgfplots@biquad@rnext@E{A} +\def\pgfplots@biquad@rnext@F{B} +\def\pgfplots@biquad@rnext@G{C} +\def\pgfplots@biquad@rnext@H{D} + +\def\pgfplotspatchclass@biquad@recursiverefine@newnames{% + \let\pgfplotspatchclass@biquad@A@=\pgfplotspatchclass@biquad@A% + \let\pgfplotspatchclass@biquad@B@=\pgfplotspatchclass@biquad@B% + \let\pgfplotspatchclass@biquad@C@=\pgfplotspatchclass@biquad@C% + \let\pgfplotspatchclass@biquad@D@=\pgfplotspatchclass@biquad@D% + \let\pgfplotspatchclass@biquad@E@=\pgfplotspatchclass@biquad@E% + \let\pgfplotspatchclass@biquad@F@=\pgfplotspatchclass@biquad@F% + \let\pgfplotspatchclass@biquad@G@=\pgfplotspatchclass@biquad@G% + \let\pgfplotspatchclass@biquad@H@=\pgfplotspatchclass@biquad@H% + \let\pgfplotspatchclass@biquad@I@=\pgfplotspatchclass@biquad@I% +}% + + +% mathematica shape functions parameterized in +% (xi,eta) in [-1,1]x[-1,1]: +%f[xi_, eta_] = +% a*1/4*(1 - xi) (1 - eta) xi*eta + +% b 1/4 (-1 - xi) (1 - eta) xi*eta + +% c* 1/4 (-1 - xi) (-1 - eta) xi*eta + +% d *1/4 (1 - xi) (-1 - eta) xi*eta + +% e * 1/2 (xi^2 - 1) (1 - eta) eta + +% f*1/2 (-1 - xi) (eta^2 - 1) xi + +% g* -1/2 (1 - xi^2) (-1 - eta) eta + +% h* -1/2 (1 - xi) (1 - eta^2) xi + +% 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) + \expandafter\edef\csname pgfplotspatchclass@biquad@\pgfplotspatchclass@biquad@no\endcsname{#1}% + \if I\pgfplotspatchclass@biquad@no + \def\pgfplotspatchclass@biquad@no{A}% + \pgfplotspatchready + \else + \expandafter\let\expandafter\pgfplotspatchclass@biquad@no\csname pgfpptchindexnext@\pgfplotspatchclass@biquad@no\endcsname + \fi + }, + first vertex=\expandafter\pgfplotspatchvertex\pgfplotspatchclass@biquad@A\endvertex, + foreach 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% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@biquad@E\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@biquad@F\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@biquad@G\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@biquad@H\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@biquad@I\endvertex #1% + }, + fill path={% + \begingroup + % Visualize the patch boundary using four bezier curves. + % + % This involves a change from Lagrange to bezier + % representation of the boundary curves. + % + % Furthermore, pdf supports only **cubic** bezier curves. What + % I am doing here is + % a) change of basis from 3-point lagrange ---> 3 point quadratic bezier + % b) expression 3 point quadratic bezier ----> 4 point cubic bezier + % + % INPUT: + % 3 langrange points (i.e. the patch passes through them) + % \PA,\PB,\PC (start,middle,end) + % + % OUTPUT: + % \PA,bezier control 1, bezier control 2, \PC. + % + \def\pgfplots@edge{% + \ifx\pgfplotspatchclass@biquad@A\PA + \pgfpathmoveto{\expandafter\pgfplotspointpatchvertex\PA\endvertex}% + \fi + \pgfpathcurveto {% + \pgfpointadd + {\pgfqpointscale{1.333333}{\expandafter\pgfplotspointpatchvertex\PB\endvertex}}% + {\pgfqpointscale{-0.333333}{\expandafter\pgfplotspointpatchvertex\PC\endvertex}}% + }{% + \pgfpointadd + {\pgfqpointscale{1.333333}{\expandafter\pgfplotspointpatchvertex\PB\endvertex}}% + {\pgfqpointscale{-0.333333}{\expandafter\pgfplotspointpatchvertex\PA\endvertex}}% + }{% + \expandafter\pgfplotspointpatchvertex\PC\endvertex + }% + }% + \let\PA=\pgfplotspatchclass@biquad@A + \let\PB=\pgfplotspatchclass@biquad@E + \let\PC=\pgfplotspatchclass@biquad@B + \pgfplots@edge + % + \let\PA=\pgfplotspatchclass@biquad@B + \let\PB=\pgfplotspatchclass@biquad@F + \let\PC=\pgfplotspatchclass@biquad@C + \pgfplots@edge + % + \let\PA=\pgfplotspatchclass@biquad@C + \let\PB=\pgfplotspatchclass@biquad@G + \let\PC=\pgfplotspatchclass@biquad@D + \pgfplots@edge + % + \let\PA=\pgfplotspatchclass@biquad@D + \let\PB=\pgfplotspatchclass@biquad@H + \let\PC=\pgfplotspatchclass@biquad@A + \pgfplots@edge + \endgroup + \pgfpathclose + }, + %-------------------------------------------------- + % stroke path={% + % \ifx\pgfplotspatchclass@biquade@AB\relax + % \pgfpathmoveto{\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@biquad@A\endvertex}% + % \pgfpathlineto{\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@biquad@B\endvertex}% + % \pgfpathlineto{\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@biquad@C\endvertex}% + % \pgfpathclose + % \else + % \if1\pgfplotspatchclass@biquade@AB + % \pgfpathmoveto{\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@biquad@A\endvertex}% + % \pgfpathlineto{\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@biquad@B\endvertex}% + % \fi + % \if1\pgfplotspatchclass@biquade@BC + % \pgfpathmoveto{\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@biquad@B\endvertex}% + % \pgfpathlineto{\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@biquad@C\endvertex}% + % \fi + % \if1\pgfplotspatchclass@biquade@CA + % \pgfpathmoveto{\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@biquad@C\endvertex}% + % \pgfpathlineto{\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@biquad@A\endvertex}% + % \fi + % \fi + % }, + %-------------------------------------------------- + stream to shader={% + \begingroup + \pgfplotspatchclass@rect@to@coonspatch@findshadingsequence@for@depth + {pgfplotspatchclass@biquad@}{\Pcur}{\Pnextseq}% + % + \let\Pstartidx\Pcur% + \pgfutil@namelet{Pstart}{pgfplotspatchclass@biquad@\Pcur}% + % + % create a tensor cubic bezier patch. + % + % Again, the outer boundary involves a map from 3 point lagrange + % representation to 4 point cubic bezier. + % + % The main complication arises to support the INNER node (\pgfplotspatchclass@biquad@I) . + % We need the four inner bezier control points to get it + % correctly. + % + % this here handles only the OUTER shaper. It is the same as + % for 'fill path'. + % See 'fill path' for docs. + % + \pgfplotspatchclass@biquad@coonsedge + % + \pgfplotspatchclass@biquad@coonsedge + % + \pgfplotspatchclass@biquad@coonsedge + % + \pgfplotspatchclass@biquad@coonsedge + % + % FIXME: + % \pgfplotspatchclass@biquad@innercontrolpoints + % + \endgroup + },% + triangulate={% + \let\pgfplotsplothandlermesh@patchclass@=\pgfplotsplothandlermesh@patchclass + \def\pgfplotsplothandlermesh@patchclass{triangle}% + \pgfplotspatchclass{\pgfplotsplothandlermesh@patchclass}{new}% + \pgfplotspatchclass{\pgfplotsplothandlermesh@patchclass}{set edge visible}01% + \pgfplotspatchclass{\pgfplotsplothandlermesh@patchclass}{set edge visible}10% + \pgfplotspatchclass{\pgfplotsplothandlermesh@patchclass}{set edge visible}20% + % Ok. Now create 4 triangles. The ordering is not arbitrary + % (unless z buffer=sort is in effect). Let's assume that the + % AB edge is BACKGROUND and the CD edge is FOREGROUND. Then + % this sequence here should have approximately the same depth + % ordering: + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@A}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@E}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@I}% + % + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@H}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@A}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@I}% + % + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@E}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@B}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@I}% + % + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@B}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@F}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@I}% + % + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@D}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@H}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@I}% + % + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@D}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@G}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@I}% + % + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@G}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@C}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@I}% + % + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@C}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@F}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@I}% + \let\pgfplotsplothandlermesh@patchclass=\pgfplotsplothandlermesh@patchclass@ + },% + %-------------------------------------------------- + % set edge visible={% + % \ifcase#1 + % \edef\pgfplotspatchclass@biquade@AB{#2}% + % \or + % \edef\pgfplotspatchclass@biquade@BC{#2}% + % \or + % \edef\pgfplotspatchclass@biquade@CA{#2}% + % \fi + % }, + %-------------------------------------------------- + serialize except vertices={% + \ifx\pgfplotspatchclass@biquade@AB\relax + \let\pgfplotsretval\pgfutil@empty% + \else + \edef\pgfplotsretval{% + \noexpand\def\noexpand\pgfplotspatchclass@biquade@AB{\pgfplotspatchclass@biquade@AB}% + \noexpand\def\noexpand\pgfplotspatchclass@biquade@BC{\pgfplotspatchclass@biquade@BC}% + \noexpand\def\noexpand\pgfplotspatchclass@biquade@CA{\pgfplotspatchclass@biquade@CA}% + }% + \fi + },% + deserialize except vertices=% + \let\pgfplotspatchclass@biquade@AB\relax + #1, + recursive refine@={% + \pgfplotspatchclass@biquad@recursiverefine@newnames + % + \pgfplotspatchclass{\pgfplotspatchclassname}{new}% + %-------------------------------------------------- + % \pgfplotspatchclass{\pgfplotspatchclassname}{set edge visible}01% + % \pgfplotspatchclass{\pgfplotspatchclassname}{set edge visible}11% + % \pgfplotspatchclass{\pgfplotspatchclassname}{set edge visible}20% + %-------------------------------------------------- + % The ordering is not arbitrary + % (unless z buffer=sort is in effect). Let's assume that the + % AB edge is BACKGROUND and the CD edge is FOREGROUND. Then + % this sequence here should have approximately the same depth + % ordering: + % + % I used the reference triangle and shape functions as listed in + % http://www.colorado.edu/engineering/CAS/courses.d/IFEM.d/, + % see above for the definition of f[xi,eta] + % + % N[{f[-1/2, -1], f[0, -1/2], f[-1/2, 0], f[-1, -1/2], f[-1/2, -1/2]}] + % {0.375` a - 0.125` b + 0.75` e, + % 0.375` e - 0.125` g + 0.75` i, + % -0.125` f + 0.375` h + 0.75` i, + % 0.375` a - 0.125` d + 0.75` h, + % 0.140625` a - 0.046875` b + 0.015625` c - 0.046875` d + + % 0.28125` e - 0.09375` f - 0.09375` g + 0.28125` h + + % 0.5625` i} + %-------------------------------------------------- + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@A\times{0.375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@B\times{-0.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@E\times{0.75}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@biquad@AE + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@E\times{0.375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@G\times{-0.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@I\times{0.75}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@biquad@EI + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@F\times{-0.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@H\times{0.375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@I\times{0.75}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@biquad@HI + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@A\times{0.375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@D\times{-0.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@H\times{0.75}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@biquad@AH + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@A\times{0.140625}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@B\times{-0.046875}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@C\times{0.015625}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@D\times{-0.046875}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@E\times{0.28125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@F\times{-0.09375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@G\times{-0.09375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@H\times{0.28125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@I\times{0.5625}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@biquad@AEIH + % + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@A@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@E@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@I@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@H@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@AE}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@EI}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@HI}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@AH}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@AEIH}% + % + #1\pgfplotspatchclass@biquad@recursiverefine@newnames + % + % N[{f[1/2, -1], f[1, -1/2], f[1/2, 0], f[1/2, -1/2]}] + % {-0.125` a + 0.375` b + 0.75` e, + % 0.375` b - 0.125` c + 0.75` f, + % 0.375` f - 0.125` h + 0.75` i, + % -0.046875 a + 0.140625 b - 0.046875 c + 0.015625 d + 0.28125 e + 0.28125 f - 0.09375 g - 0.09375 h + 0.5625 i} + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@A\times{-0.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@B\times{0.375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@E\times{0.75}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@biquad@EB + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@B\times{0.375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@C\times{-0.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@F\times{0.75}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@biquad@BF + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@F\times{0.375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@H\times{-0.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@I\times{0.75}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@biquad@FI + % + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@E\times{0.375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@G\times{-0.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@I\times{0.75}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@biquad@EI + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@A\times{-0.046875}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@B\times{0.140625}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@C\times{-0.046875}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@D\times{0.015625}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@E\times{0.28125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@F\times{0.28125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@G\times{-0.09375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@H\times{-0.09375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@I\times{0.5625}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@biquad@EBFI + % + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@E@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@B@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@F@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@I@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@EB}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@BF}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@FI}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@EI}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@EBFI}% + % + #1\pgfplotspatchclass@biquad@recursiverefine@newnames + % + % + % N[ {f[1, 1/2], f[1/2, 1], f[0, 1/2], f[1/2, 1/2]}] + % {-0.125` b + 0.375` c + 0.75` f, + % 0.375` c - 0.125` d + 0.75` g, + % -0.125` e + 0.375` g + 0.75` i, + % 0.015625` a - 0.046875` b + 0.140625` c - 0.046875` d - 0.09375` e + 0.28125` f + 0.28125` g - 0.09375` h + 0.5625` i} + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@B\times{-0.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@C\times{0.375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@F\times{0.75}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@biquad@FC + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@C\times{0.375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@D\times{-0.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@G\times{0.75}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@biquad@CG + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@E\times{-0.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@G\times{0.375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@I\times{0.75}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@biquad@GI + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@F\times{0.375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@H\times{-0.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@I\times{0.75}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@biquad@FI + % + % + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@A\times{0.015625}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@B\times{-0.046875}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@C\times{0.140625}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@D\times{-0.046875}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@E\times{-0.09375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@F\times{0.28125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@G\times{0.28125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@H\times{-0.09375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@I\times{0.5625}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@biquad@IFCG + % + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@I@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@F@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@C@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@G@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@FI}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@FC}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@CG}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@GI}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@IFCG}% + % + #1\pgfplotspatchclass@biquad@recursiverefine@newnames + % + % + % N[{f[-1/2, 1], f[-1, 1/2], f[-1/2, 1/2]}] + % {-0.125 c + 0.375 d + 0.75 g, + % -0.125 a + 0.375 d + 0.75 h, + % -0.046875 a + 0.015625 b - 0.046875 c + 0.140625 d - 0.09375 e - 0.09375 f + 0.28125 g + 0.28125 h + 0.5625 i} + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@C\times{-0.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@D\times{0.375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@G\times{0.75}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@biquad@GD + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@A\times{-0.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@D\times{0.375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@H\times{0.75}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@biquad@DH + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@E\times{-0.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@G\times{0.375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@I\times{0.75}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@biquad@GI + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@F\times{-0.125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@H\times{0.375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@I\times{0.75}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@biquad@HI + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@A\times{-0.046875}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@B\times{0.015625}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@C\times{-0.046875}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@D\times{0.140625}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@E\times{-0.09375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@F\times{-0.09375}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@G\times{0.28125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@H\times{0.28125}% + \expandafter\pgfplotspatchvertexadd\pgfplotspatchclass@biquad@I\times{0.5625}% + \pgfplotspatchvertexfinish\pgfplotspatchclass@biquad@HIGD + % + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@H@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@I@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@G@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@D@}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@HI}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@GI}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@GD}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@DH}% + \expandafter\pgfplotsplothandlermesh@setnextvertex\expandafter{\pgfplotspatchclass@biquad@HIGD}% + % + #1% + % + },% + get pdf shading type=6, + get num vertices=9, +}% + +% see docs in 'biquadratic::stream to shader' for details. +% PRECONDITION: to be used inside of 'stream to shader'. +\def\pgfplotspatchclass@biquad@coonsedge{% +%\message{EDGE \Pcur^^J}% + \expandafter\let\expandafter\PA\csname pgfplotspatchclass@biquad@\Pcur\endcsname + \edef\Pcur{\csname pgfplots@biquad@\Pnextseq next@\Pcur\endcsname}% + \expandafter\let\expandafter\PB\csname pgfplotspatchclass@biquad@\Pcur\endcsname +%\message{---> \Pcur^^J}% + \edef\Pcur{\csname pgfplots@biquad@\Pnextseq next@\Pcur\endcsname}% + \expandafter\let\expandafter\PC\csname pgfplotspatchclass@biquad@\Pcur\endcsname +%\message{---> \Pcur^^J}% + \ifx\PA\Pstart + \expandafter\pgfplotspatchvertex\PA\endvertex + \let\pgfplots@current@point@meta=\pgfplotspatchvertexmeta + \pgfplotsaxisvisphasetransformpointmeta + \pgfplotslibrarysurfstreamcoord{\pgfqpoint\pgfplotspatchvertexx\pgfplotspatchvertexy}{\pgfplotspointmetatransformed}% + \fi + \pgfplotslibrarysurfstreamcoord{% + \pgfpointadd + {\pgfqpointscale{1.333333}{\expandafter\pgfplotspointpatchvertex\PB\endvertex}}% + {\pgfqpointscale{-0.333333}{\expandafter\pgfplotspointpatchvertex\PC\endvertex}}% + }{}% + \pgfplotslibrarysurfstreamcoord{% + \pgfpointadd + {\pgfqpointscale{1.333333}{\expandafter\pgfplotspointpatchvertex\PB\endvertex}}% + {\pgfqpointscale{-0.333333}{\expandafter\pgfplotspointpatchvertex\PA\endvertex}}% + }{}% + \ifx\PC\Pstart + \else + \expandafter\pgfplotspatchvertex\PC\endvertex + \let\pgfplots@current@point@meta=\pgfplotspatchvertexmeta + \pgfplotsaxisvisphasetransformpointmeta + \pgfplotslibrarysurfstreamcoord{\pgfqpoint\pgfplotspatchvertexx\pgfplotspatchvertexy}{\pgfplotspointmetatransformed}% + \fi +}% +\def\pgfplotspatchclass@biquad@innercontrolpoints{% + \begingroup + % + % This here computes the FOUR INNER CONTROL POINTS of a tensor + % cubic bezier patch (Shading Type 7). + % + % + % the following point coordinates have been acquired from + % biquadratic::recursive refine. See above for documentation. + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexaddXY\pgfplotspatchclass@biquad@A\times{0.375}% + \expandafter\pgfplotspatchvertexaddXY\pgfplotspatchclass@biquad@B\times{-0.125}% + \expandafter\pgfplotspatchvertexaddXY\pgfplotspatchclass@biquad@E\times{0.75}% + \pgfplotspatchvertexfinishXY\pgfplotspatchclass@biquad@AE + % + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexaddXY\pgfplotspatchclass@biquad@F\times{-0.125}% + \expandafter\pgfplotspatchvertexaddXY\pgfplotspatchclass@biquad@H\times{0.375}% + \expandafter\pgfplotspatchvertexaddXY\pgfplotspatchclass@biquad@I\times{0.75}% + \pgfplotspatchvertexfinishXY\pgfplotspatchclass@biquad@HI + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexaddXY\pgfplotspatchclass@biquad@A\times{-0.125}% + \expandafter\pgfplotspatchvertexaddXY\pgfplotspatchclass@biquad@B\times{0.375}% + \expandafter\pgfplotspatchvertexaddXY\pgfplotspatchclass@biquad@E\times{0.75}% + \pgfplotspatchvertexfinishXY\pgfplotspatchclass@biquad@EB + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexaddXY\pgfplotspatchclass@biquad@F\times{0.375}% + \expandafter\pgfplotspatchvertexaddXY\pgfplotspatchclass@biquad@H\times{-0.125}% + \expandafter\pgfplotspatchvertexaddXY\pgfplotspatchclass@biquad@I\times{0.75}% + \pgfplotspatchvertexfinishXY\pgfplotspatchclass@biquad@FI + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexaddXY\pgfplotspatchclass@biquad@C\times{0.375}% + \expandafter\pgfplotspatchvertexaddXY\pgfplotspatchclass@biquad@D\times{-0.125}% + \expandafter\pgfplotspatchvertexaddXY\pgfplotspatchclass@biquad@G\times{0.75}% + \pgfplotspatchvertexfinishXY\pgfplotspatchclass@biquad@CG + % + \pgfplotspatchvertexaccumstart + \expandafter\pgfplotspatchvertexaddXY\pgfplotspatchclass@biquad@C\times{-0.125}% + \expandafter\pgfplotspatchvertexaddXY\pgfplotspatchclass@biquad@D\times{0.375}% + \expandafter\pgfplotspatchvertexaddXY\pgfplotspatchclass@biquad@G\times{0.75}% + \pgfplotspatchvertexfinishXY\pgfplotspatchclass@biquad@GD + % + % + \let\PA=\pgfplotspatchclass@biquad@AE + \let\PB=\pgfplotspatchclass@biquad@HI + \let\PC=\pgfplotspatchclass@biquad@GD + \pgfplotspatchclass@biquad@innercontrolpoints@PREPARE\pgfplotspatchclass@biquad@@A\pgfplotspatchclass@biquad@@D + % + \let\PA=\pgfplotspatchclass@biquad@EB + \let\PB=\pgfplotspatchclass@biquad@FI + \let\PC=\pgfplotspatchclass@biquad@CG + \pgfplotspatchclass@biquad@innercontrolpoints@PREPARE\pgfplotspatchclass@biquad@@B\pgfplotspatchclass@biquad@@C + % + % + \let\Pcur=\Pstartidx + \pgfplotslibrarysurfstreamcoord{\csname pgfplotspatchclass@biquad@@\Pcur\endcsname}{}% + % + \edef\Pcur{\csname pgfplots@rect@\Pnextseq next@\Pcur\endcsname}% + \pgfplotslibrarysurfstreamcoord{\csname pgfplotspatchclass@biquad@@\Pcur\endcsname}{}% + % + \edef\Pcur{\csname pgfplots@rect@\Pnextseq next@\Pcur\endcsname}% + \pgfplotslibrarysurfstreamcoord{\csname pgfplotspatchclass@biquad@@\Pcur\endcsname}{}% + % + \edef\Pcur{\csname pgfplots@rect@\Pnextseq next@\Pcur\endcsname}% + \pgfplotslibrarysurfstreamcoord{\csname pgfplotspatchclass@biquad@@\Pcur\endcsname}{}% + \endgroup +}% +\def\pgfplotspatchclass@biquad@innercontrolpoints@PREPARE#1#2{% + \pgfpointadd + {\pgfqpointscale{1.333333}{\expandafter\pgfplotspointpatchvertex\PB\endvertex}}% + {\pgfqpointscale{-0.333333}{\expandafter\pgfplotspointpatchvertex\PC\endvertex}}% + \edef#1{\global\pgf@x=\the\pgf@x\space\global\pgf@y=\the\pgf@y\space}% + % + \pgfpointadd + {\pgfqpointscale{1.333333}{\expandafter\pgfplotspointpatchvertex\PB\endvertex}}% + {\pgfqpointscale{-0.333333}{\expandafter\pgfplotspointpatchvertex\PA\endvertex}}% + \edef#2{\global\pgf@x=\the\pgf@x\space\global\pgf@y=\the\pgf@y\space}% + % +\pgfpathcircle{\expandafter\pgfplotspointpatchvertex\PA\endvertex}{1pt}\pgfusepath{fill}% +\pgfpathcircle{\expandafter\pgfplotspointpatchvertex\PB\endvertex}{1pt}\pgfusepath{fill}% +\pgfpathcircle{\expandafter\pgfplotspointpatchvertex\PC\endvertex}{1pt}\pgfusepath{fill}% +\pgfpathmoveto{\expandafter\pgfplotspointpatchvertex\PA\endvertex}% +\pgfpathcurveto{#1}{#2}{\expandafter\pgfplotspointpatchvertex\PC\endvertex}% +\pgfusepath{stroke}% +} + +% 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) + \expandafter\edef\csname pgfplotspatchclass@coons@\pgfplotspatchclass@coons@no\endcsname{#1}% + \if L\pgfplotspatchclass@coons@no + \def\pgfplotspatchclass@coons@no{A}% + \pgfplotspatchready + \else + \expandafter\let\expandafter\pgfplotspatchclass@coons@no\csname pgfpptchindexnext@\pgfplotspatchclass@coons@no\endcsname + \fi + }, + first vertex=\expandafter\pgfplotspatchvertex\pgfplotspatchclass@coons@A\endvertex, + foreach vertex={% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@coons@A\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@coons@B\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@coons@C\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@coons@D\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@coons@E\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@coons@F\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@coons@G\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@coons@H\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@coons@I\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@coons@J\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@coons@K\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@coons@L\endvertex #1% + }, + foreach cdata vertex={% + % 0, 3, 6, 9 + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@coons@A\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@coons@D\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@coons@G\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@coons@J\endvertex #1% + }, + fill path={% + \pgfpathmoveto {\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@coons@A\endvertex}% + \pgfpathcurveto {\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@coons@B\endvertex}% + {\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@coons@C\endvertex}% + {\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@coons@D\endvertex}% + \pgfpathcurveto {\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@coons@E\endvertex}% + {\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@coons@F\endvertex}% + {\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@coons@G\endvertex}% + \pgfpathcurveto {\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@coons@H\endvertex}% + {\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@coons@I\endvertex}% + {\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@coons@J\endvertex}% + \pgfpathcurveto {\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@coons@K\endvertex}% + {\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@coons@L\endvertex}% + {\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@coons@A\endvertex}% + \pgfpathclose + }, + serialize except vertices=\let\pgfplotsretval\pgfutil@empty,% + deserialize except vertices=, + get pdf shading type=6, + get num vertices=12, + get num cdata vertices=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) + \expandafter\edef\csname pgfplotspatchclass@tensor@\pgfplotspatchclass@tensor@no\endcsname{#1}% + \if P\pgfplotspatchclass@tensor@no + \def\pgfplotspatchclass@tensor@no{A}% + \pgfplotspatchready + \else + \expandafter\let\expandafter\pgfplotspatchclass@tensor@no\csname pgfpptchindexnext@\pgfplotspatchclass@tensor@no\endcsname + \fi + }, + first vertex=\expandafter\pgfplotspatchvertex\pgfplotspatchclass@tensor@A\endvertex, + foreach vertex={% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@tensor@A\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@tensor@B\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@tensor@C\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@tensor@D\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@tensor@E\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@tensor@F\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@tensor@G\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@tensor@H\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@tensor@I\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@tensor@J\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@tensor@K\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@tensor@L\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@tensor@M\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@tensor@N\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@tensor@O\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@tensor@P\endvertex #1% + }, + foreach cdata vertex={% + % 0, 3, 6, 9 + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@tensor@A\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@tensor@D\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@tensor@G\endvertex #1% + \expandafter\pgfplotspatchvertex\pgfplotspatchclass@tensor@J\endvertex #1% + }, + fill path={% + \pgfpathmoveto {\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@tensor@A\endvertex}% + \pgfpathcurveto {\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@tensor@B\endvertex}% + {\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@tensor@C\endvertex}% + {\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@tensor@D\endvertex}% + \pgfpathcurveto {\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@tensor@E\endvertex}% + {\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@tensor@F\endvertex}% + {\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@tensor@G\endvertex}% + \pgfpathcurveto {\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@tensor@H\endvertex}% + {\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@tensor@I\endvertex}% + {\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@tensor@J\endvertex}% + \pgfpathcurveto {\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@tensor@K\endvertex}% + {\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@tensor@L\endvertex}% + {\expandafter\pgfplotspointpatchvertex\pgfplotspatchclass@tensor@A\endvertex}% + \pgfpathclose + }, + serialize except vertices=\let\pgfplotsretval\pgfutil@empty,% + deserialize except vertices=, + get pdf shading type=7, + get num vertices=16, + get num cdata vertices=4, +}% |