Add a new monotonic interpolation plot handler

This handler converts each plot stream command into a curveto command, except for the first, which is converted to the previously specified action. The curveto control points are computed and adjusted so that the resulting curve respects the monotonicity of the points. If a point is a local extremum of the point set, it will also be a local extremum of the generated curve. See https://en.wikipedia.org/wiki/Monotone_cubic_interpolation for an explanation of the algorithm. The last part uses \pgfpathcurveto instead of using Hermitte base functions. The plot handler is also made available to datavisualization through the `smooth monotonic line` visualizer option. Signed-off-by: Julien '_FrnchFrgg_' RIVAUD <[email protected]>
pgf-tikz · Sep 6, 2024 · cecaf07 · cecaf07
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diff --git a/doc/generic/pgf/CHANGELOG.md b/doc/generic/pgf/CHANGELOG.md
@@ -11,6 +11,7 @@ The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/).
 ### Added
 
 - Add `RGB` and `gray` color model support for ConTeXt #1130
+- Add a new monotonic interpolation plot handler #1358
 
 ### Fixed
 

diff --git a/.../pgf/frontendlayer/tikz/libraries/datavisualization/tikzlibrarydatavisualization.code.tex b/.../pgf/frontendlayer/tikz/libraries/datavisualization/tikzlibrarydatavisualization.code.tex
@@ -1538,6 +1538,7 @@
   smooth cycle/.style={@set={\pgfplothandlerclosedcurve}{default label in legend closed path}},
   straight line/.style={@set={\pgfplothandlerlineto}{default label in legend path}},
   straight cycle/.style={@set={\pgfplothandlerpolygon}{default label in legend closed path}},
+  smooth monotonic line/.style={@set={\pgfplothandlermonotonic}{default label in legend path}},
   polygon/.style={straight cycle},% alias
   gap line/.style={@set={\pgfplothandlergaplineto}{default label in legend path}},
   gap cycle/.style={@set={\pgfplothandlergapcycle}{gap circular label in legend line}}

diff --git a/tex/generic/pgf/frontendlayer/tikz/tikz.code.tex b/tex/generic/pgf/frontendlayer/tikz/tikz.code.tex
@@ -1232,6 +1232,7 @@
 % Plot options
 \tikzoption{smooth}[]{\let\tikz@plot@handler=\pgfplothandlercurveto}%
 \tikzoption{smooth cycle}[]{\let\tikz@plot@handler=\pgfplothandlerclosedcurve}%
+\tikzoption{smooth monotonic}[]{\let\tikz@plot@handler=\pgfplothandlermonotonic}%
 \tikzoption{sharp plot}[]{\let\tikz@plot@handler\pgfplothandlerlineto}%
 \tikzoption{sharp cycle}[]{\let\tikz@plot@handler\pgfplothandlerpolygon}%
 

diff --git a/tex/generic/pgf/libraries/pgflibraryplothandlers.code.tex b/tex/generic/pgf/libraries/pgflibraryplothandlers.code.tex
@@ -269,6 +269,135 @@
 }%
 
 
+% This handler converts each plot stream command into a curveto
+% command, except for the first, which is converted to the previously
+% specified action. The curveto control points are computed and adjusted
+% so that the resulting curve respects the monotonicity of the points.
+% If a point is a local extremum of the point set, it will also be
+% a local extremum of the generated curve.
+% This handler treats the x and y direction differently, and expects
+% x values to be monotonic.
+% See https://en.wikipedia.org/wiki/Monotone_cubic_interpolation for an
+% explanation of the algorithm. The last part uses \pgfpathcurveto
+% instead of using Hermitte base functions.
+\pgfdeclareplothandler{\pgfplothandlermonotonic}{}{%
+    point macro=\pgf@plot@monotonic@dopointone,
+    jump macro=\pgf@plot@monotonic@dojump,
+    end macro=\pgf@plot@monotonic@doend
+}%
+
+\def\pgf@plot@monotonic@dojump{%
+    \pgf@plot@monotonic@doend
+    \global\pgf@plot@startedfalse
+    \global\let\pgf@plotstreampoint\pgf@plot@monotonic@dopointone
+}%
+
+\def\pgf@plot@monotonic@dopointone#1{%
+    \pgf@process{#1}%
+    \pgf@plot@first@action{\pgfqpoint{\pgf@x}{\pgf@y}}%
+    \xdef\pgf@plot@monotonic@pointone{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
+    \global\let\pgf@plotstreampoint=\pgf@plot@monotonic@dopointtwo
+}%
+
+\def\pgf@plot@monotonic@dopointtwo#1{%
+    \pgf@process{#1}%
+    \xdef\pgf@plot@monotonic@pointtwo{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
+    % compute vector:
+    \pgf@xa=\pgf@x%
+    \pgf@ya=\pgf@y%
+    \pgf@process{\pgf@plot@monotonic@pointone}%
+    \advance\pgf@xa by-\pgf@x
+    \advance\pgf@ya by-\pgf@y
+    % save left delta
+    \xdef\pgf@plot@monotonic@deltaleft{\pgf@sys@tonumber\pgf@xa}%
+    % compute slope
+    \pgfmathdivide@{\the\pgf@ya}{\the\pgf@xa}%
+    \global\let\pgf@plot@monotonic@rateleft\pgfmathresult
+    % init tangent one
+    \global\let\pgf@plot@monotonic@slopeone\pgf@plot@monotonic@rateleft
+    % prepare for next step
+    \global\let\pgf@plotstreampoint=\pgf@plot@monotonic@dopointthree
+    \global\pgf@plot@startedtrue%
+}%
+
+\def\pgf@plot@monotonic@dopointthree#1{%
+    \pgf@process{#1}%
+    \xdef\pgf@plot@monotonic@pointthree{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
+    % compute vector:
+    \pgf@xa=\pgf@x%
+    \pgf@ya=\pgf@y%
+    \pgf@process{\pgf@plot@monotonic@pointtwo}%
+    \advance\pgf@xa by-\pgf@x
+    \advance\pgf@ya by-\pgf@y
+    % save right delta
+    \xdef\pgf@plot@monotonic@deltaright{\pgf@sys@tonumber\pgf@xa}%
+    % compute slope
+    \pgfmathdivide@{\the\pgf@ya}{\the\pgf@xa}%
+    \global\let\pgf@plot@monotonic@rateright\pgfmathresult
+    % compute tangent slope
+    \pgfmathadd@{\pgf@plot@monotonic@rateleft}{\pgf@plot@monotonic@rateright}%
+    \pgf@xa=\pgfmathresult pt\relax
+    \pgf@xa=0.5\pgf@xa
+    % Fix slopes & draw curve
+    \pgf@plot@monotoniccurveto@fixdraw
+    % Prepare next:
+    \global\let\pgf@plot@monotonic@slopeone\pgf@plot@monotonic@slopetwo
+    \global\let\pgf@plot@monotonic@pointone\pgf@plot@monotonic@pointtwo
+    \global\let\pgf@plot@monotonic@pointtwo\pgf@plot@monotonic@pointthree
+    \global\let\pgf@plot@monotonic@deltaleft\pgf@plot@monotonic@deltaright
+    \global\let\pgf@plot@monotonic@rateleft\pgf@plot@monotonic@rateright
+}%
+
+\def\pgf@plot@monotoniccurveto@fixdraw{%
+    % fix extremums
+    % \pgf@xa is slope two
+    \pgf@ya=\pgf@plot@monotonic@rateleft pt\relax
+    \pgf@yb=\pgf@plot@monotonic@rateright\pgf@ya
+    \ifdim\pgf@yb<0.0001pt\relax
+        \pgf@xa=0pt\relax
+    \else
+    % fix motonicity
+        \pgf@ya=3\pgf@ya
+        \ifdim\pgf@xa>0pt\relax
+            \ifdim\pgf@xa>\pgf@ya \pgf@xa=\pgf@ya\fi
+        \else
+            \ifdim\pgf@xa<\pgf@ya \pgf@xa=\pgf@ya\fi
+        \fi
+        \pgf@ya=\pgf@plot@monotonic@rateright pt\relax
+        \pgf@ya=3\pgf@ya
+        \ifdim\pgf@xa>0pt\relax
+            \ifdim\pgf@xa>\pgf@ya \pgf@xa=\pgf@ya\fi
+        \else
+            \ifdim\pgf@xa<\pgf@ya \pgf@xa=\pgf@ya\fi
+        \fi
+    \fi
+    \xdef\pgf@plot@monotonic@slopetwo{\pgf@sys@tonumber\pgf@xa}%
+    % compute points for left bezier
+    % (\pgf@x,\pgf@y) is point two
+    \pgf@ya=\pgf@plot@monotonic@deltaleft pt\relax
+    \pgf@ya=0.333333\pgf@ya
+    \advance \pgf@x by -\pgf@ya
+    \advance \pgf@y by -\pgf@plot@monotonic@slopetwo\pgf@ya
+    \xdef\pgf@plot@monotonic@supporttwo{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
+    \pgf@process{\pgf@plot@monotonic@pointone}%
+    \advance \pgf@x by \pgf@ya
+    \advance \pgf@y by \pgf@plot@monotonic@slopeone\pgf@ya
+    \xdef\pgf@plot@monotonic@supportone{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
+    % draw left curve:
+    \pgfpathcurveto{\pgf@plot@monotonic@supportone}{\pgf@plot@monotonic@supporttwo}{\pgf@plot@monotonic@pointtwo}%
+}%
+
+\def\pgf@plot@monotonic@doend{%
+    \ifpgf@plot@started
+        % fixdraw needs (\pgf@x,\pgf@y) as point two
+        % and \pgf@xa as slope two
+        \pgf@process{\pgf@plot@monotonic@pointtwo}%
+        \pgf@xa=\pgf@plot@monotonic@rateleft pt\relax
+        \pgf@plot@monotoniccurveto@fixdraw
+    \fi
+}%
+
+