Inconsistent behavior of RegionFunction in ContourPlot and ListContourPlot

[Alexey Popkov]

Hello folks,

When trying to plot a non-covex set of datapoints ListContourPlot produces a
convex graph effectively extrapolating values outside of the actual range of
the original dataset:

pts = {{1, 1, 1}, {2, 1.2, .8}, {3, 1.3, .7}, {3, 2, 1}, {1.5, 2,
1}, {1.5, 1.5, 1}};
epilog = {FaceForm[None], EdgeForm[Red], Polygon[Most /@ pts]};
ListContourPlot[pts, Epilog -> epilog]

(the red polygon shows the actual range of the data).

I need to remove the extrapolated parts of the graph and define
RegionFunction:

leftBorder =
Interpolation[pts[[{5, 6, 1}, {2, 1}]], InterpolationOrder -> 1];
bottomBorder =
Interpolation[pts[[{1, 2, 3}, {1, 2}]], InterpolationOrder -> 1];
ListContourPlot[pts, Epilog -> epilog,
RegionFunction ->
Function[{x, y, z},
x >= leftBorder[y] && y >= bottomBorder[x]]]

But as you see, nothing happens! The drawn region of the plot still contains
areas outside of the area allowed by the RegionFunction.

There is no such problem with ContourPlot:

ContourPlot[Sin[x y], {x, 1, 3}, {y, 1, 2}, Epilog -> epilog,
RegionFunction ->
Function[{x, y, z}, x >= leftBorder[y] && y >= bottomBorder[x]]]

Is it a bug in ListContourPlot? How to achieve consistent behavior of
RegionFunction in both ContourPlot and ListContourPlot?

Thanks in advance!

[djmpark]

It's a disappointment! I thought I would demonstrate John Browne's Grassmann
algebra by using its routines to generate a RegionFunction.

The idea is:
1) There is a simple Grassmann algebra expression that determines whether a
test point is on the same side of a line as a reference point.
2) You can then test if a point is inside a triangle by applying the test to
each side with the opposite vertex as the reference point.
3) You can then triangulate any polygon, convex or not, and test if a point
is in any of the triangles.

For your polygon I generated, by this method, the following RegionFunction:

inPolygon =
Function[{x, y},
(NonNegative[3. - 0.75 x - 1.25 y] &&
NonNegative[1.25 x - 1.25 y] &&
NonNegative[-2. - 0.5 x + 2.5 y]) || (NonNegative[-3. + 2. x] &&
NonNegative[-4.8 + 1.2 x + 2. y] &&
NonNegative[8.8 - 3.2 x - 2. y]) || (NonNegative[2.5 - 1.25 y] &&
NonNegative[-1.83333 + 0.666667 x + 0.416667 y] &&
NonNegative[0.333333 - 0.666667 x + 0.833333 y]) || (NonNegative[
3. - 1. x] && NonNegative[-0.571429 + 1.14286 x - 1.42857 y] &&
NonNegative[-1.42857 - 0.142857 x + 1.42857 y])]

This all works very well and I can even make a dynamic diagram with a spoken
voice that says "Inside" or "Outside" whenever a point locator crosses the
boundary.

But the sad fact is that ListContourPlot has a bug and does not implement
RegionFunction properly - neither your function nor my function. It does
appear to work properly in other plot types: ContourPlot or RegionPlot.

A possible work around is to use RegionPlot with ! inPolygon to mask the
undesired region.

Show[
{ListContourPlot[pts],
RegionPlot[! inPolygon[x, y], {x, 0.4, 3.6}, {y, 0.4, 2.6},
MaxRecursion -> 4,
PlotStyle -> White]},
AspectRatio -> Automatic,
PlotRange -> {{0.5, 3.5}, {0.5, 2.5}},
Frame -> True,
BaseStyle -> {FontSize -> 12},
ImageSize -> 400]


David Park
djm...@comcast.net
http://home.comcast.net/~djmpark/index.html