Re: Inconsistent behavior of RegionFunction in ContourPlot and ListContourPlot

*To*: mathgroup at smc.vnet.net*Subject*: [mg127757] Re: Inconsistent behavior of RegionFunction in ContourPlot and ListContourPlot*From*: "djmpark" <djmpark at comcast.net>*Date*: Sat, 18 Aug 2012 20:37:34 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <12810930.143850.1345276053586.JavaMail.root@m06>

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 djmpark at comcast.net http://home.comcast.net/~djmpark/index.html From: Alexey Popkov [mailto:lehin.p at gmail.com] 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!