Skip to main content

bugs - The unexpected behavior of region calculate


Bug introduce in version 10 and presist in 11.2


In my this answer,I get some overlapped disk like this placed with red arrow point out


But actually that function of diskMake is designed to produce nonoverlapping disk.And I don't think I write a wrong code. :) For this question I have some digs like following:


wordRegion = 

BoundaryDiscretizeGraphics[
Text[Style["21", FontFamily -> "Arial"]], _Text];
disks = {Disk[{-2.4107273705611387`, 3.2155412094306577`},
0.10357806335605606`],
Disk[{-1.4610266485101935`, -0.1848766412849958`},
0.1371293137456506`],
Disk[{3.9597015795674757`, -2.0248306466733403`},
0.21070473733708972`],
Disk[{-1.4133143443551681`, -0.5609218789129127`},
0.2141073441827654`],

Disk[{3.4232452614725304`, 1.1487829210947051`},
0.062352195066279315`]};
disk = Fold[RegionDifference, wordRegion,
BoundaryDiscretizeRegion /@ disks];
r = .3;(*You can change the value to 0.3 or 0.6*)
Row[Magnify[#, 5] & /@
MapThread[
Labeled, {{disk,
Show[Graphics[{Opacity[.2], Red, Disk[{-1.5, 3}, r]}],
RegionDifference[disk,

DiscretizeRegion@Disk[{-1.5, 3}, r]]]}, {Style[
"Before RegionDifference", 6, Red],
Style["After RegionDifference", 6, Blue]}}]]

You can find the small disk I have point out with red arrow will disappear when the $r<0.3$.$\color{red}{\text{I think I get these overlapped disks caused by this}}$.



What about this?And how to avoid it?



Answer



It is confirmed as an improper behavior of RegionDifference by Wolfram support([CASE:3624735]).


Here is their workaround:




Instead of using boundary representation of geometric regions as given below, try using just the geometric regions in geometric computations.



To be specific, here is the solution to this problem. Assuming wordRegion and disks have been initialized as given, and compare the old and new code:


old = Fold[RegionDifference, wordRegion, BoundaryDiscretizeRegion /@ disks];
RegionDifference[old, BoundaryDiscretizeRegion[Disk[{-1.5, 3}, 0.3]]]

enter image description here


new = Fold[RegionDifference, wordRegion, disks];
BoundaryDiscretizeRegion@RegionDifference[new, Disk[{-1.5, 3}, 0.3]]


enter image description here


As you can see, the small circle on the left of 1 is not missing anymore.


Comments

Popular posts from this blog

plotting - Plot 4D data with color as 4th dimension

I have a list of 4D data (x position, y position, amplitude, wavelength). I want to plot x, y, and amplitude on a 3D plot and have the color of the points correspond to the wavelength. I have seen many examples using functions to define color but my wavelength cannot be expressed by an analytic function. Is there a simple way to do this? Answer Here a another possible way to visualize 4D data: data = Flatten[Table[{x, y, x^2 + y^2, Sin[x - y]}, {x, -Pi, Pi,Pi/10}, {y,-Pi,Pi, Pi/10}], 1]; You can use the function Point along with VertexColors . Now the points are places using the first three elements and the color is determined by the fourth. In this case I used Hue, but you can use whatever you prefer. Graphics3D[ Point[data[[All, 1 ;; 3]], VertexColors -> Hue /@ data[[All, 4]]], Axes -> True, BoxRatios -> {1, 1, 1/GoldenRatio}]

plotting - Filling between two spheres in SphericalPlot3D

Manipulate[ SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, Mesh -> None, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], {n, 0, 1}] I cant' seem to be able to make a filling between two spheres. I've already tried the obvious Filling -> {1 -> {2}} but Mathematica doesn't seem to like that option. Is there any easy way around this or ... Answer There is no built-in filling in SphericalPlot3D . One option is to use ParametricPlot3D to draw the surfaces between the two shells: Manipulate[ Show[SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], ParametricPlot3D[{ r {Sin[t] Cos[1.5 Pi], Sin[t] Sin[1.5 Pi], Cos[t]}, r {Sin[t] Cos[0 Pi], Sin[t] Sin[0 Pi], Cos[t]}}, {r, 1, 2 - n}, {t, 0, Pi}, PlotStyle -> Yellow, Mesh -> {2, 15}]], {n, 0, 1}]

plotting - Mathematica: 3D plot based on combined 2D graphs

I have several sigmoidal fits to 3 different datasets, with mean fit predictions plus the 95% confidence limits (not symmetrical around the mean) and the actual data. I would now like to show these different 2D plots projected in 3D as in but then using proper perspective. In the link here they give some solutions to combine the plots using isometric perspective, but I would like to use proper 3 point perspective. Any thoughts? Also any way to show the mean points per time point for each series plus or minus the standard error on the mean would be cool too, either using points+vertical bars, or using spheres plus tubes. Below are some test data and the fit function I am using. Note that I am working on a logit(proportion) scale and that the final vertical scale is Log10(percentage). (* some test data *) data = Table[Null, {i, 4}]; data[[1]] = {{1, -5.8}, {2, -5.4}, {3, -0.8}, {4, -0.2}, {5, 4.6}, {1, -6.4}, {2, -5.6}, {3, -0.7}, {4, 0.04}, {5, 1.0}, {1, -6.8}, {2, -4.7}, {3, -1....