88 votes
Accepted

How can we make publication-quality PlotMarkers without version 10?

Based on Oleksandr's excellent design idea here is my re-implementation of his package which offers a much richer set of shapes. UPDATE from July 2022 A minor update: now the form ...
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45 votes

How can we make publication-quality PlotMarkers without version 10?

Fortunately, Wikipedia has the answer, as long as we are content to restrict ourselves to non-intersecting closed polygons. This will probably be an acceptable limitation, given that excessively ...
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  • 22.6k
29 votes
Accepted

Rounding the Corners of a Shape

UPDATE: The previous version of my answer worked, but did not give control on the rounding radius, nor did it fully work with as a starting point for a geometric region for further calculations. Here ...
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  • 61.6k
27 votes

How can we make publication-quality PlotMarkers without version 10?

Here is an alternative answer. Of course, since you answered your own question, you may not need this. But I think the following is a viable alternative that may end up looking comparable, and has ...
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  • 95.3k
21 votes

Filling Space with Pursuit Polygons

The reason that these are called "pursuit polygons" is because they are formed from a dynamical system in which different agents pursue each other. Example: In this image, one agent starts in each ...
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  • 68.9k
20 votes

Rounding the Corners of a Shape

Just wanted to add purely mathematical approach using complex mapping technique. ...
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  • 16.1k
18 votes
Accepted

Pentagonal spiral in Mathematica

Late to the party~ A slight modification to make them more similar: ...
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  • 9,178
17 votes

Rounding the Corners of a Shape

Since you mention that you want to use the rounded polygon in NDSolve[] as a region, you might want to look at the following construction: ...
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16 votes
Accepted

How can I build a 3D slab of hexagons or a thick hexagon mesh?

Does this do what you are looking for? The following function takes a parameterization surface and a region region and tries to ...
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15 votes

Rounding the Corners of a Shape

FilledCurve will do the job because it can be styled by JoinForm: ...
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  • 68.9k
15 votes

Rounding the Corners of a Shape

Here is a more general method for producing polygons with rounded corners. Using a bit of vector algebra and trigonometry, I came up with the following: ...
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15 votes

Pentagonal spiral in Mathematica

This might do the trick: ...
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  • 265k
15 votes

Pentagonal spiral in Mathematica

It's something like this: steps = Table[{r, 1.001 (2 Pi/5)}, {r, 1, 25, 0.1}]; Graphics[{Red, Line@AnglePath[steps]}, Background -> Black]
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  • 68.9k
15 votes
Accepted

A Smooth and Round Voronoi Mesh

1 + 4 We can discretize the rounded Polygon objects and then add the negative of the mesh through Prolog. ...
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  • 33.3k
15 votes
Accepted

On the ordering of the vertices of a polygon

One way to solve the case provided is to apply a DistanceFunction to FindShortestTour. Here, I apply a stiff penalty to the next ...
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  • 16k
14 votes

Polygon mesh: Compute vertex normals for smooth shading

In case the undocumented internal function Region`Mesh`MeshCellNormals[meshregion, dimension] is of use to someone: ...
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  • 220k
14 votes

Rounding an Irregular Polygon

A quick hack, essentially interpolating a point travelling at constant speed on polygon edge and averaging the position over a time interval: ...
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  • 15k
13 votes
Accepted

Plot polygonal surface

(grabbing a lot of code from this answer) This is just to get you started, adding in colors to the final GraphicsComplex should be pretty easy. ...
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  • 63.5k
13 votes
Accepted

Exact symbolic area of an intersection of two polygons with parameters

Having Area generate conditions is informative: ...
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  • 61.6k
12 votes
Accepted

2D Polygon in 3D

Look at the TranslationTransform and RotationTransform ...
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  • 31.1k
11 votes

RegionMember[ ] in polygon

This seems like a bug. It might even be a bug I have reported in the past. In particular, your polygon is slightly degenerate: it has {-3, 16} twice in a row, ...
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  • 15k
11 votes

Unexpected behavior of the procedure `Area` on the object 'Polygon'

EDIT: Reported to WRI as CASE:4237867 - fixed on V12. :) Seems like a bug in my opinion. Consider the following: ...
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  • 15k
11 votes
Accepted

Rounding an Irregular Polygon

Not an anwser, yet. This is how the curve shorthening flow would act on the cells: As you can see, the cells lose contact. So this is probably not what you are looking for, right? Something similar ...
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10 votes
Accepted

Geographics: Can I get a US Map silhouette without the Great Lakes?

This ought to do it: ...
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  • 10.6k
10 votes
Accepted

RegionMember[ ] in polygon

I think it's worth reporting this to support. As a workaround you can numericize the polygon: ...
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  • 124k
10 votes
Accepted

Unexpected behavior of the procedure `Area` on the object 'Polygon'

This is a packed array issue: Area @ Polygon[Developer`ToPackedArray @ {{0, 0}, {4, 0}, {2, 2}, {4, 4}, {0, 4}}] Area[Polygon[{{0, 0}, {4, 0}, {2, 2}, {4, 4}, {...
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  • 124k
9 votes
Accepted

How to make sure polygon is drawn flat in 3D?

A shot in the dark: Reverse the orientation. Hey, it works...but I don't know why...??? Graphics3D[Polygon /@ Reverse@*pentagram /@ (vert[[#]] & /@ ind)] A ...
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  • 220k
9 votes
Accepted

Two 5-gons - One with a concave vertex and another with a convex vertex

H3110 customer, thank you for contacting StackExchange coding service. We propose the following solution to your urgent problem: ...
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  • 111k
9 votes

Plot polygonal surface

...
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  • 123k
9 votes

Filling Space with Pursuit Polygons

Here's an extension of @C.E.'s code to non-triangular polygons - polygons taken from a Voronoi mesh of roughly equidistributed (https://mathematica.stackexchange.com/a/141215/3056) 31 points over a ...
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  • 15k

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