29 votes
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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 ...
MarcoB's user avatar
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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 ...
C. E.'s user avatar
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20 votes

Rounding the Corners of a Shape

Just wanted to add purely mathematical approach using complex mapping technique. ...
yarchik's user avatar
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19 votes

How to create a random zonogon?

We can using Minkowski Sum (RegionDilation) of any Line's from the fixed point ...
cvgmt's user avatar
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18 votes
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Pentagonal spiral in Mathematica

Late to the party~ A slight modification to make them more similar: ...
Wjx's user avatar
  • 9,558
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: ...
J. M.'s missing motivation's user avatar
16 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: ...
J. M.'s missing motivation's user avatar
16 votes
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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 ...
Henrik Schumacher's user avatar
16 votes
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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 ...
Tim Laska's user avatar
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15 votes

Rounding the Corners of a Shape

FilledCurve will do the job because it can be styled by JoinForm: ...
C. E.'s user avatar
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15 votes

Pentagonal spiral in Mathematica

This might do the trick: ...
Mr.Wizard's user avatar
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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]
C. E.'s user avatar
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15 votes
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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. ...
Greg Hurst's user avatar
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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: ...
Michael E2's user avatar
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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: ...
kirma's user avatar
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13 votes
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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. ...
Jason B.'s user avatar
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13 votes
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Exact symbolic area of an intersection of two polygons with parameters

Having Area generate conditions is informative: ...
MarcoB's user avatar
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13 votes
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Reproducing two of Victor Vasarely's colored cuboids (Eroed-Per and Gestalt-Bleu)

Eroed-Per Seed polygon coordinates: ...
kglr's user avatar
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12 votes
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2D Polygon in 3D

Look at the TranslationTransform and RotationTransform ...
rhermans's user avatar
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12 votes
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Create a regular polygon with n vertices given two points

AnglePath. For two point {x1,y1} and {x2,y2}, at first we locate at ...
cvgmt's user avatar
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11 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 ...
kirma's user avatar
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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, ...
kirma's user avatar
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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: ...
kirma's user avatar
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11 votes
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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 ...
Henrik Schumacher's user avatar
10 votes
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RegionMember[ ] in polygon

I think it's worth reporting this to support. As a workaround you can numericize the polygon: ...
Carl Woll's user avatar
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10 votes
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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}, {...
Carl Woll's user avatar
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10 votes
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Programming twisted pyramids based on polygon spirals

Original For two points a and b, we rotation and scale the segment t*a + (1 - t)*b in the ...
cvgmt's user avatar
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10 votes
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How do I draw the vertices of the following hollow polygon and connect them in the way I want?

Use StadiumShape to draw the blank shape. ...
cvgmt's user avatar
  • 72.7k
10 votes

Create a regular polygon with n vertices given two points

You can use CirclePoints. You just need to transform them: ...
flinty's user avatar
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10 votes
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How to create a random zonogon?

You can get some shapes with AffineTransform and Rotate. Define: ...
Vitaliy Kaurov's user avatar

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