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 ...
- 58.6k
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 ...
- 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 ...
- 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 ...
- 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 ...
- 68.9k
20
votes
Rounding the Corners of a Shape
Just wanted to add purely mathematical approach using complex mapping technique.
...
- 16.1k
18
votes
Accepted
Pentagonal spiral in Mathematica
Late to the party~
A slight modification to make them more similar:
...
- 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:
...
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 ...
- 96.4k
15
votes
Rounding the Corners of a Shape
FilledCurve will do the job because it can be styled by JoinForm:
...
- 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:
...
15
votes
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]
- 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.
...
- 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 ...
- 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:
...
- 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:
...
- 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.
...
- 63.5k
13
votes
Accepted
Exact symbolic area of an intersection of two polygons with parameters
Having Area generate conditions is informative:
...
- 61.6k
12
votes
Accepted
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, ...
- 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:
...
- 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 ...
- 96.4k
10
votes
Accepted
10
votes
Accepted
RegionMember[ ] in polygon
I think it's worth reporting this to support. As a workaround you can numericize the polygon:
...
- 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}, {...
- 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 ...
- 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:
...
- 111k
9
votes
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 ...
- 15k
Only top scored, non community-wiki answers of a minimum length are eligible