Questions tagged [polygons]

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64
votes
3answers
6k views

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

Suppose that for certain reasons we are not yet using Mathematica version 10, or we have a version with buggy PlotMarkers. It is well known that the default markers ...
1
vote
0answers
33 views

Finding the shared edged between two polygons

Imagine I have two convex polygons pol1 and pol2 with a shared edge. Take, as an example, ...
2
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0answers
61 views

Inner polygon approximation

Suppose you want to perform an inner approximation of a planar semialgebraic set by a finite set of polygons. The following is a quick way to yield an approximation but I am not convinced that it is ...
0
votes
1answer
55 views

On the geometric transformations of polygons

Each starry set has the following property: ...
9
votes
1answer
261 views

On the ordering of the vertices of a polygon

Writing: pts = {{1, 0}, {2, 0}, {2, 3}, {3, 3}, {3, 4}, {0, 4}, {0, 3}, {1, 3}, {1, 0}}; Graphics[{Red, Point[pts], Blue, Line[pts]}] we get: and all of this ...
6
votes
3answers
366 views

Efficiently compute Minkowski sum of a 2D Region and a Disc of radius r?

Given a 2D Mathematica Region, e.g. A = Region[RegionDifference[Disk[{0, 0}, 2], Disk[{2, 0}, 1]]], how can I grow the region by an arbitrary radius r? For example, ...
4
votes
1answer
213 views

Programming twisted pyramids based on polygon spirals

I'm interested in polygonal spirals and after reading Filling Space with Pursuit Polygons, I was curious if I could extend the program to create twisted pyramids as 3D-objects. My goal is something ...
1
vote
1answer
82 views

Fix (decompose) Degenerate Polygon (vertex coincides with edge)

The code Polygon[{{0,0},{3,0},{3,3},{1,3},{1,1},{2,2},{2,1},{0,1}}] produces, according to Mathematica, a disconnected polygon with 0 area. The vertex ...
0
votes
0answers
22 views

How to find points within a polygon region [duplicate]

I have a set of points, and a polygon region, I was wondering how can I used RegionMemmber to find the points that are within or outside the region? like their exact coordinates
1
vote
1answer
44 views

Failed to compute the area of a polygon or to use a polygon as a region of NMaximize function

I have a polygon generated by some data. Sometimes, I cannot compute the area of some of the generated polygons and I cannot correctly apply function NMaxmize on ...
1
vote
2answers
58 views

Exact symbolic area of an intersection of two regular pentagons with parameters

The question of finding the area of intwrsection of two regions with parameters has been answered here using and RegionIntersection with delimeter ...
5
votes
1answer
188 views

Exact symbolic area of an intersection of two polygons with parameters

On the one hand, can handle expressions which include parameters, including polygons, for example: Area[Polygon[{{1, 2}, {-1, 1}, {2, 5}, {1, a}}]] returns ...
0
votes
4answers
170 views

How to create a simple polygon

I am trying to create a simple (with no self-intersections) polygon having four given points as vertices, for example to calculate its perimeter later. However, it seems there is nothing for this ...
1
vote
0answers
23 views

Problem NIntegrating over 3D Polygon region with 4 points

I am trying to NIntegrate a non-planar polygonal region defined by 4 points, something like this: ...
11
votes
4answers
194 views

Polygon with an extended Boundary

I have a (not necessarily convex) Polygon, and want to create another Region that can be seen as an extended boundary of the ...
6
votes
2answers
225 views

How does CirclePoints function actually work when drawing a polygon?

By reading that CirclePoints gives the positions of n points equally spaced around the unit circle, I understood that : ...
49
votes
6answers
8k views

Filling a polygon with a pattern of insets

I am trying to fill a shape with diagonal lines. I am aware of Texture, but it rasterizes the fill pattern, which is not desirable. Here was my crack at it: ...
15
votes
3answers
1k views

Rounding an Irregular Polygon

Consider a random irregular convex polygon, for example, the 6-side polygon I want to define a function that, given a certain parameter r (roundness), rounds each ...
14
votes
2answers
676 views

A Smooth and Round Voronoi Mesh

I want the edges of a VoronoiMesh to be smooth and round. I have found the following code from this answer ...
2
votes
0answers
43 views

PolygonCoordinates extract the submits in the “wrong” order

I don't understand why, in the example below, PolygonCoordinates seems unable to correctly extract the summits of a rectangle in the "right" order so we can ...
5
votes
2answers
348 views

How to draw the outline of an icon made of several polygons?

I have an icon defined like that: speakerIcon = Graphics[{ Triangle[{{0, -1}, {1,1},{-1,1}}], Rectangle[{-1, -1},{1, 0}] }, ImageSize->20] I can ...
0
votes
0answers
57 views

Workaround for Opacity + Magnify bug in version 12?

Is there a workaround for the following bug in version 12.0.0. This is in MacOSX. ...
8
votes
0answers
82 views

Order of PolygonCoordinates[] is undefined in Mathematica 12?

Probably I am missing something fundamental. I try to get a polygon's ordered coordinates, but PolygonCoordinates[] yields something pretty unordered. Am I missing some essential function? ...
4
votes
1answer
127 views

Speed-up calculation of Area of Polygons

I have a complicated polygon in the 2d plane, that is an RegionIntersection of RegionUnion of triangles. Finally, I want to ...
1
vote
2answers
200 views

Parametric equation of rolling polygon (cyclogon)

Abraham Gadalla tried (but failed) to post the following question. Why does the red point not continue to follow the square (and the curve) for the full range $0\le x\le 2\pi$? ...
1
vote
1answer
204 views

Point lattice leading to triangle lattice

My main purpose is to eventually generate a triangle lattice from one original point, let's say the origin. So I want to start with the origin and generate 6 points around it, which are the vertices ...
1
vote
0answers
52 views

Deforming a unit square into a cylinder [duplicate]

I am new to Mathematica and I am trying to create a flat unit square in the x-z plane made out of polygons with vertices that divide it into equal-length intervals on each side. Then manipulate this ...
1
vote
0answers
89 views

Combining MeshRegions of generated 3D shapes and RandomPolygons

I am interested in generating 3D a joint BoundaryMeshRegion or a MeshRegion from different shapes and polygons. This works for <...
0
votes
0answers
100 views

Discrete Sum of Function over a Region

I might have completely missed something in my search. I want to discretely sum over a function, $f(x_i,y_j)$ multiplied by some other function $g$ over a general region $S$. $$\sum_{(x,y)\in S}f(x,...
6
votes
3answers
1k views

Polygons crash kernel?

Having some problems Generating random Polygons and then filtering by Area, specifically filter out degenerated polygons with ...
2
votes
0answers
97 views
10
votes
3answers
311 views

RegionMember[ ] in polygon

Bug introduced in 10.0 and fixed in 12.0. I am seeing a difference in RegionMember[ ] testing a point inside a 3-vertex polygon and testing a point inside a more ...
1
vote
3answers
327 views

Creating a MeshRegion object from a Graphics object

I am looking to convert a simple Graphics object that is defined by overlapping polygons into a MeshRegion object. For example, here is code that will create three overlapping triangles ...
1
vote
2answers
67 views

Problem defining a polygon

I have two polygons that are very similar as: ...
3
votes
1answer
167 views

Area of Generalized Koch Snowflake

I asked on the Math Stack Exchange here how I could find the area of a "generalized Koch snowflake". An $n$th generalized Koch snowflake, in my case, is formed almost the same as the Koch snowflake - ...
12
votes
2answers
274 views

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

Bug introduced in 11.3 or earlier and fixed on 12.0. Sometimes get a results, sometimes left unevaluated. For instance ...
5
votes
3answers
310 views

How to get size of each polygon of a Voronoi diagram using Shoelace formula?

The following code gets all vertices of all polygons (mesh cells) of VoronoiMesh[pts]: ...
2
votes
3answers
761 views

Is it possible to draw a hollow circle using polygon?

The question is simple. I have the following commands ...
3
votes
2answers
2k views

Calculate the total length of line segments within polygon

So we have a polygon with N vertices located on grid. All vertices are located at the intersection of cells (so their coordinates are integers). The objective is to calculate the total length of line ...
1
vote
1answer
104 views

Triangulations/quadrangulations of polygon

Is there a nice way I can find all possible triangulations (or quadrangulations) of a polygon (say 10-gon)? I want to have all possible diagrams with the diagonals marked (i.e. with unique name). ...
8
votes
2answers
233 views

Detect and fix invalid polygon

I have a polygon given by ...
4
votes
1answer
187 views

Others problems with Graphics`PolygonUtils`PolygonCombine

As a continuation of this question, writing: ...
8
votes
2answers
248 views

Problem with Graphics`PolygonUtils`PolygonCombine

Writing: Normal@ParametricPlot[{x, x^2 t}, {x, 0, 2}, {t, 0, 1}] /. p : {__Polygon} :> Graphics`PolygonUtils`PolygonCombine[p] I get: but if I write: ...
4
votes
3answers
664 views

How can I get the vertices of each polygon of a Voronoi diagram?

For the following image; How can I get the vertices (which are highlighted by orange dots) of each Voronoi polygon of the following Voronoi diagram? The picture is from the Internet. It is just for ...
8
votes
1answer
245 views

Getting random points on a mesh region

So I have a region defined by a MeshRegion,like ...
10
votes
2answers
393 views

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

So I tried this code for 2D, but I would like to have say a slab with a defined thickness The code for 2D is ...
0
votes
0answers
120 views

Graphics3D ignores EdgeForm

Works great: Graphics[{FaceForm[White], EdgeForm[AbsoluteThickness[10]], Polygon[{{0, 0}, {1, 0}, {0, 1}}]}] Ignores color and thickness: ...
3
votes
1answer
214 views

Manipulate a polygon

I am an absolute beginner in Mathematica. For a small test project, I am supposed to change the following code such that the corners of the polygon {0, 0, 0}, {1, 1, 1}, {0, 1, 0}, {1, 0, 1} can be ...
27
votes
2answers
1k views

Filling Space with Pursuit Polygons

I want to make a program which can fill a 2D space with "pursuit polygons". The following picture will help you understand better what I mean. You can also look up "pursuit curves" or mice problem or ...
1
vote
0answers
73 views

What's the meaning of rspec?

In the RegularPolygon page, I notice the reference RegularPolygon[{x,y},rspec,n]. What's the rspec?