Questions tagged [polygons]

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0answers
18 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
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4answers
171 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
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2answers
211 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 : ...
47
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6answers
7k 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: ...
14
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3answers
903 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 ...
12
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2answers
591 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
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0answers
34 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
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2answers
308 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
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0answers
47 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
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0answers
64 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
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1answer
116 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
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2answers
136 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 $0\le x\le 2\pi$? ...
0
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0answers
45 views

Mapping a flat unit plane composed of polygons onto a cylinder

I'm looking to map a flat plane composed of triangles onto a cylinder, and then ultimately use a manipulate function to show the plane wrapping into a cylinder. Here is the code I have so far, I've ...
0
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1answer
163 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 ...
61
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3answers
5k 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
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0answers
51 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
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0answers
58 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
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0answers
69 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
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3answers
1k views

Polygons crash kernel?

Having some problems Generating random Polygons and then filtering by Area, specifically filter out degenerated polygons with ...
2
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0answers
60 views
10
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3answers
281 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
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3answers
293 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
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2answers
59 views

Problem defining a polygon

I have two polygons that are very similar as: ...
3
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1answer
125 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
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2answers
270 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
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3answers
255 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
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3answers
612 views

Is it possible to draw a hollow circle using polygon?

The question is simple. I have the following commands ...
3
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2answers
1k 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
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1answer
84 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
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2answers
197 views

Detect and fix invalid polygon

I have a polygon given by ...
4
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1answer
173 views

Others problems with Graphics`PolygonUtils`PolygonCombine

As a continuation of this question, writing: ...
8
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2answers
240 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
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3answers
485 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
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1answer
214 views

Getting random points on a mesh region

So I have a region defined by a MeshRegion,like ...
10
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2answers
355 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
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0answers
98 views

Graphics3D ignores EdgeForm

Works great: Graphics[{FaceForm[White], EdgeForm[AbsoluteThickness[10]], Polygon[{{0, 0}, {1, 0}, {0, 1}}]}] Ignores color and thickness: ...
3
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1answer
177 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
903 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
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0answers
62 views

What's the meaning of rspec?

In the RegularPolygon page, I notice the reference RegularPolygon[{x,y},rspec,n]. What's the rspec?
8
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3answers
879 views

Polygon mesh: Compute vertex normals for smooth shading

MeshRegion has a "SmoothShading" PlotTheme which automatically computes the ...
2
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2answers
93 views

Inconsistent behavior from RegionMeasure on the RegionIntersection between a Polygon and a Line

Consider a Polygon with lines drawn between two of its vertices, ...
0
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1answer
627 views

Create a 3D polygon

We can look at the dimension of a shape using RegionDimension, for example RegionDimension /@ {Cuboid[], Cone[], Ball[]} ...
0
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0answers
160 views

Drawing convex cone with given vectors

I have vectors in matrix form. By using Mathematica, I want to draw it as convex cone and intersect. Let me explain, my intent is to create a new cone which is created by intersection of a null spaced ...
3
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1answer
308 views

How to display a GeoTIFF raster in GeoGraphics?

I have a GeoTIFF raster file which I would like to display superimposed on a map in GeoGraphics and combine it with other GeoListPlot graphics. Since I know the corners of the GeoTIFF raster, I am ...
4
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1answer
247 views

How to draw a generic 3D closed shape to be analyzed in AceFEM?

I would like to draw a 3D shape to test my AceGen procedure. I will insert the AceFEM part of my code. In this example, I have performed the analysis on a hexahedron element. ...
0
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1answer
256 views

Two ways to plot a triangle

Writing: ...
4
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3answers
218 views

Generate the complement of the Earth's land mass polygons

I would like to get polygon covering of all water area of earth. I though of doing by inverting Polygon[EntityClass["Country", "LandMasses"]] How do i invert ...
7
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1answer
216 views

How to test if a GeoPosition is inside a geographic Polygon?

I have tried the following: ...
1
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1answer
193 views

Measure eccentricity of a polygon

I am trying to compute the eccentricity of a polygon in Mathematica. I see that I can do something similar with ComponentMeasurements, but I am not sure how to get ...
2
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1answer
157 views

Minimal set of perimeter points such that one is always visible any point inside a polygon [duplicate]

I've encountered this problem, and I'd like to know how is possible to solve it in Mathematica: There's a bar that has a room with a very irregular shape. From every point inside the room it must ...