# Questions tagged [polygons]

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### 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 ...
48 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 ...
170 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 ...
131 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 ...
19 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: ...
942 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 ...
36 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 ...
325 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 ...
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. ...
617 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 ...
69 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? ...
121 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 ...
180 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 ...
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 ...
163 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 $0\le x\le 2\pi$? ...
65 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 <...
79 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,...
1k views

### Polygons crash kernel?

Having some problems Generating random Polygons and then filtering by Area, specifically filter out degenerated polygons with ...
73 views

### How to remove unwanted lines in Graphics3D [duplicate]

When I run the following code: ...
64 views

### Problem defining a polygon

I have two polygons that are very similar as: ...
178 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 ...
145 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 - ...
272 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 ...
218 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 : ...
682 views

### Is it possible to draw a hollow circle using polygon?

The question is simple. I have the following commands ...
91 views

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). ...
269 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]: ...
211 views

### Detect and fix invalid polygon

I have a polygon given by ...
179 views

### Others problems with GraphicsPolygonUtilsPolygonCombine

As a continuation of this question, writing: ...
244 views

### Problem with GraphicsPolygonUtilsPolygonCombine

Writing: Normal@ParametricPlot[{x, x^2 t}, {x, 0, 2}, {t, 0, 1}] /. p : {__Polygon} :> GraphicsPolygonUtilsPolygonCombine[p] I get: but if I write: ...
290 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 ...
557 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 ...
228 views

### Getting random points on a mesh region

So I have a region defined by a MeshRegion,like ...
109 views

### Graphics3D ignores EdgeForm

Works great: Graphics[{FaceForm[White], EdgeForm[AbsoluteThickness], Polygon[{{0, 0}, {1, 0}, {0, 1}}]}] Ignores color and thickness: ...
192 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 ...
65 views

### What's the meaning of rspec?

In the RegularPolygon page, I notice the reference RegularPolygon[{x,y},rspec,n]. What's the rspec?
367 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 ...
690 views

### Create a 3D polygon

We can look at the dimension of a shape using RegionDimension, for example RegionDimension /@ {Cuboid[], Cone[], Ball[]} ...
183 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 ...
257 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. ...
296 views

Writing: ...
225 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 ...
205 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 ...
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 ...
310 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 ...
954 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 ...
189 views

### Open pyramid flower-like by rotating its faces

I'm trying to animate a pyramid (with any base) opening its lateral faces like a flower. I found the best way to this to be the Rotate function. The problem is, I have no clue how it works. I have ...
156 views

### How to define a 3D region delimited by a prism with base given by the vertices of a polygon?

I have an arbitrary polygon, not necessarily convex, described by the coordinates of its vertices. I need to obtain the 3D Region R delimited by a prism with base ...