Questions tagged [polygons]

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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 ...
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2answers
61 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 $0\le x\le 2\pi$? ...
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0answers
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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 <...
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0answers
42 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,...
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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 ...
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0answers
16 views

Issue connecting vertex coordinates

To make it simple, I have generated a list where sub-lists are vertex coordinates of regular or non-regular polytope. For example, here's a list that can be generated: ...
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0answers
40 views

How to remove unwanted lines in Graphics3D [duplicate]

When I run the following code: ...
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0answers
38 views

Regions detecting/counting

Recently, I solved an analytical problem on the number of possible regions in a similar figure: I conducted numerical experiments on Mathematica to verify the results. Intersection points are easy to ...
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2answers
52 views

Problem defining a polygon

I have two polygons that are very similar as: ...
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1answer
109 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 ...
3
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1answer
108 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 - ...
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2answers
265 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 ...
6
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2answers
183 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 : ...
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3answers
463 views

Is it possible to draw a hollow circle using polygon?

The question is simple. I have the following commands ...
1
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1answer
76 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). ...
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3answers
178 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]: ...
8
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2answers
166 views

Detect and fix invalid polygon

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

Others problems with Graphics`PolygonUtils`PolygonCombine

As a continuation of this question, writing: ...
8
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2answers
225 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: ...
10
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3answers
256 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 ...
4
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3answers
320 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 ...
7
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1answer
186 views

Getting random points on a mesh region

So I have a region defined by a MeshRegion,like ...
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0answers
83 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
139 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 ...
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0answers
46 views

What's the meaning of rspec?

In the RegularPolygon page, I notice the reference RegularPolygon[{x,y},rspec,n]. What's the rspec?
10
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2answers
308 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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1answer
463 views

Create a 3D polygon

We can look at the dimension of a shape using RegionDimension, for example RegionDimension /@ {Cuboid[], Cone[], Ball[]} ...
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0answers
128 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 ...
4
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1answer
225 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
193 views

Two ways to plot a triangle

Writing: ...
4
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3answers
195 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 ...
1
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1answer
144 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
148 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 ...
1
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3answers
250 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 ...
26
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2answers
753 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 ...
2
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2answers
164 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 ...
1
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1answer
135 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 ...
2
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1answer
153 views

Cutting polygons [duplicate]

The code below was created to get a list with the coordinates of the lower left corners that will serve as a reference for my polygons ...
4
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1answer
260 views

Finding non-collinear vertices of a convex hull

I'm fairly new to Mathematica (and programming in general tbh) and need this for a math project I'm working on. I generate large collections of (rational, 2d) points and need to find which of these ...
9
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2answers
316 views

Plot polygonal surface

I have a list of 120 elements of the form $\{q,x,y,z\}$. In fact, each element of the represents the nuclear charge and 3 coordinates of an atom of some large molecule. ...
7
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3answers
285 views

PDF export of polygons: How to get rid of polygon boundary lines?

I have the following polygon: generated using this code (extracted from my previous question): ...
3
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1answer
269 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 ...
8
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3answers
671 views

Polygon mesh: Compute vertex normals for smooth shading

MeshRegion has a "SmoothShading" PlotTheme which automatically computes the ...
1
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1answer
223 views

Working with wavefront obj files

Mathematica can easily import obj shape files. I wonder, is it possible to access individual faces? What I actually need is to calculate area of each face and its normal. This can be done from scratch ...
14
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1answer
436 views

How could I perform Region or Polygon Clipping in mathematica?

I need to clip several regions reg: like Rectangle, Polygon, Ellipse... My goal isn't to plot the clipping but to have a representation of each new region. I searched if there was any package or ...
8
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2answers
252 views

How to create a mesh of convex polygons (of maximal size) from a boundary mesh region

I can create a boundary mesh region that consists of a rectangular region with two independently-rotated pentagonal regions excluded using the following code: ...
3
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0answers
48 views
18
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3answers
1k views

Pentagonal spiral in Mathematica

I would like to plot an image of what I call a pentagonal spiral with Mathematica. A sample image of what I'd like to obtain is this (sorry for low-quality): My initial idea was to get some kind of ...
-3
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1answer
83 views

Two 5-gons - One with a concave vertex and another with a convex vertex

I don't know if I may ask this question here, but I want someone could make a simple construction by Mathematica. Could anyone be able to construct a 5-gon with only one concave vertex and the same 5-...
4
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3answers
608 views

How to color the edges of a triangle?

I'd like to draw a triangle (given the side lengths) with the sides colored separately. I tried ...