# Questions tagged [polygons]

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### Polygon mesh: Compute vertex normals for smooth shading

MeshRegion has a "SmoothShading" PlotTheme which automatically computes the ...
300 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 ...
500 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 ...
301 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: ...
51 views

### Graphics3D plot Polygon (Joined Table) gets different results with and without decimal point

Without decimal point ...
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 ...
84 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-...
649 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 ...
744 views

### Finding area of intersection regions

I want to be able to find the area of the intersection between a hexagon and a slice. I have tried RegionMeasure or Area but I ...
215 views

### Using loops to draw multiple polygons and discretizing them

I am trying to plot the first eigenvalue of the Laplacian operator with zero Dirichlet condition on following figure against decreasing values of $\varepsilon$. I used ...
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, ...
215 views

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

I have tried the following: ...
215 views

### How Can I plot two concentric circles with a polygon inscribed in one and circumscribed about the other however I want the polygon to manipulated

So this code is to plot two concentric circles with a polygon inscribed in one and circumscribed about the other: ...
114 views

### When Graphics3D renders a Polygon with non planar points, how does it triangulate to two separate polygons?

If we try to make a Polygon with nonplanar points, the documentation says Non-planar polygons are accepted in Graphics3D and ...
268 views

### What is a robust way to determine if two polygons overlap? Possible bug in RegionIntersection or Area

When trying to determine if two polygon objects overlap, I think the intuitive way to do this would be to use the RegionIntersection function to find the ...
2k views

### Rounding the Corners of a Shape

I was wondering whether there is an option in Mathematica that enables me to smooth the corners of a shape. The example I want to start with is the pentagon. This can be crudely specified as ...
173 views

### Create a square polygon that can be used as the base of a pyramid

For example I want to use the design generated by this code as the base of a pyramid as well as other iterations of the design ...
292 views

### Cannot combine GeoPosition polygons in version 10.4

I was using with Mathematica 10 for plotting different kinds of maps the function PolygonCombine. It seems that this fucntion has disappeared with the version 10.4? Here is a classical example for the ...
168 views

### Handling Self-Intersecting Regions

I am trying to test various parametric regions of a function for membership of the origin (point {0,0}). I generate the boundary by creating four parametric boundary curves, and then use RegionMember ...
498 views

### Connecting the points surrounding the adjacent polygons

I'm trying to connect the points surrounding the adjacent polygons. I know how to find the adjacent polygons on a Voronoi mesh. However, I'm unable to adjacent of the adjacent polygons. What I'm ...
207 views

### Graphics option to suppress lines between adjoining polygons

In 10.3.1 there was a Graphics option -- it might be a sub-option of Method -- which erases the thin line visible at the join ...
85 views

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154 views

### Delete/Extract some certain data from a list?

These are some polygons for Voronoi mesh. ...
150 views

### How to find point within polygons and connect them

I have the following figure: Here, I have the following values of 25 image corner-points: ...
161 views

### Unit of measurement for the area of the polygon

I have an image. I found the dimensions of the image as the following code: ImageDimensions[img] I found the image dimension as {224, 88}. Now, I run the ...
166 views

### How to compare two polygons?

I have these polygon points which are like these: ...
463 views

### How to extract the vertices value of a polygon? [closed]

I developed a code where I can extract the vertices of the polygon with highest adjacent. These are the index values of each polygon: ...
1k views

### intersection between polygon. Algorithm to check it [closed]

I'm working on an algorithm which should check if two polygons, described by their vertex coordinates, are: one inside the other, are intersecting or are separated image below describe this three ...
838 views

### Geographics: Can I get a US Map silhouette without the Great Lakes?

I'd like to get a nice silhouette of the land area of the US lower 48 states using Mathematica's GeoGraphics method. I tried: ...
208 views

### RegionIntersection fails for some values with polygons

Bug introduced in 10.1 and fixed in 10.3.0 I want to find the intersection (region) of 2 polygons. I use RegionInstersection but it only works for some sizes, for ...
493 views

### How to make sure polygon is drawn flat in 3D?

Bug introduced in 8.0 or earlier and fixed in 10.4 I'm working on this SE question about pentagrams on top of dodecahedron for exercising. Both solutions are basically connecting different sets of ...
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 ...
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 ...