# Tagged Questions

Questions on constructing graphical objects using relatively complex computations relating to the mathematical structures defining those objects. Examples include convex hulls, mathematical constructions, symmetries, genuses of curves and graphs and programmatic constructions of polyhedra.

5answers
282 views

### How to check if a line segment intersects with a polygon?

The naive method is to bisect the line segment iteratively as asked here, and then check the bisection points using How to check if a 2D point is in a polygon?. Would there be an other way? I'm ...
0answers
75 views

### Obtain polygons describing all intersections of many polygons

I have 6894 polygons describing zones in a state plane (i.e., cartesian) coordinate system. Most are not very complex, and I believe none have holes. A random example is Polygon[{{351633., ...
0answers
38 views

### How to determine if a point is within a geopositioned RegionMember

I have a KML file which contains an area of interest, I also have a number of lat/long geo positions. I'm trying to filter out the points not within my AOI. So I have my KML file. I convert it to a ...
1answer
45 views

### RegionUnion issues with many Regions

The new RegionUnion[] function is just what I needed if only I could get it to work. I have many non-overlapping regions that I will need to use as plotting domains ...
2answers
95 views

### Finding the equation for the upper frontier of the convex hull of a 2 dimensional set of points

Suppose you have ...
5answers
192 views

### Find the nearest locations for multiple points

Assume that there are many holes with their locations fixed, and the same number of balls distributed randomly. What is the smallest total distance for the balls fitting into the holes on the ...
0answers
58 views

### projecting a RegionProduct into 3D space

Apparently, RegionProduct should allow you to generate convolution-generated shapes. For instance, take a 1D curve and a sphere, and the region product I would ...
2answers
147 views

### Rotating a plane about an arbitrary axis

I would like to rotate a plane by $k$ degrees about an arbitrary axis. How should I do it using RotationTransform? hmm i realise if I do the following ...
1answer
252 views

### Areas of Voronoi cells from image file

I have an binary image with non-point objects. Does anyone have any suggestions how to determine area of each Voronoi cell in Voronoi diagram (goal is area distribution)? Thank you in advance.
1answer
109 views

### Collision detection algorithm (discrete) with sweep and prune algorithm

For a more complex collision detection approach, I need an efficient (aka fast) algorithm to prune the elements by using boundary boxes. A classical algorithm is the so called sweep and prune (SAP) ...
3answers
203 views

### Triangulated Mesh from Voronoi Diagram

I want to generate a mesh (using Mathematica 10) in the following manner: Generate a Voronoi diagram, like so: and then triangulate each individual Voronoi grain, were an edge is formed by ...
1answer
75 views

### Region plot of transformed region giving odd result

I tried applying a transformation to a rectangle: RegionPlot[TransformedRegion[Rectangle[{0, 0}, {1, 1}], {#1^(1/3) + #2, 1 + #2} &]] giving In reality, ...
3answers
606 views

### Finding the surface area of a 3D convex hull

I have noted several instances here and here where ConvexHullMesh, introduced in v10 has been used to greatly simplify some geometry problems. Determining the ...
0answers
47 views

1answer
88 views

### how to find the vector intersection in a collection of triangulated 3D points?

I'm trying to calculate the 3D point coordinates for the intersection of a vector with a plane. I have been using the following code to do this: ...
1answer
229 views

### How to draw quantum circuit with mathematica?

How to draw quantum circuit as the following one with mathematica? I only find the quantum package which is designed for MMA 7.0 as the author said. But the version of my Mathematica is 9.0 and when ...
6answers
1k views

### Finding length of intersection of two surfaces

I would like to know how we find the length of the intersection of two surfaces. For instance, in the following example,a surface intersects with a plane: How do we find the length of intersection ...
3answers
255 views

### Site - Cell Correspondence in Voronoi Diagram obtained via VoronoiMesh

Consider the following: ...
2answers
397 views

### Object separation from a 2.5D surface

I'm trying to identify the shape and the boundaries of objects. The data was generated with a laser scanner and represent the surface of an area in which many boulders lay on the ground and making up ...
5answers
245 views

### Ordering the Boundary points of a Polygon

I feel like this should be simple, but I keep running into walls. Say someone gives you the coordinates of the vertices of a pentagon and the center point of the hexagon. Is there any way to get an ...
2answers
258 views

### How can I only draw outer common tangent to two circles?

I have code worked for drawing common tangent lines to two circles(http://en.wikipedia.org/wiki/Tangent_lines_to_circles), now I want to delete the inner common tangent lines, how? ...
0answers
114 views

### Convex hull of a large data set of 3D points

I recently needed to deal with a large data set of 600.000 points in three dimensions. My task was to find a convex hull for this data. I have Mathematica 10, so I could use the function ...
3answers
329 views

### Torus triangulation

I'd like to plot something similar to this but with a triangle instead of a pentagon. Also, I'd like to triangulate the faces, that is, to insert the diagonals for each face of the 3 prisms used. In ...
1answer
125 views

### RegionPlot3D run forever when plotting 3D ParametricRegion

when working with 2D, RegionPlot works fine with ParametricRegion as can be seen in this example: ...
1answer
134 views

### Is it necessary to introduce ImplicitRegion and ParametricRegion in version 10?

In version 10.0, Mathematica introduced a new function about region plotting: ImplicitRegion. But I'm wondered that haven't this function been already existed in the older version? That is, ...
2answers
225 views

### How can I decide whether a closed surface is intersected by a triangle?

A closed surface consisted of Polygons or GraphicsComplex and a triangle made by 3 points are in a 3D space. How can I decide ...
1answer
113 views

### Problem with clipping of tick labels

Please look at Show[DiscretizeGraphics[Graphics3D[{Cone[]}]], Axes -> True, Boxed -> True] Well, there are some ...
1answer
108 views

### Numerical Functions Compatible with Regions Fail with MeshRegions and BoundaryMeshRegions

Given a MeshRegion: region = DelaunayMesh[RandomReal[1, {50, 3}]] We can numerically ...
1answer
158 views

### How do I get a MeshRegion from an obj file, or from Geometry3D

How do I read in an obj file as a MeshRegion so I can e.g. compute its area? If I just import the object and try Area[O] it ...
1answer
129 views

### Possible Bug in DiscretizeRegion with Option MaxCellMeasure

Consider the following ImplicitRegion: reg = ImplicitRegion[x^2 + y^2 + z^2 == 16, {x, y, z}]; We can discretize it using ...
1answer
109 views

### User-defined DistanceFunction for RegionNearest

In the function Nearest , I can define my custom function using the DistanceFunction option. e.g: ...
1answer
156 views

### How can one compute a 3D Periodic Delaunay Triangulation using DelaunayMesh?

Given a non-periodic point set, one can easily tetrahedralize it using the new (in V10) DelaunayMesh function. e.g.: ...
2answers
140 views

### Probable Bug in HighlightMesh with 2D Convex Hulls created via ConvexHullMesh

One nice way to view the new and exciting Mesh objects introduced in Version 10 is by utilizing the function HighlightMesh, so ...
0answers
71 views

### How to make equidistant or split ListPoint [duplicate]

How to split the curve with more equidistant points? ...
3answers
356 views

### How to measure cross sectional area of Tube

I have modified my question to a simple version. I have vertex clusters, polygons and a list of center points. Attached pts and polygons of 3d tube are: ...
1answer
104 views

### How to draw a 3D convex hull of a set of points with styling

IÂ´m trying to obtain the convex hull (with transparent faces) of a small number of points. I would like the Plot to have the points shown with small spheres numbers 1, 2, 3, ... along the axes ...
2answers
313 views

### Probable Bug in ConvexHullMesh

Consider points taken from the following parametric plot. See this question ...
1answer
89 views

### About TetGenTetrahedralize Mesh Size

I have used TetGenTetrahedralize to generated a cubic mesh. I want that the edge size of the triangle to be 0.2, how can realized this? And What does the word "pq1.414a1" mean? inst1 = ...
1answer
140 views

### Can't plot rotated region

I was experimenting with the code from this question when I ran into another problem with regions. ...
0answers
142 views

### How to define two polyhedron intersect or not?

Recently I have used Mathematica to simulate the concrete structure. The most important point is generate random concrete aggregate. As you know, concrete aggregate can be looked as a polyhedron. We ...
1answer
112 views

### What kind of object results from RegionIntersection function?

I'm trying to use RegionIntersection in a couple of Polygons. The polygons are the following: ...
2answers
154 views

### “The function DiscretizeGraphics is not implemented for GraphicsComplex” confusion

Why does DiscretizeGraphics seems to work on one GraphicsComplex and not the other? Here is an example that works: ...
0answers
95 views

### Death of parallel sub-kernels

EDIT : Finally, the new Mathematica 10.0 seems to fix it. I have a little parallelization problem. I wrote a code to generate a quasicrystal by dynamical generation. Here the code: ...
1answer
185 views

### Finding corresponding vertex from 3d to 2d

I have this simple 3d data points: ...
1answer
231 views

### Difference (or intersection) of two convex polyhedra

I have two convex polyhedra stored in the following form: a set of vertices vertices = {{x1,y1,z1},...}, a set of faces, where each face is a convex polygon ...
1answer
167 views

### Find area of polygon on a sphere from a set of latitude-longitude points

Given a list of latitude and longitudes say ...
1answer
100 views

### how to find iso-cost contours on a 2d plot efficiently

Consider a 2D plot in which dimension 1 and 2 represent quantity 1 and 2 respectively ranging over 0 to 100. Each point in the space corresponding to (x,y) represent cost of choosing quantity 1 as x ...
2answers
445 views

### How to get UV mapping of 3D tube

Here is cylinder data: file We can mesh the surface, thanks to lalmei, Belisarius and Simon (link) How to achieve uv mapping from a 3d straight and curved tube? Working code: ...