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

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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 ...
8
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0answers
97 views

Is this a bug in DiscretizeRegion in 10.4?

Bug introduced in 10.4 and persists through 10.4.1 Consider the following implicit region: ...
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0answers
79 views

Defining a MeshRegion from a list of points and Polygons with duplicate points does not work in 10.4

Bug introduced in 10.4 and persists through 10.4.1 This code produces a MeshRegion in versions 10.0 through 10.3.1, ...
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3answers
388 views

Finding the two points on a heart-shaped curve which have maximal distance between them

The question originates from Max & min distance between two moving points. I think it can be solved easily because of the function is a parametic function. My heat-shaped curve is given by ...
7
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3answers
1k views

Generating a non-convex polyhedron from a list of vertex coordinates

I want to include a figure in a paper I am writing on Combinatorial Geometry which features a non-convex polyhedron given by the following vertices, EDIT: I was unaware that Mathematica could convert ...
7
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2answers
3k views

Delaunay Triangulation for 3D Surface Data

I want to do a Delaunay triangulation on scattered 3D surface data. Mathematica itself does it only for 2D through the command DelaunayTriangulation[], which gives ...
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3answers
3k views

How to check if a 3D point is in a planar polygon?

Following up on ndroock1's question, I naively tried to apply the solutions to a 3D point and polygon and they didn't work. For example, functions involving ArcTan ...
7
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2answers
958 views

Voronoi Diagram: Displaying site specific color in a voronoi diagram

I am using Voronoi Poligonization as a support form simulating island erosion; my data are the output of VoronoiDiagram, ...
7
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2answers
693 views

Finding concave hull for separated small clusters

Data : data3D = Import[file, "VertexData"]; Graphics3D[Point[data3D]] How to find concave polygon for separated small clusters.
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2answers
255 views

A question regarding “DiscretizeGraphics”

I want to find the volume of a torus torus = RevolutionPlot3D[{2 + Cos[t], Sin[t]}, {t, 0, 2 Pi}] ...
7
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1answer
203 views

DiscretizeGraphics and BoundaryDiscretizeGraphics Fail on CapsuleShape and SphericalShell

It seems the new Graphics3D primitives have some incomplete features. Earlier, I uncovered a problem with computing their exact surface area see here. Now, I ...
7
votes
2answers
179 views

How do I get ConvexHullMesh to return polygons instead of triangle as surface mesh?

I would need to identify the types of regular polygons forming the surface of a convex hull of 3D points. If I e.g. take the following example of a regular polyhedron ...
7
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1answer
141 views

Why is RegionMeasure so slow when calculating intersection area of a 2D and a 3D object?

If you think this description is too long, you can read the problem directly I know normally when one wants to calculate an region, this guide is useful. However, when it comes to calculating an ...
7
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1answer
250 views

Finding corresponding vertex from 3d to 2d

I have this simple 3d data points: ...
7
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1answer
139 views

How to convert a graph to a mesh region

As we know,the region is very convenient in Mathematica.And we can convert a MeshRegion into graph like this ...
7
votes
1answer
268 views

Can't plot rotated region

I was experimenting with the code from this question when I ran into another problem with regions. ...
7
votes
1answer
414 views

Smooth 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 ...
7
votes
1answer
66 views

DiscretizeRegion fails for a triangular region

I define an implicit region like R = ImplicitRegion[ 0 < Sin[u]/Cos[v] < 1 && 0 < Sin[v]/Cos[u] < 1, {{u, 0, 2}, {v, 0, 2}}] But when I ...
7
votes
2answers
195 views

A method to discretize a three-dimensional solid

Consider the following region: ...
7
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0answers
81 views

RegionIntersection: Point or Line?

This may be a minor point, but I'm wondering why RegionIntersectionof the two rectangles below gives 3 Lines rather than 2 Lines and 1 Point. ...
6
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7answers
1k views

Choosing $n$ equidistant points on a circle with given radius and center

I would like to have a function circle which takes two inputs: a tuple {x,y} and a real number ...
6
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4answers
218 views

Getting ordered coordinates out of ConvexHullRegion

I'm trying to get the ordered coordinates of a convex hull using MeshCoordnates[ConvexHullMesh[data]], but the coordinates are uselessly out of order: ...
6
votes
3answers
250 views

Speed of ConvexHullMesh

Pick $N$ random points on the surface of the sphere, then use ConvexHullMesh[] to compute their convex hull. Empirically, this takes time quadratic time in $N,$ ...
6
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3answers
4k views

Mathematica function intersection points with 3D grid

I need to produce a 3-dimensional equispaced grid over a given function in a way, that I can calculate intersection points of the function with the grids edges. So my first question is how to produce ...
6
votes
3answers
223 views

Lloyd relaxation on VoronoiMesh

How can we apply Lloyd's relaxation algorithm to a VoronoiMesh? Thanks. UPDATE Thanks a lot KennyColnago for your answer. Based on Simon Woods suggestion of ...
6
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6answers
694 views

How to find the vertices of a regular tetrahedron? a dodecahedron?

My question is: how to find the coordinates of the vertices of regular tetrahedron and dodecahedron? I tried to find the coordinates of the vertices of a regular tetrahedron as the solutions of a ...
6
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2answers
245 views

Discretizing regions with pointy boundaries

I'm trying to discretize a region with "pointy" boundaries to study dielectric breaking on electrodes with pointy surfaces. So far I've tried 3 types of boundaries, but the meshing functions stall ...
6
votes
1answer
201 views

Need help on the proper use of a formula to produce a cambered airfoil

Following the book on "The Theory of Thin Wing Sections" page #112 describes the method to combine a camber line (i.e Mean Line) and a thickness distribution to form a cambered wing section. Data ...
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2answers
1k views

Extracting polygons from 3D contour plot surface

Edit: This question turned out to be two parts so I am going to make this question about only the first part a kguler provided an excellent answer. Here is a better representation. My actual data ...
6
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2answers
268 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: ...
6
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2answers
133 views

Voronoi diagram using RegionPlot, using the hyperbolic metric

I want to compute the Voronoi diagram on the unit disk, using the hyperbolic metric. So, I want to input a list of points and obtain a plot of the cells associated with each of the points. I defined ...
6
votes
2answers
254 views

ToElementMesh problem on Ball defined by ImplicitRegion?

Bug introduced in 10.0 and fixed in 10.2 Could any one please confirm the following bug in mathematica 10.0.2 ? If I define this ball ...
6
votes
1answer
338 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 ...
6
votes
1answer
298 views
6
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1answer
729 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) ...
6
votes
1answer
1k views

Construct a simple mesh or tetrahedral mesh from 3D image surface

I have a 3D Y-Shape hollow tube, not so good surface. Import["http://dl.dropbox.com/u/68983831/tube02.vtk", "Graphics3D"] I tried to use following vertex data ...
6
votes
3answers
131 views

How to generate higher dimensional convex hull?

I like the function ConvexHullMesh very much, since I often need to take a look at the convex hull of points in 2D and 3D, which as an example can be generated and ...
6
votes
2answers
158 views

Test existence of a path from one side of a graph to another

I'm trying to determine how I can test if a path exists from one side of a graph to another as efficiently as possible. If I have the Lines given by: ...
6
votes
1answer
123 views

Error from BoundedDiagram

I cannot understand the meaning of the error BoundedDiagram::notuniq: BoundedDiagram requires that boundary vertices lie in unique Voronoi polygons. >> BoundedDiagram::nobd: Bounded ...
6
votes
1answer
97 views

Expensive MeshRefinementFunction

I want to discretize a region using DiscretizeRegion. Now, I want the mesh to be more refined, when the curvature of a certain function ...
6
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2answers
2k views

Calculating a minimum bounding box for a set of 3-space coordinates / spheres

I have a set of 3-space coordinates for the atoms of a molecule (I could also transform them into spheres with radii corresponding to the atoms they represent). I would like to place this molecule ...
6
votes
1answer
189 views

How to draw Kobon triangles

I would like to know if Mathematica is capable of constructing Kobon triangles; that is, a figure consisting of the largest number of non-overlapping triangles that can be constructed using $n$ lines, ...
6
votes
1answer
316 views

Behavior of Graphics`Mesh`InPolygonQ with self-intersecting polygons

Playing around with some of the answers in the question How to check if a 2D point is in a polygon? I noticed that: Graphics`Mesh`InPolygonQ[poly,pt] Displays ...
6
votes
1answer
280 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., ...
6
votes
1answer
161 views

Numerical Functions Compatible with Regions Fail with MeshRegions and BoundaryMeshRegions

Bug introduced in 10.0.0 and fixed in 10.0.2 Given a MeshRegion: region = DelaunayMesh[RandomReal[1, {50, 3}]] We can ...
6
votes
1answer
543 views

How to get vertices of a polytope given by equalities and inequalities?

I have a polytope given by some equalities and inequalities, how can I get all the vertices of the polytope? If there's a way to deal with the one given by inequalities only, how can I reduce the ...
6
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0answers
135 views

Possible Bug with Options in DelaunayMesh

Bug introduced in 10.2 and persisting through 10.4 Update: It turns out after some testing, none of the Options work in ...
5
votes
3answers
255 views

Point belonging to a Disk in a Cartesian Coordinate System

The image below represents a human subject fixations while observing this abstract pattern for 3 seconds. I would like to know how much time they spent looking at the actual disk. That is a red point ...
5
votes
3answers
301 views

Removing cells from Voronoi mesh if they exceed a certain area or circumference

I start with the example in Finding the perimeter, area and number of sides of a Voronoi cell with RunnyKine's answer: ...
5
votes
3answers
1k views

How to create a planar graph from a set of random points

Question Given a set of points in the plane, how can you create a planar graph in the standard graph representation of Mathematica (version 9 or higher), from these points? Background A planar ...