# Tagged Questions

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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### 4 circular arcs, how plot the minimal surface?

By using Sjoerd de Vries code for circular arcs: ...
572 views

### Bounded Voronoi Diagram

I am trying to compute a Voronoi diagram bounded by a box. In some cases, the points used to compute the diagram form a diagram such that at least two boundary points are within the same polygon. For ...
712 views

### How to simulate the true reflective movement of a particle bouncing around in an ellipse?

Please help me to simulate the movement of a particle inside a region with elliptical walls such that particle is reflected from the walls and continues to move. A friend was able write code to ...
709 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 ...
587 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 ...
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### BoundedDiagram Error

Although BoundedDiagram function worked well for a small data set, I got errors in a specific case that I cannot explain. I am sorry I am pasting here a large list ...
206 views

### Are there built-in functions for testing if a point lies within Graphics3D primitives?

I noticed in this question, Behavior of GraphicsMeshInPolygonQ with self-intersecting polygons, that Mathematica has some "psuedo-hidden" functionality for allowing one to quickly perform a winding ...
463 views

### Calculate scalar potential from electric field

Is it possible for Mathematica to solve an equation like $\nabla f(\mathbf{r}) = - \mathbf{E}(\mathbf{r})$ for $f(\mathbf{r})$? I tried ...
468 views

### ListPlot3D of a set of points in a non-convex region

I would like to plot a set of points in the same style as ListPlot3D does, but only in a non-convex region that I can specify (e.g. using a ...
347 views

### Selecting for 2D points that are within a threshold distance of an upper- and lower-bound number of points

I have a very large set of 2D points: numberOf2DPoints = 10^6; pointList = RandomReal[{0, 1000}, {numberOf2DPoints, 2}]; I'd like to find a way to quickly ...
277 views

### Finding an optimal overlay of two point clouds

Imagine I have two sets of points: ...
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### Imposing a Periodic Boundary Condition in Nearest Neighbour Search

I am trying to find first nearest neighbour distributions of randomly dispersed point-like objects in an infinite system. To do this I make a finite sized box unit cell with a chosen concentration of ...
2k views

### Insphere for Irregular Tetrahedron

I am looking for existing Mathematica code to compute the unique sphere inscribed inside an irregular tetrahedron. I can write it myself, but I would love to find that someone already performed this ...
994 views

### Using TetGen in Mathematica to get 3D Voronoi diagram

In this post, the use of TetGen for 3D Voronoi tesselation has been briefly discussed. However there is still no info about the use of TetGen to generate a 3D Voronoi diagram. The TetGen documentation ...
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### 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 ...
1k 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, ...
2k views

### Generate a Random Polygon

Does some package exist with a function that takes a parameter $n$ and generates a random 2D $n$-sided simple polygon (convex or non-convex), possibly within a certain bounding box? It does not ...
335 views

### Behavior of GraphicsMeshInPolygonQ 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: GraphicsMeshInPolygonQ[poly,pt] Displays ...
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### Complex surface: Finding the perimeter of the union of multiple disc intersections

Consider a system of $N$ circles($N>40$) Each of radius $5$ and the center of these circles along a circle at origin of radius $3$ [as given in code]. Code for above description :- ...
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### Implementing an algorithm for finding the largest circle that contains a single point in a set (and no other point)

This question concerns the implementation of an algorithm proposed by Rahul Narain on a former question of mine that was migrated to math.stackexchange: http://math.stackexchange.com/questions/483845/...
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### Generating an obstacle-avoiding closed-curve with a fixed perimeter and a target area

I was wondering if there was a neat way to solve the following problem in Mathematica v9 - Provided a binarized image (where we call black pixels "obstacles" or vice versa, whichever is most ...
531 views

### Cropping a Voronoi diagram

Someone know how can I get the correct crop of this Voronoi image using RegionFunction? As you can see, there is a lot of undesired white regions inside the left ...
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### How to use a ConvexHull as RegionFunction?

I have a set of data supported over a region in 2D. I want to use RegionPlot and ContourPlot on interpolations of my data, but want to restrict the Plots to the region over which my data is supported. ...
257 views

### Partitioning a list of 2D points into sublists that fit into non-overlapping equal-sized squares [duplicate]

I have a set of {x, y} coordinates, for example: ...
549 views

### I can't understand FindShortest Tour

I can't understand the function FindShortestTour because of the result: FindShortestTour[{ {0, 1}, {5, 1}, {2, 1}, {10, 1}}] ...
1k views

### How to integrate a function over a 3D planar polygon?

I am trying to integrate a function over a planar polygon in 3D. In 2D, this is fairly straightforward, using either answer from this question (I use the second answer). If we use an equilateral ...
1k views

### How to split compound polygons into convex polygons?

Is it possible to split non-convex polygons into convex plygons with Mathematica 9? For example: ...
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### Why BoundedDiagram fails?

I have a set of points: ...
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### rule-based implementation of an algorithm

When I first started learning about rule-based programming with Mathematica, I tried to translate this algorithm for computing the convex hull of a set of 2-D points in $O(n \log(n))$ time, to use ...
2k views

### How to calculate the volume of a convex hull?

Given a spatial curve represented by a parametric equation, is it possible in Mathematica 9 to calculate symbolically (or at least numerically) the volume of its convex hull?
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### Finding integral points on a surface

Suppose I have a dimension formula (for a Lie algebra representation) that is as follows: $$d(a,b) = {(a+1)(b+1)(a+b+2) \over 2}$$ Now consider the surface $F(a,b,n) = 0 = d(a,b) -n$ where \$n \in \...
643 views

### Translating a “Point-to-Triangle” distance script from MATLAB to Mathematica

Update - Thanks everyone for your responses! After fixing a problem with vector normalization, the code below now works. I'm a new user, and I was attempting to port some Mathematica code from ...
4k views

### How do I draw a hemisphere?

I want to draw a solid or partially transparent hemisphere above a partially transparent cuboid object in Graphics3D. However, I do not know how to do this s.t. only half the sphere is drawn. Here's ...
3k views

### Graphics3D: Finding intersection of 3d objects and lines

I found these two nice links 1) intersecting graphics 2) Implementation of Balaban's Line intersection algorithm in Mathematica which works for 2d. However, I need to find whether a ray(line) ...
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### Determining if a point is inside or outside a 3DS (.3ds) or 3DS MAX (.max) object? [duplicate]

Imagine I import some 3DS (i.e. 3D studio) file (http://reference.wolfram.com/mathematica/ref/format/3DS.html) or a 3DS MAX file. How could I place this model (say, the 747.3ds file in the ...
615 views

### Creating hexahedral finite elements in Mathematica

Is it possible to do FEM using hexahedral elements in Mathematica? If it possible, is there any help to do that?
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 ...
248 views

### Cover a rectangle with size constrained rectangular regions

I have a big grid (indicated on the image in grey) that is divided in several blocks (each with a maximum width of 3 units). Now I would like to divide a region (indicated on the grid in red) by the ...
4k views

### Creating a 2D meshing algorithm in Mathematica

As what is proving to be a difficult, but entertaining task, I am attempting to adapt a 2D meshing algorithm created for MATLAB and port it to Mathematica. I understand meshing functions already exist ...
3k views

### Create triangular mesh from random list of points

I have a list of points. I would like to take these points and create a mesh of triangles from them, making sure triangles don't overlap. So here's a list of points: ...
553 views

### Equidistant points on a polyline

Set of 2D-points connected by a polyline B-spline function: ...
2k views

### Convex hull of a 3D object?

I am trying to find a convex hull command for a Graphics3D object. Does it exist in Mathematica? ...
490 views

### How to make 3D object smooth?

This thread considers mathematical methods here to make the 3D object smooth but this question consider how to achieve the goal of smoothing a 3D object in Mathematica. I want to get smoother ...
338 views

### Computing Ehrhart's polynomial for a convex polytope

Is there a Mathematica implementation for computing the Ehrhart polynomial of a convex polytope which is specified either by its vertices or by a set of inequalities? I am interested in knowing this ...
362 views

### Integrating polynomial functions over polytopes with an add-on package

There is a Mathematica package to evaluate integrals over polytopes: http://library.wolfram.com/infocenter/Books/3652/ In the documentation (Functions.nb file) I ...
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 ...
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### Voronoi diagrams for generators other than points

Any suggestions how to determine Voronoi diagram for sites other than points, as e.g. in the picture below? Input is a raster image.
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### Finding the perimeter, area and number of sides of a Voronoi cell

Does anyone have any suggestions how to determine the perimeter, area and number of sides of each Voronoi cell in Voronoi diagram?
### A GraphicsMeshConvexHull[] peculiarity
I have been unable to explain the behavior of GraphicsMeshConvexHull[] on the following (highly simplified) example: ...