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.

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3
votes
2answers
399 views

Image processing: extracting ordered contour

Continuing the question How to extract the edge from a set of points and its answer by Simon Woods, I would like to ask if there is a way to extract the boundary of obtained as ...
0
votes
1answer
198 views

Area of a convex polygon with a set of points [duplicate]

I have a set of points Pts[a_,b_,c_]:={{a, b}, {b, a}, {c, a}, {a, c}, {b, c}, {c, b}} which define a convex polygon and I would like to find its area. There is ...
6
votes
6answers
342 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 ...
2
votes
0answers
240 views

Visualising Special Relativity

Mathematica newbie learning by doing (or not so far, in this case). Problem: Special Relativity - consider two inertial frames $A$ & $A'$ in relative motion. At a time $t0$ as measured in $S$, ...
-6
votes
1answer
127 views

Poincaré section for 3BP

I try to plot the Poincaré section for the 3BP i use the following code that works very well: ...
1
vote
2answers
180 views

intersection between function and plane

I try to solve a ODE system of equations and i want to plot the intersection of the 3D solutions with a costant plane. To do this i use the follow code: ...
2
votes
0answers
143 views

4 circular arcs, how plot the minimal surface?

By using Sjoerd de Vries code for circular arcs: ...
27
votes
3answers
1k views

Create a torus with a hexagonal mesh for 3D-printing

I am new to Mathematica, and I'm looking for a way to create patterns on the surface of 3D objects. One thing I have not been able to do is create a hexagonal mesh on a torus. What I would like to ...
2
votes
1answer
284 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 ...
3
votes
6answers
418 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 ...
4
votes
0answers
183 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 ...
3
votes
1answer
97 views

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 ...
2
votes
2answers
138 views

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

I noticed in this question, Behavior of Graphics`Mesh`InPolygonQ with self-intersecting polygons, that Mathematica has some "psuedo-hidden" functionality for allowing one to quickly perform a winding ...
2
votes
1answer
250 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 ...
4
votes
1answer
268 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 ...
3
votes
2answers
222 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 ...
5
votes
1answer
170 views

Finding an optimal overlay of two point clouds

Imagine I have two sets of points: ...
6
votes
1answer
328 views

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 ...
10
votes
3answers
608 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 ...
4
votes
1answer
85 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 ...
5
votes
2answers
533 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, ...
16
votes
3answers
743 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 ...
6
votes
1answer
193 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 ...
1
vote
1answer
157 views

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 :- ...
12
votes
2answers
361 views

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: ...
3
votes
0answers
172 views

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 ...
5
votes
2answers
230 views

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. ...
0
votes
1answer
167 views
7
votes
3answers
377 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}}] ...
3
votes
3answers
672 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 ...
3
votes
0answers
358 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: ...
3
votes
1answer
82 views

Why BoundedDiagram fails?

I have a set of points: ...
13
votes
1answer
458 views

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 ...
18
votes
4answers
840 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?
2
votes
2answers
184 views

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 ...
1
vote
2answers
454 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 ...
7
votes
6answers
2k 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 ...
11
votes
2answers
2k 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) ...
0
votes
0answers
238 views

Determining if a point is inside or outside a 3DS (.3ds) or 3DS MAX (.max) object?

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 ...
2
votes
1answer
434 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?
4
votes
3answers
456 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 ...
0
votes
3answers
218 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 ...
26
votes
3answers
2k 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 ...
12
votes
3answers
1k 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: ...
14
votes
2answers
373 views

Equidistant points on a polyline

Set of 2D-points connected by a polyline B-spline function: ...
8
votes
3answers
1k 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? ...
3
votes
0answers
345 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 ...
5
votes
0answers
235 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 ...
0
votes
2answers
250 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 ...
6
votes
2answers
928 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 ...