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.
10
votes
1answer
141 views
Has anyone implemented cohomology for complex manifolds?
I'm investigating the cohomology of complex manifolds, and need to construct chain complexes, Mayer-Vietoris sequences etc. I use Mathematica for numerically tracing manifolds with geodesics, but ...
4
votes
1answer
182 views
A Graphics`Mesh`ConvexHull[] peculiarity
I have been unable to explain the behavior of Graphics`Mesh`ConvexHull[] on the following (highly simplified) example:
...
13
votes
2answers
233 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?
3
votes
0answers
70 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
50 views
13
votes
1answer
198 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 ...
17
votes
2answers
1k views
How to calculate volume of convex hull and volume of a 3D object
I have a random 3D data points.
How to calculate volume of the convex hull and volume of the object.
2
votes
2answers
98 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
165 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 ...
-1
votes
0answers
42 views
Returning a non-degenerate list of triangles that (strictly) define the outer mesh of a 3-polytope using PolyhedronData?
I'm looking for a simple method of returning a list of triangles that strictly define the outer surface of a 3-polytope using PolyhedronData?
For example:
...
7
votes
6answers
386 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 ...
10
votes
2answers
424 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) ...
2
votes
3answers
233 views
How to find all graph isomorphisms in FindGraphIsomorphism
I found the second definition of the function FindGraphIsomorphism not working.
Here's the definition Mathematica 8 gives:
...
4
votes
0answers
102 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 ...
10
votes
3answers
671 views
Computing the genus of an algebraic curve
How-to compute the genus of an algebraic curve in Mathematica ?
In my case the algebraic curve is explicitly defined by a polynomial.
2
votes
2answers
175 views
Create a planar graph from a set of random points
A planar graph is a graph embedded in the plane in such a way that the edges intersect at vertices. This is an example of a planar graph:
g = GridGraph[{3, 3}]
...
20
votes
3answers
720 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 ...
0
votes
0answers
91 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 ...
8
votes
0answers
335 views
Proving inequalities with Mathematica
Question summary: I would like to learn some tips and tricks on how to prove inequalities with Mathematica.
I'm studying various inequalities in triangle that have the form $R+ar + bs\geq 0$, where ...
2
votes
1answer
228 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?
6
votes
2answers
292 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?
...
19
votes
1answer
592 views
How to create regular (planar) graphs?
How to programmatically create and plot regular planar graphs with $k = 3, 4$ or $6$ (not hypercubes) and regular nonplanar graphs of $k = 8$ (see figure)? Note that what matters is the average ...
0
votes
3answers
153 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 ...
7
votes
2answers
326 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:
...
13
votes
2answers
211 views
2
votes
0answers
162 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 ...
0
votes
1answer
82 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
297 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 ...
18
votes
5answers
609 views
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.
8
votes
1answer
197 views
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?
18
votes
3answers
489 views
Efficiently determining if 3D points are within a surface composed of polygons
This is the 2nd part of a previous question which I edited to make into 2 separate questions: Extracting polygons from 3D contour plot surface
As an extension of my earlier question involving simple ...
2
votes
1answer
294 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
votes
3answers
365 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 ...
14
votes
5answers
475 views
How can I define a 3D version of the built-in VoronoiDiagram function?
Can anybody point me in a direction that will guide me to extend the VoronoiDiagram function in Mathematica to handle 3D (three dimensional) situations (i.e. points in 3D)? Any help will be greatly ...
17
votes
2answers
424 views
Movable text on a curve
Having an arbitrary curve defined as InterpolatingFunction, what is the best way to place a text on this curve? The text generally has two rows, for example: ...
6
votes
1answer
651 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 ...
7
votes
1answer
182 views
9
votes
2answers
359 views
Checking if a point is in a convex 3D polyhedron
Extending from these questions How to check if a 3D point is in a planar polygon? and How to check if a 2D point is in a polygon?.
I'm trying to do this to render specific shapes made up of spheres.
...
5
votes
3answers
284 views
How to ensure that Polygon[list] plots a simple polygon?
Consider the following code which plots a triangle.
p = {{0, 0}, {.2, 0}, {0, .2}};
{Cyan, Polygon[Dynamic[p]]} // Graphics
Then adding (for example) ...
2
votes
1answer
265 views
How can Mathematica be used to detect an area surrounded by the most lines?
I have an array of lines that produce random shapes. These lines define edge boundaries from an array that I would like to use to reconstruct the main feature of the array. Can Mathematica find the ...
13
votes
2answers
444 views
Generating convex polyhedron from face planes?
Suppose I have lists of normals and points for planes. There's a convex polyhedron whose faces lie on these planes and are bounded by plane intersections. What would be the easiest way to produce an ...
12
votes
3answers
602 views
How to speed up the function DelaunayTriangulation?
First define a function meshGrid to generate some points:
...
5
votes
3answers
1k 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 ...
11
votes
1answer
389 views
Implementation of Balaban's Line intersection algorithm in Mathematica
I'm trying to implement a Brillouin Zone algorithm within Mathematica, including the generation of Brillouin zones of higher order in 2D and 3D. There is a nice implementation of generating these ...
4
votes
2answers
173 views
Vectors in a spherical shell
I have written code that randomly generates a 3D vector of random magnitude. I now want to create a histogram of how many vectors lie in the concentric spherical shells (n*delta r, (n+1)delta r) ...
6
votes
3answers
719 views
Randomly packing spheres of fixed radius within a cube
How can I have Mathematica randomly place spheres in a cube so they won't overlap? The cube is $20 \times 20 \times 20$, and the spheres have a radius of $0.7$.
35
votes
8answers
4k views
How to check if a 2D point is in a polygon?
Background: I use code from An Efficient Test For A Point To Be In A Convex Polygon Wolfram Demonstration to check if a point ( mouse pointer ) is in a ( convex ) polygon. Clearly this code fails for ...
5
votes
2answers
689 views
How to process .vtk file
I want to extract the cluster of points inside 3D box, is there any way one can do this in Mathematica?
-3
votes
1answer
200 views
Perimeter and area are positive integers
In Geometry 3D, How can I create a triangle whose perimeter and area are positive integers with Mathematica?
I found three triangles. For example $A(-6,1,2)$, $B(-9,1,2)$, $C(-9,1,6)$ or ...
15
votes
2answers
525 views
Efficient way of finding shortest distance between two sets of points in mathematica
I have two sets of 3D points, say
a = RandomReal[1, {10, 3}];
b = RandomReal[1, {10, 3}];
I wanna find the first N pairs that have shortest distance between the ...
