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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Does anyone have any suggestions how to determine equal size Voronoi cells in a Bounded Voronoi diagram?
Does anyone have any suggestions how to determine equal size Voronoi cells in a Bounded Voronoi diagram?
The answer for Finding the perimeter, area and number of sides of a Voronoi cell was useful, ...
10
votes
1answer
194 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
63 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
199 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?
2
votes
2answers
146 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}]
...
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3answers
135 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 ...
17
votes
3answers
558 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 ...
7
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2answers
250 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:
...
12
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2answers
196 views
6
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2answers
213 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?
...
2
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0answers
141 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 ...
4
votes
0answers
81 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
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1answer
62 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
211 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
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5answers
549 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.
7
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1answer
172 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?
4
votes
1answer
169 views
A Graphics`Mesh`ConvexHull[] peculiarity
I have been unable to explain the behavior of Graphics`Mesh`ConvexHull[] on the following (highly simplified) example:
...
16
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3answers
363 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
266 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 ...
10
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0answers
95 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 ...
13
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5answers
433 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
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2answers
400 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: ...
9
votes
2answers
311 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.
...
2
votes
1answer
257 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 ...
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2answers
195 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:
...
13
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2answers
387 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 ...
11
votes
1answer
349 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 ...
12
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3answers
565 views
How to speed up the function DelaunayTriangulation?
First define a function meshGrid to generate some points:
...
4
votes
2answers
167 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
642 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 $0.7$.
6
votes
1answer
568 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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votes
1answer
193 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 ...
5
votes
2answers
405 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 ...
5
votes
3answers
264 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) ...
34
votes
8answers
3k 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 ...
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vote
1answer
197 views
Code to draw geometry doesn't run
I'm new to Mathematica and have no background whatsoever in programming, although I will teach myself soon. I was wondering if one of you programming pros could help me out. I received a code from ...
6
votes
2answers
324 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.
11
votes
2answers
578 views
Finding a Concave Hull
I have a 3d clustered data:
Is there any other way to get concavehull of 3D data points?
19
votes
3answers
446 views
Build a refined grid based on intersecting line
I honestly have no idea where to begin with this problem. In summary, I have a 2D coarse grid with an intersecting line. For an easy example, let's assume it's a 4x4 grid.
I wish to pass through ...
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 ...
20
votes
6answers
2k views
Circuit drawing in Mathematica
This past semester I taught an introductory electromagnetism course and had quite a nice time using Mathematica to draw all sorts of figures and diagrams (mostly for problems and etc.). However, I was ...
5
votes
2answers
663 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?
7
votes
1answer
172 views
7
votes
1answer
428 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
330 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 ...
15
votes
2answers
863 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.
38
votes
2answers
4k views
How can I calculate a jigsaw puzzle cut path?
I want to generate a path to cut an arbitrary shape into a set of jigsaw puzzle pieces.
All pieces must be unique to preclude placing a piece in the wrong spot.
Pieces must be interlocking such that ...
8
votes
0answers
313 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 ...
1
vote
1answer
267 views
Implementing Central Symmetry
I'm interested in implementing symmetry groups. So it would be useful to have central symmetry (isometry transformation). There are built-in functions: ...
7
votes
3answers
249 views
Distances between points in periodic cube
How can one implement more efficiently/elegantly/memory savvily the following function which returns a matrix of all Euclidian distances between points in 3D within a cube of width ...
