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.
73
votes
3answers
8k views
How to create word clouds?
Word clouds are rather useless fancy and visually appealing plots, where words are plotted with different sizes according to their frequency in a corpus. Many applications exist out there (Wordle, ...
57
votes
4answers
4k views
How to peel the labels from marmalade jars using Mathematica?
How can I detect and peel the label from the jar below (POV, cylinder radius, jar contents are all unknown)
to get something like this, which is the original label before it was stuck on the jar?
...
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 ...
34
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 ...
27
votes
2answers
841 views
Animating a Voronoi Diagram
edit: Excellent answers have been provided and I made an animation which is suitable for my use, however, all the examples rely on bitmap/rasterized data; is there a vector based approach?
I would ...
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 ...
19
votes
3answers
456 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 ...
19
votes
1answer
577 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 ...
18
votes
5answers
594 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.
18
votes
3answers
450 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 ...
18
votes
3answers
658 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 ...
17
votes
2answers
409 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: ...
17
votes
1answer
532 views
How can the {x,y,z} points that fall on the outer boundary of a set of values be selected and smoothly surfaced?
For a given set of x,y,z values, that may, or may not form a uniform shape, how can the center of the data cloud be found, and the surface points be located and a solid smooth surface created from ...
16
votes
3answers
500 views
Procedure to find direction of triangle
I'm trying to write a procedure or function to find the direction in which a 2D triangle points. The triangle is assumed to be isosceles. While I can see the basic outline of what I want to do, making ...
16
votes
2answers
941 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.
15
votes
2answers
494 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 ...
13
votes
5answers
448 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 ...
13
votes
2answers
206 views
13
votes
2answers
423 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
448 views
How to determine the convex hull of some text?
How can I get the co-ordinates of the convex hull of a piece of Text?
12
votes
3answers
579 views
How to speed up the function DelaunayTriangulation?
First define a function meshGrid to generate some points:
...
12
votes
4answers
287 views
Arranging connector lines
Heike gave an absolutely wonderful answer to my question about arranging subplots around a main plot and including connector lines. This is the result:
Starting from Heike's answer, what is the ...
12
votes
2answers
659 views
How to get actual triangles from DelaunayTriangulation[]?
The ComputationalGeometry package has a DelaunayTriangulation[] function. It returns a list of points connected to each point, ...
11
votes
2answers
600 views
Finding a Concave Hull
I have a 3d clustered data:
Is there any other way to get concavehull of 3D data points?
11
votes
1answer
378 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 ...
10
votes
3answers
659 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.
10
votes
2answers
330 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) ...
10
votes
0answers
100 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 ...
9
votes
2answers
333 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.
...
8
votes
1answer
190 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?
8
votes
0answers
326 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 ...
7
votes
3answers
255 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 ...
7
votes
2answers
288 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:
...
7
votes
1answer
176 views
7
votes
1answer
455 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
6answers
327 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 ...
6
votes
3answers
347 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 ...
6
votes
2answers
260 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?
...
6
votes
2answers
339 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.
6
votes
3answers
682 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
612 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 ...
6
votes
2answers
258 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 ...
5
votes
3answers
214 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
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 ...
5
votes
3answers
275 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) ...
5
votes
2answers
673 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?
5
votes
2answers
449 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 ...
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) ...
4
votes
0answers
92 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 ...
4
votes
1answer
171 views
A Graphics`Mesh`ConvexHull[] peculiarity
I have been unable to explain the behavior of Graphics`Mesh`ConvexHull[] on the following (highly simplified) example:
...
