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.
16
votes
2answers
960 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
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 ...
1
vote
1answer
274 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
256 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 ...
4
votes
0answers
159 views
How to compute the genus of a Graph?
What's the simplest way to compute the genus of a graph using Mathematica? I have looked for a Genus function (even in the ...
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?
...
10
votes
3answers
660 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.
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 ...
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 ...
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 ...
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?
17
votes
1answer
533 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 ...
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, ...
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, ...
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 ...
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 ...
