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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4
votes
2answers
221 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) ...
8
votes
3answers
2k 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
2answers
2k 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 ...
-2
votes
1answer
301 views

Perimeter and area are positive integers

In Geometry 3D, How can I find the vertices with integer coordinates of a triangle whose perimeter and area are positive integers with Mathematica? Suppose its vertices $(x,y,z)$ has coordinates ...
7
votes
3answers
1k 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 ...
6
votes
3answers
441 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) ...
45
votes
10answers
8k 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 ...
1
vote
1answer
255 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 ...
5
votes
2answers
519 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
1k 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
744 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 ...
6
votes
3answers
3k 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 ...
29
votes
8answers
4k 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 ...
4
votes
2answers
871 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?
6
votes
1answer
232 views
6
votes
1answer
771 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
703 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 ...
17
votes
3answers
2k views

How to calculate volume of convex hull and volume of a 3D object

I have a set of random 3D data points. How can I calculate the volume of the convex hull?
43
votes
2answers
6k 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 ...
12
votes
1answer
666 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
361 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
4answers
421 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 ...
67
votes
4answers
5k 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? ...
11
votes
3answers
1k 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
246 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 ...
11
votes
1answer
244 views

Finding minimal region with padding and linear map to circle

Suppose I have n ordered points. I would like to find a simple region that contains all the points and is close to the smallest region that contains the points except it is smooth and has some ...
16
votes
3answers
704 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
1k 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 ...
16
votes
4answers
706 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?
16
votes
1answer
720 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 ...
94
votes
3answers
12k 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
332 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 ...
34
votes
7answers
4k views

Intersecting graphics

Does the Mathematica graphics system have any concept of intersecting graphics? I've not found much in the documents so far. For example, if I want to show the intersection of two shapes: ...
16
votes
4answers
1k 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, ...
21
votes
1answer
907 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 ...
19
votes
2answers
1k 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 ...