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.
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 ...
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 ...
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?
...
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 ...
12
votes
3answers
579 views
How to speed up the function DelaunayTriangulation?
First define a function meshGrid to generate some points:
...
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 ...
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: ...
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?
...
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?
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 ...
16
votes
2answers
964 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.
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 ...
2
votes
3answers
227 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:
...
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 ...
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 ...
13
votes
2answers
206 views
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.
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 ...
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, ...
2
votes
1answer
283 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 ...
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 ...
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?
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?
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:
...
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 ...
9
votes
2answers
334 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.
...
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 ...
0
votes
0answers
82 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 ...
