# Tagged Questions

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.

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, ...
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? ...
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 ...
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 ...
2answers
838 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 ...
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 ...
3answers
455 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 ...
1answer
574 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 ...
5answers
586 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.
3answers
418 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 ...
3answers
643 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 ...
2answers
407 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: ...
1answer
528 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 ...
3answers
499 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 ...
2answers
491 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 ...
2answers
906 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.
5answers
446 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 ...
2answers
202 views

### Equidistant points on a polyline

Set of 2D-points connected by a polyline B-spline function: ...
2answers
418 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 ...
3answers
443 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?
3answers
576 views

### How to speed up the function DelaunayTriangulation?

First define a function meshGrid to generate some points: ...
4answers
285 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 ...
2answers
652 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, ...
2answers
595 views

### Finding a Concave Hull

I have a 3d clustered data: Is there any other way to get concavehull of 3D data points?
1answer
369 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 ...
3answers
655 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.
2answers
302 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) ...
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 ...
2answers
328 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. ...
1answer
188 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?
0answers
322 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 ...
3answers
253 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 ...
2answers
277 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: ...
1answer
173 views

...
1answer
446 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 ...
6answers
283 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 ...
3answers
342 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 ...
2answers
252 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? ...
2answers
335 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.
3answers
675 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 $0.7$.
1answer
598 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 ...
2answers
245 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 ...
3answers
213 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 ...
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 ...
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) ...
2answers
670 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?
2answers
436 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 ...
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) ...
0answers
89 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 ...
1answer
170 views

### A GraphicsMeshConvexHull[] peculiarity

I have been unable to explain the behavior of GraphicsMeshConvexHull[] on the following (highly simplified) example: ...
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 0, "mathjax_asciimath": 2, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9017321467399597, "perplexity_flag": "middle"}