Questions on constructing graphical objects using relatively complex computations relating to the mathematical structures defining those objects. Examples include convex hulls, Voronoi diagrams, Delaunay triangulations, mathematical constructions, symmetries, genuses of curves and graphs and ...

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64
votes
11answers
13k 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 ...
42
votes
7answers
6k 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: ...
126
votes
4answers
18k 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, ...
81
votes
4answers
7k 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? ...
22
votes
2answers
1k 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 ...
17
votes
2answers
686 views

How to simulate the true reflective movement of a particle bouncing around in an ellipse?

Please help me to simulate the movement of a particle inside a region with elliptical walls such that particle is reflected from the walls and continues to move. A friend was able write code to ...
22
votes
6answers
2k views

How to speed up the function DelaunayTriangulation?

First define a function meshGrid to generate some points: ...
40
votes
8answers
7k 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 ...
24
votes
4answers
4k 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 ...
9
votes
3answers
2k 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? ...
10
votes
3answers
3k 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 $0.7$.
8
votes
2answers
294 views

DelaunayMesh in a specified closed region - creating a concave hull from a set of points

I have a list of discrete points wich I want to use as nodes for creating a 2D mesh. I used DelaunayMesh and it works fine. The problem that I have is that some elements/polygons are outside of the ...
14
votes
3answers
2k views

Finding a Concave Hull

I have a 3d clustered data: Is there any other way to get concavehull of 3D data points?
9
votes
3answers
697 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) ...
30
votes
4answers
4k 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 ...
35
votes
6answers
2k views

Finding length of intersection of two surfaces

I would like to know how we find the length of the intersection of two surfaces. For instance, in the following example,a surface intersects with a plane: How do we find the length of intersection ...
25
votes
2answers
949 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: ...
15
votes
3answers
3k 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: ...
11
votes
1answer
301 views

Can I get the curvature at any point of a random curve?

Random curve like the above, for example. The data source is an image file. I don't have an expression. I want to start by curve fitting and then compute curvature. Is it possible?
18
votes
5answers
466 views

Is there a numerical method/built-in to calculate the boundary of a set of graphs?

Recently, I encounted a geometry problem in my work. For a curve-family that owns the following parametric equation: $$E(t,\theta)= \begin{pmatrix} x_E(t,\theta) \\ y_E(t,\theta) \end{pmatrix}$$ ...
14
votes
2answers
532 views

Equidistant points on a polyline

Set of 2D-points connected by a polyline B-spline function: ...
7
votes
3answers
3k 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 ...
35
votes
3answers
1k views

Can Mathematica solve Plateau's problem (finding a minimal surface with specified boundary)?

Given a closed curve $\mathcal C$ in three dimensions, is it possible to use Mathematica's built-in functionality to compute a minimal surface whose boundary is $\mathcal C$? For simplicity, let us ...
23
votes
2answers
2k 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 ...
10
votes
6answers
4k 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 ...
23
votes
4answers
791 views

Site - Cell Correspondence in Voronoi Diagram obtained via VoronoiMesh

Consider the following: ...
31
votes
5answers
1k 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.
20
votes
3answers
1k 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 ...
35
votes
2answers
2k 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 ...
30
votes
5answers
2k views

How can I define a 3D version of the built-in VoronoiDiagram (VoronoiMesh in V10) 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 ...
17
votes
3answers
3k 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?
19
votes
1answer
1k views

Faster way to compute the distance from a point to a surface in 3D

I am trying to compute the shortest distance between a point and a triangle in 3D ...
19
votes
6answers
492 views

Find the nearest locations for multiple points

Assume that there are many holes with their locations fixed, and the same number of balls distributed randomly. What is the smallest total distance for the balls fitting into the holes on the ...
12
votes
2answers
3k 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) ...
15
votes
3answers
2k 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.
17
votes
4answers
875 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
4answers
2k 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, ...
12
votes
2answers
281 views

How to convert a surface into a solid

Context I am interested in converting surfaces into solids (so I can make a 3D mesh out of them using ToElementMesh) Say I have the following cool surface ...
11
votes
1answer
210 views

Is DiscretizeRegion not yet ready ro discretize 3D-solids?

In the DiscretizeRegion documentation: "The region reg can be anything that is ConstantRegionQ and RegionEmbeddingDimension less than or equal to 3." With DiscretizeRegion there could be an easy way ...
6
votes
7answers
1k views

Choosing $n$ equidistant points on a circle with given radius and center

I would like to have a function circle which takes two inputs: a tuple {x,y} and a real number ...
4
votes
2answers
152 views

How to take something from DelaunayMesh and similar family of functions

I was looking at this question here and I tried the suggested idea by Anton Antonov to use DelaunayMesh It will look like this: ...
12
votes
2answers
299 views

Possible Bug in DiscretizeRegion with Option MaxCellMeasure

Bug introduced in 10.0.0 and fixed in 10.0.2 Consider the following ImplicitRegion: ...
11
votes
2answers
237 views

Probable Bug in HighlightMesh with 2D Convex Hulls created via ConvexHullMesh

Bug introduced in 10.0 and fixed in 10.2 One nice way to view the new and exciting Mesh objects introduced in Version 10 is by utilizing the function ...
3
votes
1answer
385 views

How to map vertex points from the surface of a straight pipe onto 2D plane

How to map vertex points from the surface of a straight pipe onto 2D plane. The 3D surface points of the straight pipe can be found here: data Working code: ...
42
votes
2answers
1k views

Numerically solving Helmholtz equation in 3D for arbitrary shapes

Context While studying manifold Learning I got interested in finding the eigenvectors of the Laplacian. (also in connection to this problem of solving the heat equation) Following this and that ...
21
votes
3answers
2k views

Generate a Random Polygon

Does some package exist with a function that takes a parameter $n$ and generates a random 2D $n$-sided simple polygon (convex or non-convex), possibly within a certain bounding box? It does not ...
19
votes
2answers
901 views

Difference (or intersection) of two convex polyhedra

I have two convex polyhedra stored in the following form: a set of vertices vertices = {{x1,y1,z1},...}, a set of faces, where each face is a convex polygon ...
21
votes
2answers
642 views

Convert binary voxel image to geometric region

I have a binary voxel image which described a contiguous region in space. Example: ...
9
votes
2answers
792 views

How to get UV mapping of 3D tube

Here is cylinder data: file We can mesh the surface, thanks to lalmei, Belisarius and Simon (link) How to achieve uv mapping from a 3d straight and curved tube? Working code: ...
15
votes
3answers
2k 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. ...