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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2
votes
0answers
25 views

Region Intersection for MeshRegion objects embedded in 3D

How can I create a logical intersection of MeshRegion objects that are three-dimensional? The RegionIntersection function will ...
6
votes
1answer
78 views

Need help on the proper use of a formula to produce a cambered airfoil

Following the book on "The Theory of Thin Wing Sections" page #112 describes the method to combine a camber line (i.e Mean Line) and a thickness distribution to form a cambered wing section. Data ...
-3
votes
0answers
77 views

A polyhedron convex test

I want to write a test function to see if this polyhedron is convex or not: ...
56
votes
11answers
10k 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 ...
0
votes
1answer
31 views

Parse notation recursively

For a special notation I would like to get the help of Mathematica to expand complex expressions through a set of Notation rules. However since this tasks involves applying the notation recursively ...
19
votes
2answers
1k 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 ...
8
votes
1answer
108 views

Decomposition of a semialgebraic set into connected components

Is there any built-in function for doing decomposition of a semialgebraic set into connected components? The only way I now can think of is to use ...
1
vote
1answer
127 views

Distinguishing left from right adjacent triangles in triangle mesh

What I'm trying to do: I'm trying to create a path-drawing function which will produce a path like the one I-P in the diagram below. The way this path was generated requires me to swap between the ...
0
votes
0answers
32 views
1
vote
1answer
63 views

Package for symbolic computation of christoffel symbols and parallel transports in Riemannian geometry, given the metric

I've no knowledge in mathematica (but I do in matlab), but I'd really appreciate if someone could mention what is/are the best and easy to learn mathematica package(s) for symbolic and numerical ...
1
vote
0answers
43 views

How to speed up geometric Resolve query involving $\exists$ and $\forall$?

I would want to test connectedness of semialgebraic sets with naive code like this: ...
8
votes
3answers
562 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) ...
-2
votes
1answer
51 views

Solve on parametric equation produces inequal results

I have a parametric (parameter t) equation in two dimensions (vectors). s = Solve[pt[t] == qt[t], {a, b}] Both pt and qt are parametric lines using a and b as ...
38
votes
3answers
1k views

Create a torus with a hexagonal mesh for 3D-printing

I am new to Mathematica, and I'm looking for a way to create patterns on the surface of 3D objects. One thing I have not been able to do is create a hexagonal mesh on a torus. What I would like to ...
12
votes
3answers
1k views

Finding a Concave Hull

I have a 3d clustered data: Is there any other way to get concavehull of 3D data points?
2
votes
1answer
143 views

Region bounded by Ellipse and Line

I have an ellipse defined either as algebraic or geometric: algebraic: ax^2 + bxy +cy^2 + dx +ey +f = 0 geometric: major Axis, minor Axis, x center, y center, ...
0
votes
0answers
50 views

Broad Phase Collision Detection with Mathematica and using CUDA

In this and this post, I asked the question about a fast sweep and prune algorithm implementation for broad phase collision detection. To further speed up things a CUDA implementation would be even ...
24
votes
2answers
312 views

Bug in ArcLength?

fixed in 10.1 (windows) With Mathematica 10.0.2: ArcLength[Line[{{0, 0}, {1, 0}, {2, 0}}]] ArcLength[Line[{{0}, {1}, {2}}]] (* 2 *) (* 2 *) However, ...
2
votes
0answers
72 views

Differential Geometry on a MeshRegion

For many many years (honestly, since 1987) I've had my own MMa computational geometry code for dealing with 3D meshes. I principally (there's a joke there somewhere) use it to calculate coordinate ...
114
votes
4answers
14k 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, ...
1
vote
0answers
87 views

Collision detection algorithm (discrete) with sweep and prune algorithm for periodic boundary conditions

EDIT: Question Updated with solution approach, but solution much slower than original implementation. Any ideas to speed up implementation? In the discussion on collision detection (see here) I asked ...
26
votes
3answers
654 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 ...
2
votes
3answers
242 views

Surface area of a cylinder [closed]

Evaluating expr = {Sin[t], Cos[t], Sin[p]}; ParametricPlot3D[expr, {t, 0, 2 π}, {p, 0, 2 π}] Area[expr, {t, 0, 2 π}, {p, 0, 2 π}] gives an area of ...
2
votes
2answers
224 views

Finding if a point is in a region bounded by a curve and the axes (curve made of discrete points)

Here's a small example this is not the real curve but a simple example I made for this question. Here's the plot of a list with a point A of known coordinates. Now I need to find if the point A ...
19
votes
6answers
1k views
1
vote
0answers
57 views

Implementation of Lubaehevsky-Stillinger Algorithm to pack hard spheres

To generate a model of a polycrystalline material with specified grain size distribution (e.g coming from a Monte Carlo Grain Growth simulation) the Paper "Effects of grain size distribution and ...
2
votes
0answers
122 views

Fitting a rotated ellipse to data points [closed]

I have a bunch of x,y scatter data and I am trying to fit an ellipse through them. I understand that this question has been asked before and there are resources for this, e.g.: Fitting ellipse to 5 ...
0
votes
0answers
77 views

Von Neumann's method to generate points uniformly distributed on a region of a n-sphere surface

I am trying to generate points uniformly distributed on a region of a single n-sphere surface (all angles in hyperspheric coordinates are between 0 and Pi/2). I decided to use von Neumann's method ...
14
votes
2answers
484 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 ...
0
votes
0answers
79 views

Meshing of a cube

I want to mesh a cube and what I use is ToElementMesh[Cuboid[ {-1, -1, -1}, {1, 1, 1}]]. This creates a regular grid of the cube. Is there a way to specify that ...
13
votes
1answer
422 views

Cropping a Voronoi diagram

Someone know how can I get the correct crop of this Voronoi image using RegionFunction? As you can see, there is a lot of undesired white regions inside the left ...
6
votes
2answers
141 views

Discretizing regions with pointy boundaries

I'm trying to discretize a region with "pointy" boundaries to study dielectric breaking on electrodes with pointy surfaces. So far I've tried 3 types of boundaries, but the meshing functions stall ...
5
votes
0answers
196 views

Convex hull of a large data set of 3D points

I recently needed to deal with a large data set of 600.000 points in three dimensions. My task was to find a convex hull for this data. I have Mathematica 10, so I could use the function ...
17
votes
5answers
310 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 ...
5
votes
3answers
142 views

Find Unconnected Subregions

If I have a region, how can I identify sub regions that may be disconnected, if any exist? region defines a rectangular region given two diagonally opposed ...
6
votes
1answer
140 views

Numerical Functions Compatible with Regions Fail with MeshRegions and BoundaryMeshRegions

Bug introduced in 10.0.0 and fixed in 10.0.2 Given a MeshRegion: region = DelaunayMesh[RandomReal[1, {50, 3}]] We can ...
1
vote
0answers
59 views

How can I define a metric in xAct?

I'm using "xAct" package and I want to define a my metric, that is a non standard metric. For example, my metric is diagonal ...
4
votes
2answers
183 views

Extracting ragged array from an image

I have a list of points, which represent positions of peaks in an image. The nature of the image itself shouldn't matter, as I already have the peak positions. As a simple example, consider the ...
4
votes
3answers
246 views

Cut a polygon by a line

I have a polygon, says, Polygon[{0,0},{10,0},{10,10}{0,10}]. I would like to cut it by a line (through two points) and take one half of it. Could you please suggest ...
1
vote
2answers
156 views

Only show part of a cube below an intersecting plane

I plot a cube and a plane. I just want to show the part below the plane. The code: ...
11
votes
2answers
166 views

Possible Bug in DiscretizeRegion with Option MaxCellMeasure

fixed in 10.0.2 Consider the following ImplicitRegion: reg = ImplicitRegion[x^2 + y^2 + z^2 == 16, {x, y, z}]; We can ...
5
votes
2answers
145 views

Test existence of a path from one side of a graph to another

I'm trying to determine how I can test if a path exists from one side of a graph to another as efficiently as possible. If I have the Lines given by: ...
6
votes
1answer
183 views

Obtain polygons describing all intersections of many polygons

I have 6894 polygons describing zones in a state plane (i.e., cartesian) coordinate system. Most are not very complex, and I believe none have holes. A random example is Polygon[{{351633., ...
6
votes
5answers
957 views

How to check if a line segment intersects with a polygon?

The naive method is to bisect the line segment iteratively as asked here, and then check the bisection points using How to check if a 2D point is in a polygon?. Would there be an other way? I'm ...
12
votes
0answers
688 views

Using TetGen in Mathematica to get 3D Voronoi diagram

In this post, the use of TetGen for 3D Voronoi tesselation has been briefly discussed. However there is still no info about the use of TetGen to generate a 3D Voronoi diagram. The TetGen documentation ...
0
votes
0answers
53 views

How to determine if a point is within a geopositioned RegionMember

I have a KML file which contains an area of interest, I also have a number of lat/long geo positions. I'm trying to filter out the points not within my AOI. So I have my KML file. I convert it to a ...
2
votes
1answer
61 views

RegionUnion issues with many Regions

The new RegionUnion[] function is just what I needed if only I could get it to work. I have many non-overlapping regions that I will need to use as plotting domains ...