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.

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12
votes
5answers
164 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 ...
1
vote
0answers
55 views

projecting a RegionProduct into 3D space

Apparently, RegionProduct should allow you to generate convolution-generated shapes. For instance, take a 1D curve and a sphere, and the region product I would ...
1
vote
2answers
130 views

Rotating a plane about an arbitrary axis

I would like to rotate a plane by $k$ degrees about an arbitrary axis. How should I do it using RotationTransform? hmm i realise if I do the following ...
5
votes
1answer
249 views

Areas of Voronoi cells from image file

I have an binary image with non-point objects. Does anyone have any suggestions how to determine area of each Voronoi cell in Voronoi diagram (goal is area distribution)? Thank you in advance.
6
votes
1answer
100 views

Collision detection algorithm (discrete) with sweep and prune algorithm

For a more complex collision detection approach, I need an efficient (aka fast) algorithm to prune the elements by using boundary boxes. A classical algorithm is the so called sweep and prune (SAP) ...
5
votes
3answers
193 views

Triangulated Mesh from Voronoi Diagram

I want to generate a mesh (using Mathematica 10) in the following manner: Generate a Voronoi diagram, like so: and then triangulate each individual Voronoi grain, were an edge is formed by ...
3
votes
1answer
69 views

Region plot of transformed region giving odd result

I tried applying a transformation to a rectangle: RegionPlot[TransformedRegion[Rectangle[{0, 0}, {1, 1}], {#1^(1/3) + #2, 1 + #2} &]] giving In reality, ...
-2
votes
0answers
48 views

How to find intersections of intervals? [duplicate]

Let a finite set of closed intervals in the plane be given. How to find all the intersections of these, outputing the intersection points together with the intersecting intervals? This is a problem of ...
11
votes
3answers
580 views

Finding the surface area of a 3D convex hull

I have noted several instances here and here where ConvexHullMesh, introduced in v10 has been used to greatly simplify some geometry problems. Determining the ...
1
vote
0answers
45 views

Use of Mathematica to put equation into vector form

Is there a way to put the following equation of a line into vector form using Mathematica (or a Mathematical package)? $\displaystyle ...
6
votes
2answers
171 views

A question regarding “DiscretizeGraphics”

I want to find the volume of a torus torus = RevolutionPlot3D[{2 + Cos[t], Sin[t]}, {t, 0, 2 Pi}] ...
6
votes
3answers
208 views

Speed of ConvexHullMesh

Pick $N$ random points on the surface of the sphere, then use ConvexHullMesh[] to compute their convex hull. Empirically, this takes time quadratic time in $N,$ ...
1
vote
1answer
82 views

how to find the vector intersection in a collection of triangulated 3D points?

I'm trying to calculate the 3D point coordinates for the intersection of a vector with a plane. I have been using the following code to do this: ...
7
votes
1answer
223 views

How to draw quantum circuit with mathematica?

How to draw quantum circuit as the following one with mathematica? I only find the quantum package which is designed for MMA 7.0 as the author said. But the version of my Mathematica is 9.0 and when ...
27
votes
6answers
1k 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 ...
16
votes
3answers
249 views
18
votes
2answers
367 views

Object separation from a 2.5D surface

I'm trying to identify the shape and the boundaries of objects. The data was generated with a laser scanner and represent the surface of an area in which many boulders lay on the ground and making up ...
3
votes
5answers
230 views

Ordering the Boundary points of a Polygon

I feel like this should be simple, but I keep running into walls. Say someone gives you the coordinates of the vertices of a pentagon and the center point of the hexagon. Is there any way to get an ...
8
votes
2answers
254 views

How can I only draw outer common tangent to two circles?

I have code worked for drawing common tangent lines to two circles(http://en.wikipedia.org/wiki/Tangent_lines_to_circles), now I want to delete the inner common tangent lines, how? ...
3
votes
0answers
104 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 ...
8
votes
3answers
319 views

Torus triangulation

I'd like to plot something similar to this but with a triangle instead of a pentagon. Also, I'd like to triangulate the faces, that is, to insert the diagonals for each face of the 3 prisms used. In ...
2
votes
1answer
117 views

RegionPlot3D run forever when plotting 3D ParametricRegion

when working with 2D, RegionPlot works fine with ParametricRegion as can be seen in this example: ...
1
vote
1answer
131 views

Is it necessary to introduce ImplicitRegion and ParametricRegion in version 10?

In version 10.0, Mathematica introduced a new function about region plotting: ImplicitRegion. But I'm wondered that haven't this function been already existed in the older version? That is, ...
10
votes
2answers
214 views

How can I decide whether a closed surface is intersected by a triangle?

A closed surface consisted of Polygons or GraphicsComplex and a triangle made by 3 points are in a 3D space. How can I decide ...
4
votes
1answer
111 views

Problem with clipping of tick labels

Please look at Show[DiscretizeGraphics[Graphics3D[{Cone[]}]], Axes -> True, Boxed -> True] Well, there are some ...
6
votes
1answer
101 views

Numerical Functions Compatible with Regions Fail with MeshRegions and BoundaryMeshRegions

Given a MeshRegion: region = DelaunayMesh[RandomReal[1, {50, 3}]] We can numerically ...
5
votes
1answer
152 views

How do I get a MeshRegion from an obj file, or from Geometry3D

How do I read in an obj file as a MeshRegion so I can e.g. compute its area? If I just import the object and try Area[O] it ...
11
votes
1answer
124 views

Possible Bug in DiscretizeRegion with Option MaxCellMeasure

Consider the following ImplicitRegion: reg = ImplicitRegion[x^2 + y^2 + z^2 == 16, {x, y, z}]; We can discretize it using ...
7
votes
1answer
106 views

User-defined DistanceFunction for RegionNearest

In the function Nearest , I can define my custom function using the DistanceFunction option. e.g: ...
5
votes
1answer
136 views

How can one compute a 3D Periodic Delaunay Triangulation using DelaunayMesh?

Given a non-periodic point set, one can easily tetrahedralize it using the new (in V10) DelaunayMesh function. e.g.: ...
8
votes
2answers
137 views

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

One nice way to view the new and exciting Mesh objects introduced in Version 10 is by utilizing the function HighlightMesh, so ...
0
votes
0answers
71 views

How to make equidistant or split ListPoint [duplicate]

How to split the curve with more equidistant points? ...
5
votes
3answers
347 views

How to measure cross sectional area of Tube

I have modified my question to a simple version. I have vertex clusters, polygons and a list of center points. Attached pts and polygons of 3d tube are: ...
2
votes
1answer
97 views

How to draw a 3D convex hull of a set of points with styling

I´m trying to obtain the convex hull (with transparent faces) of a small number of points. I would like the Plot to have the points shown with small spheres numbers 1, 2, 3, ... along the axes ...
11
votes
2answers
310 views

Probable Bug in ConvexHullMesh

Consider points taken from the following parametric plot. See this question ...
2
votes
1answer
89 views

About TetGenTetrahedralize Mesh Size

I have used TetGenTetrahedralize to generated a cubic mesh. I want that the edge size of the triangle to be 0.2, how can realized this? And What does the word "pq1.414a1" mean? inst1 = ...
7
votes
1answer
133 views

Can't plot rotated region

I was experimenting with the code from this question when I ran into another problem with regions. ...
1
vote
0answers
133 views

How to define two polyhedron intersect or not?

Recently I have used Mathematica to simulate the concrete structure. The most important point is generate random concrete aggregate. As you know, concrete aggregate can be looked as a polyhedron. We ...
3
votes
1answer
105 views

What kind of object results from RegionIntersection function?

I'm trying to use RegionIntersection in a couple of Polygons. The polygons are the following: ...
6
votes
2answers
151 views

“The function DiscretizeGraphics is not implemented for GraphicsComplex” confusion

Why does DiscretizeGraphics seems to work on one GraphicsComplex and not the other? Here is an example that works: ...
2
votes
0answers
85 views

Death of parallel sub-kernels

EDIT : Finally, the new Mathematica 10.0 seems to fix it. I have a little parallelization problem. I wrote a code to generate a quasicrystal by dynamical generation. Here the code: ...
6
votes
1answer
179 views

Finding corresponding vertex from 3d to 2d

I have this simple 3d data points: ...
5
votes
1answer
222 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 ...
2
votes
1answer
157 views

Find area of polygon on a sphere from a set of latitude-longitude points

Given a list of latitude and longitudes say ...
2
votes
1answer
93 views

how to find iso-cost contours on a 2d plot efficiently

Consider a 2D plot in which dimension 1 and 2 represent quantity 1 and 2 respectively ranging over 0 to 100. Each point in the space corresponding to (x,y) represent cost of choosing quantity 1 as x ...
6
votes
2answers
433 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: ...
3
votes
1answer
243 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: ...
17
votes
1answer
973 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 ...
5
votes
1answer
123 views

How to create bounded diagram plot?

I have set of points: ...