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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1
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0answers
94 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 y=\frac{cos(s_n)-cos(s_{n+1})}{sin(s_{n+1})-sin(s_n)}(x-sin(s_n))-...
7
votes
2answers
267 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
250 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 $N,$ ...
2
votes
1answer
138 views

How could I make visible the convex hull of 3 point inside this region?

Small version of the question How can I control the color and the Thickness of this graph?? ...
1
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1answer
180 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: ...
8
votes
1answer
535 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 ...
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 ...
27
votes
5answers
857 views

Site - Cell Correspondence in Voronoi Diagram obtained via VoronoiMesh

Consider the following: ...
20
votes
2answers
616 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 ...
4
votes
5answers
930 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 "...
10
votes
2answers
385 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? ...
7
votes
1answer
434 views

Smooth 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 ...
9
votes
3answers
541 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 ...
3
votes
1answer
228 views

RegionPlot3D run forever when plotting 3D ParametricRegion

when working with 2D, RegionPlot works fine with ParametricRegion as can be seen in this example: ...
0
votes
1answer
254 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
303 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
180 views

Problem with clipping of tick labels

Please look at Show[DiscretizeGraphics[Graphics3D[{Cone[]}]], Axes -> True, Boxed -> True] Well, there are some Ticks,...
6
votes
1answer
163 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 ...
6
votes
1answer
345 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 ...
12
votes
2answers
308 views

Possible Bug in DiscretizeRegion with Option MaxCellMeasure

Bug introduced in 10.0.0 and fixed in 10.0.2 Consider the following ImplicitRegion: ...
8
votes
1answer
175 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
354 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.: ...
11
votes
2answers
243 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 ...
0
votes
0answers
107 views

How to make equidistant or split ListPoint [duplicate]

How to split the curve with more equidistant points? ...
5
votes
3answers
630 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
290 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
463 views

Probable Bug in ConvexHullMesh

Bug introduced in 10.0 and persisting through 10.2 or later Consider points taken from the following parametric plot. See this question ...
2
votes
1answer
107 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
283 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
191 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 ...
4
votes
1answer
226 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
283 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: ...
4
votes
0answers
354 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: ...
7
votes
1answer
254 views

Finding corresponding vertex from 3d to 2d

I have this simple 3d data points: ...
19
votes
2answers
946 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
553 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
146 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 ...
9
votes
2answers
824 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
396 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: ...
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 ...
2
votes
2answers
462 views

Convert DelaunayTriangulation-> Graph->AdjacencyMatrix

Is there a way to convert a Delaunay Triangulation into a Graph structure so that one can generate an AdjacenyMatrix of the Delaunay?
5
votes
1answer
177 views

How to create bounded diagram plot?

I have set of points: ...
2
votes
0answers
54 views

Voronoi diagram for line segments in Mathematica [duplicate]

I know that mathematica has built in functions for creating triangulations and Voronoi diagrams. However I haven't found a function that would create a Voronoi diagram for line segments. Is there a ...
1
vote
0answers
126 views

Trying to study the three points theorem of the Mobius Transformation

I am trying to study the three points theorem of the Mobius transformation. This theorem says that the Mobius transformation $M$ maps three distinct points p, q, r to three distinct points p', q', r'. ...
3
votes
1answer
128 views

Problem with PlanarGraphPlot And ConvexHull

I'm getting a lot of strange errors when using PlanarGraphPlot with a simple list of 11 points. This is using Mma 9.0.1 64-bit Mac OS X. ...
4
votes
2answers
772 views

Image processing: extracting ordered contour

Continuing the question How to extract the edge from a set of points and its answer by Simon Woods, I would like to ask if there is a way to extract the boundary of obtained as ...
0
votes
1answer
510 views

Area of a convex polygon with a set of points [duplicate]

I have a set of points Pts[a_,b_,c_]:={{a, b}, {b, a}, {c, a}, {a, c}, {b, c}, {c, b}} which define a convex polygon and I would like to find its area. There is ...
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 ...
-6
votes
1answer
247 views

Poincaré section for 3BP

I try to plot the Poincaré section for the 3BP i use the following code that works very well: ...
1
vote
2answers
515 views

intersection between function and plane

I try to solve a ODE system of equations and i want to plot the intersection of the 3D solutions with a costant plane. To do this i use the follow code: ...