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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1
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0answers
17 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 ...
0
votes
0answers
53 views

Can mathematica compute area of region defined by inequalities? [on hold]

Suppose I have a region in the plane bounded by a few straight lines and circles, so it's defined by inequalities of the form $y\leq mx+ b$ and $(x-c)^2+(y-d)^2 \leq r$. Is it possible that ...
3
votes
1answer
60 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
47 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 ...
10
votes
3answers
544 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
43 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
156 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
198 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
74 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
209 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 ...
15
votes
3answers
226 views
18
votes
2answers
350 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
213 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
241 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
97 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
302 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
113 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
125 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
204 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
106 views

Problem with clipping of tick labels

Please look at Show[DiscretizeGraphics[Graphics3D[{Cone[]}]], Axes -> True, Boxed -> True] Well, there are some ...
5
votes
1answer
98 views

Numerical Functions Compatible with Regions Fail with MeshRegions and BoundaryMeshRegions

Given a MeshRegion: region = DelaunayMesh[RandomReal[1, {50, 3}]] We can numerically ...
4
votes
1answer
125 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
121 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
102 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
134 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.: ...
7
votes
2answers
131 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
68 views

How to make equidistant or split ListPoint [duplicate]

How to split the curve with more equidistant points? ...
5
votes
3answers
338 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
90 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
303 views

Probable Bug in ConvexHullMesh

Consider points taken from the following parametric plot. See this question ...
2
votes
1answer
88 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 = ...
6
votes
1answer
116 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
128 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
102 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
145 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: ...
1
vote
0answers
74 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
173 views

Finding corresponding vertex from 3d to 2d

I have this simple 3d data points: ...
5
votes
1answer
207 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
131 views

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

Given a list of latitude and longitudes say ...
1
vote
1answer
84 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
417 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
232 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: ...
16
votes
1answer
946 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
117 views

How to create bounded diagram plot?

I have set of points: ...
2
votes
0answers
39 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
77 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
97 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. ...
2
votes
2answers
376 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
182 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 ...