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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6
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2answers
1k views

Extracting polygons from 3D contour plot surface

Edit: This question turned out to be two parts so I am going to make this question about only the first part a kguler provided an excellent answer. Here is a better representation. My actual data ...
6
votes
1answer
138 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 ...
6
votes
2answers
246 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: ...
6
votes
2answers
205 views

ToElementMesh problem on Ball defined by ImplicitRegion?

Bug introduced in 10.0 and fixed in 10.2 Could any one please confirm the following bug in mathematica 10.0.2 ? If I define this ball ...
6
votes
1answer
309 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 ...
6
votes
1answer
280 views
6
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1answer
639 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) ...
6
votes
1answer
1k views

Construct a simple mesh or tetrahedral mesh from 3D image surface

I have a 3D Y-Shape hollow tube, not so good surface. Import["http://dl.dropbox.com/u/68983831/tube02.vtk", "Graphics3D"] I tried to use following vertex data ...
6
votes
2answers
157 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
87 views

Expensive MeshRefinementFunction

I want to discretize a region using DiscretizeRegion. Now, I want the mesh to be more refined, when the curvature of a certain function ...
6
votes
2answers
2k views

Calculating a minimum bounding box for a set of 3-space coordinates / spheres

I have a set of 3-space coordinates for the atoms of a molecule (I could also transform them into spheres with radii corresponding to the atoms they represent). I would like to place this molecule ...
6
votes
1answer
292 views

Behavior of Graphics`Mesh`InPolygonQ with self-intersecting polygons

Playing around with some of the answers in the question How to check if a 2D point is in a polygon? I noticed that: Graphics`Mesh`InPolygonQ[poly,pt] Displays ...
6
votes
1answer
256 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
1answer
155 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
453 views

How to get vertices of a polytope given by equalities and inequalities?

I have a polytope given by some equalities and inequalities, how can I get all the vertices of the polytope? If there's a way to deal with the one given by inequalities only, how can I reduce the ...
6
votes
0answers
103 views

Possible Bug with Options in DelaunayMesh

Update: It turns out after some testing, none of the Options work in DelaunayMesh when 3D point sets are involved. Original ...
6
votes
0answers
321 views

Computing Ehrhart's polynomial for a convex polytope

Is there a Mathematica implementation for computing the Ehrhart polynomial of a convex polytope which is specified either by its vertices or by a set of inequalities? I am interested in knowing this ...
5
votes
3answers
253 views

Point belonging to a Disk in a Cartesian Coordinate System

The image below represents a human subject fixations while observing this abstract pattern for 3 seconds. I would like to know how much time they spent looking at the actual disk. That is a red point ...
5
votes
3answers
974 views

How to create a planar graph from a set of random points

Question Given a set of points in the plane, how can you create a planar graph in the standard graph representation of Mathematica (version 9 or higher), from these points? Background A planar ...
5
votes
3answers
558 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: ...
5
votes
3answers
142 views

Lloyd relaxation on VoronoiMesh

How can we apply Lloyd's relaxation algorithm to a VoronoiMesh? Thanks. UPDATE Thanks a lot KennyColnago for your answer. Based on Simon Woods suggestion of ...
5
votes
1answer
350 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.
5
votes
1answer
254 views

Finding an optimal overlay of two point clouds

Imagine I have two sets of points: ...
5
votes
2answers
490 views

How to use a ConvexHull as RegionFunction?

I have a set of data supported over a region in 2D. I want to use RegionPlot and ContourPlot on interpolations of my data, but want to restrict the Plots to the region over which my data is supported. ...
5
votes
2answers
180 views

Separate boundaries of multiply connected region

I have a multiply connection two-dimensional region such as the following: br = BoundaryDiscretizeGraphics@Graphics[Disk[#, 8/9] & /@ CirclePoints[9]] I am ...
5
votes
3answers
566 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 ...
5
votes
3answers
163 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 ...
5
votes
1answer
431 views

ListPlot3D of a set of points in a non-convex region

I would like to plot a set of points in the same style as ListPlot3D does, but only in a non-convex region that I can specify (e.g. using a ...
5
votes
2answers
145 views

RegionPlot of ImplicitRegion is incorrect

Why does RegionPlot of the ImplicitRegion give an incorrect plot? Also, will how does this affect calculations with ...
5
votes
1answer
148 views

How to fill the closed region by ParametricPlot with solid color?

I am interested in the following implicit curve with parametric equation: $$ \left\{\quad \begin{array}{rl} x=& 9 \sin 2 t+5 \sin 3 t \\ y=& 9 \cos 2 t-5 \cos 3 t \\ \end{array} \right. $$ ...
5
votes
2answers
234 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 ...
5
votes
1answer
114 views

Error from BoundedDiagram

I cannot understand the meaning of the error BoundedDiagram::notuniq: BoundedDiagram requires that boundary vertices lie in unique Voronoi polygons. >> BoundedDiagram::nobd: Bounded ...
5
votes
1answer
96 views

Minimal perimeter of all possible polygons

We had a fun problem for a student activity today: Let $P(z) = z^8 + \left(4\sqrt{3} + 6\right)z^4 - \left(4\sqrt{3} + 7\right)$. What is the minimum perimeter among all the $8$-sided polygons in the ...
5
votes
1answer
297 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.: ...
5
votes
1answer
115 views

Intersecting cones for weighted Voronoi diagram - DiscretizeRegion was unable to discretize the region

I want to make a diagram (and also a Graph of the vertex + edge config) of the orthogonal projection of the intersections of a set of conical surfaces in order to ...
5
votes
1answer
169 views

How to create bounded diagram plot?

I have set of points: ...
5
votes
0answers
305 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 ...
4
votes
2answers
274 views

Vectors in a spherical shell

I have written code that randomly generates a 3D vector of random magnitude. I now want to create a histogram of how many vectors lie in the concentric spherical shells (n*delta r, (n+1)delta r) ...
4
votes
5answers
768 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 ...
4
votes
2answers
1k views

How to process .vtk file

I want to extract the cluster of points inside 3D box, is there any way one can do this in Mathematica?
4
votes
3answers
287 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 ...
4
votes
2answers
664 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 ...
4
votes
2answers
84 views

MeshRefinementFunction missing points

I'm doing some FEM on a rectangular region with a spherical cavity: ...
4
votes
1answer
1k views

How to split compound polygons into convex polygons?

Is it possible to split non-convex polygons into convex plygons with Mathematica 9? For example: ...
4
votes
1answer
98 views

DelaunayMesh in a specified closed region

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 ...
4
votes
1answer
161 views

Problem with clipping of tick labels

Please look at Show[DiscretizeGraphics[Graphics3D[{Cone[]}]], Axes -> True, Boxed -> True] Well, there are some ...
4
votes
1answer
199 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: ...
4
votes
1answer
395 views

A Graphics`Mesh`ConvexHull[] peculiarity

I have been unable to explain the behavior of Graphics`Mesh`ConvexHull[] on the following (highly simplified) example: ...
4
votes
0answers
53 views

ParallelTable slow down, Region functions

I am experiencing speed issues with ParallelTable. There are a few related problems on SX posted here and here, but no resolution. The various respondents to those ...
4
votes
0answers
122 views

How to draw Kobon triangles

I would like to know if Mathematica is capable of constructing Kobon triangles; that is, a figure consisting of the largest number of non-overlapping triangles that can be constructed using $n$ lines, ...