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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5
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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
823 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
484 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
1answer
325 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
237 views

Finding an optimal overlay of two point clouds

Imagine I have two sets of points: ...
5
votes
2answers
388 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
3answers
435 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
1answer
257 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 ...
5
votes
3answers
153 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
387 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
1answer
119 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
213 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
2answers
150 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: ...
5
votes
1answer
132 views

DiscretizeGraphics and BoundaryDiscretizeGraphics Fail on CapsuleShape and SphericalShell

It seems the new Graphics3D primitives have some incomplete features. Earlier, I uncovered a problem with computing their exact surface area see here. Now, I ...
5
votes
1answer
272 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
157 views

How to create bounded diagram plot?

I have set of points: ...
5
votes
0answers
239 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
263 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
577 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
267 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
546 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
1answer
112 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 ...
4
votes
1answer
823 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
53 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
148 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
170 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
376 views

A Graphics`Mesh`ConvexHull[] peculiarity

I have been unable to explain the behavior of Graphics`Mesh`ConvexHull[] on the following (highly simplified) example: ...
3
votes
6answers
547 views

How to find the vertices of a regular tetrahedron? a dodecahedron?

My question is: how to find the coordinates of the vertices of regular tetrahedron and dodecahedron? I tried to find the coordinates of the vertices of a regular tetrahedron as the solutions of a ...
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votes
3answers
1k views

How to integrate a function over a 3D planar polygon?

I am trying to integrate a function over a planar polygon in 3D. In 2D, this is fairly straightforward, using either answer from this question (I use the second answer). If we use an equilateral ...
3
votes
2answers
274 views

Selecting for 2D points that are within a threshold distance of an upper- and lower-bound number of points

I have a very large set of 2D points: numberOf2DPoints = 10^6; pointList = RandomReal[{0, 1000}, {numberOf2DPoints, 2}]; I'd like to find a way to quickly ...
3
votes
1answer
397 views

How can Mathematica be used to detect an area surrounded by the most lines?

I have an array of lines that produce random shapes. These lines define edge boundaries from an array that I would like to use to reconstruct the main feature of the array. Can Mathematica find the ...
3
votes
1answer
106 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, ...
3
votes
1answer
115 views

BoundedDiagram Error

Although BoundedDiagram function worked well for a small data set, I got errors in a specific case that I cannot explain. I am sorry I am pasting here a large list ...
3
votes
1answer
138 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 ...
3
votes
1answer
316 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: ...
3
votes
1answer
120 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. ...
3
votes
1answer
86 views

Why BoundedDiagram fails?

I have a set of points: ...
3
votes
0answers
60 views

Simple ways to implement vector dilation

Suppose we have a singly connected but not necessarily convex polygon. Something like shape = CountryData["Chad", "Coordinates"]. Is there a simple way to ...
3
votes
1answer
84 views

ConvexHullMesh sometimes excludes valid points from convex hull

I have a sequence of polytopes that I am trying to visualize, and I find that ConvexHullMesh sometimes excludes points from the convex hull, and it does so inconsistently. In particular, notice these ...
3
votes
0answers
104 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 ...
3
votes
0answers
89 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 ...
3
votes
0answers
224 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: ...
3
votes
0answers
204 views

Generating an obstacle-avoiding closed-curve with a fixed perimeter and a target area

I was wondering if there was a neat way to solve the following problem in Mathematica v9 - Provided a binarized image (where we call black pixels "obstacles" or vice versa, whichever is most ...
3
votes
0answers
411 views

How to make 3D object smooth?

This thread considers mathematical methods here to make the 3D object smooth but this question consider how to achieve the goal of smoothing a 3D object in Mathematica. I want to get smoother ...
2
votes
2answers
223 views

Finding integral points on a surface

Suppose I have a dimension formula (for a Lie algebra representation) that is as follows: $$ d(a,b) = {(a+1)(b+1)(a+b+2) \over 2} $$ Now consider the surface $F(a,b,n) = 0 = d(a,b) -n$ where $n \in ...
2
votes
3answers
252 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
277 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 ...
2
votes
1answer
178 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, ...
2
votes
1answer
74 views

Clean & efficient bounding box non-intersection test

I would like a quick test to tell me that segments $ab$ and $cd$ cannot intersect in the plane. If the maximum $x$-coordinate of $a$ and $b$ is less than the minimum $x$-coordinate of $c$ and $d$, ...