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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11
votes
2answers
844 views

Finding the perimeter, area and number of sides of a Voronoi cell

Does anyone have any suggestions how to determine the perimeter, area and number of sides of each Voronoi cell in Voronoi diagram?
16
votes
2answers
296 views

How to implement Bresenham’s algorithm as a system of equations?

Bresenham's line drawing algorithm is usually implemented via loops. But in Mathematica we can take advantage of its ability to solve Diophantine equations. From educational viewpoint it is quite ...
8
votes
5answers
2k views

How to check if a line segment intersects with a polygon?

The naive method is to bisect the line segment iteratively as asked here, and then check the bisection points using How to check if a 2D point is in a polygon?. Would there be an other way? I'm ...
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
1answer
721 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
3answers
4k views

Mathematica function intersection points with 3D grid

I need to produce a 3-dimensional equispaced grid over a given function in a way, that I can calculate intersection points of the function with the grids edges. So my first question is how to produce ...
5
votes
1answer
452 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 ...
18
votes
5answers
1k views

Insphere for Irregular Tetrahedron

I am looking for existing Mathematica code to compute the unique sphere inscribed inside an irregular tetrahedron. I can write it myself, but I would love to find that someone already performed this ...
8
votes
1answer
226 views

Decomposition of a semialgebraic set into connected components

Is there any built-in function for doing decomposition of a semialgebraic set into connected components? The only way I now can think of is to use ...
3
votes
2answers
337 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
3answers
241 views

Help with finding the point(s) inside a closed shape with the highest average ray length?

I am trying to find the point(s) with the highest average ray length of any implicit relation that is closed shape (ex. $x^2+y^2+\sin(4x)+\sin(4y)=4$). I have some idea of how to mathematically ...
3
votes
0answers
126 views

Differential Geometry on a MeshRegion [closed]

NB- see this question for a more formal request. 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 ...
2
votes
0answers
272 views

Fitting a rotated ellipse to data points [closed]

I have a bunch of x,y scatter data and I am trying to fit an ellipse through them. I understand that this question has been asked before and there are resources for this, e.g.: Fitting ellipse to 5 ...
2
votes
1answer
447 views

Calculate scalar potential from electric field

Is it possible for Mathematica to solve an equation like $\nabla f(\mathbf{r}) = - \mathbf{E}(\mathbf{r})$ for $f(\mathbf{r})$? I tried ...
20
votes
4answers
2k views

How to calculate the volume of a convex hull?

Given a spatial curve represented by a parametric equation, is it possible in Mathematica 9 to calculate symbolically (or at least numerically) the volume of its convex hull?
14
votes
4answers
251 views

Administrative Divisions bordering a geographic region (e.g. an ocean)

Update 3 I've worked out a solution that is bearable for a small number of subregions in the neighbour and added it as an answer. I'm going to make a post for optimisation help. Update 2 For a ...
6
votes
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 ...
21
votes
4answers
510 views

Find the volume of Phobos and Deimos

How can we calculate the volume of a 3D object using the new-in-10 computational geometry functions? For simple objects this works: ...
12
votes
1answer
158 views

RegionNearest and neighborhoods

In this previous question we see that RegionNearest isn't quite as 'capable' as Nearest for some things. Similarly, I need to ...
21
votes
0answers
194 views

Regression /Bug in DelaunayMesh from 10.3.1 to 10.4

Bug introduced in V10.4 and persists through 10.4.1 In answering this question, I realized the OP and I were obtaining different results from the alphaShapes2D ...
14
votes
2answers
242 views

Why is DiscretizeGraphics missing points on my curve?

I have a graphics expression which renders nicely as a closed curve when put in Graphics, I don't understand why I can't get the lines from DiscretizeGraphics or ...
11
votes
1answer
395 views

Finding minimal region with padding and linear map to circle

Suppose I have n ordered points. I would like to find a simple region that contains all the points and is close to the smallest region that contains the points except it is smooth and has some ...
6
votes
2answers
107 views

How to generate higher dimensional convex hull?

I like the function ConvexHullMesh very much, since I often need to take a look at the convex hull of points in 2D and 3D, which as an example can be generated and ...
14
votes
1answer
520 views

Cropping a Voronoi diagram

Someone know how can I get the correct crop of this Voronoi image using RegionFunction? As you can see, there is a lot of undesired white regions inside the left ...
14
votes
1answer
664 views

rule-based implementation of an algorithm

When I first started learning about rule-based programming with Mathematica, I tried to translate this algorithm for computing the convex hull of a set of 2-D points in $O(n \log(n))$ time, to use ...
12
votes
4answers
367 views

Arranging connector lines

Heike gave an absolutely wonderful answer to my question about arranging subplots around a main plot and including connector lines. This is the result: Starting from Heike's answer, what is the ...
8
votes
1answer
170 views

User-defined DistanceFunction for RegionNearest

In the function Nearest , I can define my custom function using the DistanceFunction option. e.g: ...
6
votes
2answers
251 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 ...
8
votes
2answers
131 views

How to assign Element marker at boundary edges

How to assign marker at the boundary edges as 1, 2, 3, 4 respectively and set all of the inside elements of region as 0? for example: Code: ...
7
votes
1answer
250 views

Finding corresponding vertex from 3d to 2d

I have this simple 3d data points: ...
6
votes
3answers
216 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 ...
6
votes
2answers
268 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: ...
27
votes
2answers
354 views

Bug in ArcLength?

fixed in 10.1 (windows) With Mathematica 10.0.2: ArcLength[Line[{{0, 0}, {1, 0}, {2, 0}}]] ArcLength[Line[{{0}, {1}, {2}}]] (* 2 *) (* 2 *) However, ...
10
votes
2answers
145 views

Possible Bug in Computing Surface Area of Certain Geometric Regions

Mathematica 10.2 introduced some new geometric regions. Two of the new regions include SphericalShell and CapsuleShape. ...
9
votes
1answer
88 views

MeshCoordinates from a RegionBoundary no longer in proper order in version 10.4

Bug introduced in V10.4 and persists through 10.4.1 Given that I have the following data set ...
7
votes
1answer
267 views

Can't plot rotated region

I was experimenting with the code from this question when I ran into another problem with regions. ...
6
votes
1answer
316 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 ...
5
votes
2answers
122 views

MeshRefinementFunction missing points

I'm doing some FEM on a rectangular region with a spherical cavity: ...
5
votes
2answers
195 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
2answers
248 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 ...
4
votes
0answers
77 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
2answers
738 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
401 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
1answer
74 views

MaxCellMeasure fails in 3D?

Question How come MaxCellMeasure works in 2D but fails in 3D? Indeed if I try ...
2
votes
1answer
555 views

Bounded Voronoi Diagram

I am trying to compute a Voronoi diagram bounded by a box. In some cases, the points used to compute the diagram form a diagram such that at least two boundary points are within the same polygon. For ...
0
votes
0answers
255 views

Determining if a point is inside or outside a 3DS (.3ds) or 3DS MAX (.max) object? [duplicate]

Imagine I import some 3DS (i.e. 3D studio) file (http://reference.wolfram.com/mathematica/ref/format/3DS.html) or a 3DS MAX file. How could I place this model (say, the 747.3ds file in the ...
7
votes
2answers
193 views

A method to discretize a three-dimensional solid

Consider the following region: ...
7
votes
1answer
203 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 ...
6
votes
1answer
200 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
1answer
161 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 ...