# Tagged Questions

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 ...

2answers
300 views

### How to implement Bresenhamâ€™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 ...
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 ...
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 ...
1answer
460 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 ...
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 ...
1answer
233 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 ...
2answers
345 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 ...
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 ...
1answer
457 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 ...
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?
6answers
963 views

### Is there a simple strategy to determine whether a point is inside a boundary?

For a ellipse $E(\theta)$, which owns the parametric equation as follows: $\begin{cases} x = a \sin\theta + b \cos\theta + c \\ y = d \sin\theta + e \cos\theta + f \\ \end{cases}$ Now, I have a ...
4answers
261 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 ...
2answers
864 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?
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 ...
4answers
525 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: ...
1answer
161 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 ...
0answers
197 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 ...
3answers
523 views

### How to speed up estimation of Mean and Gaussian curvatures on triangular meshes?

I am trying to estimate curvatures on a triangulated surface/manifold using the algorithm of : Meyer, M., Desbrun, M., SchrÃ¶der, P., & Barr, A. H. (2003). Discrete differential-geometry operators ...
2answers
251 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 ...
1answer
399 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 "...
3answers
138 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 ...
1answer
668 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 ...
1answer
526 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 ...
1answer
173 views

### User-defined DistanceFunction for RegionNearest

In the function Nearest , I can define my custom function using the DistanceFunction option. e.g: ...
3answers
250 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 ...
2answers
265 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 ...
2answers
137 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: ...
1answer
150 views

### How to convert a graph to a mesh region

As we know,the region is very convenient in Mathematica.And we can convert a MeshRegion into graph like this ...
1answer
251 views

### Finding corresponding vertex from 3d to 2d

I have this simple 3d data points: ...
1answer
747 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) ...
2answers
277 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: ...
2answers
356 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, ...
2answers
146 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. ...
1answer
89 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 ...
1answer
276 views

### Can't plot rotated region

I was experimenting with the code from this question when I ran into another problem with regions. ...
1answer
332 views

### Behavior of GraphicsMeshInPolygonQ 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: GraphicsMeshInPolygonQ[poly,pt] Displays ...
2answers
197 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 ...
2answers
128 views

### MeshRefinementFunction missing points

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

### A GraphicsMeshConvexHull[] peculiarity

I have been unable to explain the behavior of GraphicsMeshConvexHull[] on the following (highly simplified) example: ...
2answers
761 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 ...
0answers
84 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 ...
2answers
126 views

### Visibility Graph of Polygon

Could anyone provide a function that takes a polygon as input and outputs its visibility graph ? Visibility Graph If not, is there a function that checks whether a line segment lies inside a polygon?
1answer
75 views

### MaxCellMeasure fails in 3D?

Question How come MaxCellMeasure works in 2D but fails in 3D? Indeed if I try ...
1answer
565 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 ...
2answers
452 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?
0answers
256 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 ...
2answers
196 views

### A method to discretize a three-dimensional solid

Consider the following region: ...
1answer
205 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 ...
1answer
162 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 ...
1answer
395 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: ...