# Questions tagged [computational-geometry]

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 programmatic constructions of polyhedra.

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### Using TetGen in Mathematica to get 3D Voronoi diagram

In this post, the use of TetGen for 3D Voronoi tesselation has been briefly discussed. However there is still no info about the use of TetGen to generate a 3D Voronoi diagram. The TetGen documentation ...
238 views

### Possible Bug with Options in DelaunayMesh

Bug introduced in 10.2 and persisting through 11.1 Update: It turns out after some testing, none of the Options work in ...
142 views

### How to make a function for image recognition

For example given a big set of random points, and I extract a small section of the random set of points, how can I find the small set on the big set? As a first approach I tried to do a Delaunay ...
181 views

### Higher order Laplacian flows

Given disjoint surfaces $q_i$ in 3D and their 1D boundary curves $\partial q_i = \gamma_i$, I seek a surface $p$ that joins the $q_i$, where $p \cup q_i$ forms a (piecewise) $C^k$ surface that ...
679 views

### How to fit B-splines to unstructured grids (triangulated surfaces)?

As a continuation of trying to calculate curvature tensors on triangulated surfaces (here), I am interested in trying other methods. One approach is to use NURBS. To be more precise I would like to be ...
581 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 ...
78 views

### What may the arguments be to Region (11.1)?

In Mathematica version 11.1, there is a new function Region. While the Documentation Center page ref/Region has a number of ...
356 views

### Anamorphic projection onto the corner of a room

I want to use a router to carve anamorphic projections of polyhedron wireframes onto two adjacent walls of my office. Like this: In order to do this I need to transfer the positions of the vertices ...
853 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 ...
777 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: ...
65 views

### Memory leak in FindMinValue?

I was running some geometric optimisation code today using FindMinValue and for some reason at one point the memory usage goes upwards of 14GB, making the kernel ...
184 views

### How to obtain the adjacency matrix of morphological components?

I am wondering if there's a simple way to obtain the adjacency matrix of the morphological components of a segmented image. Consider the following example (originally, from this question): ...
140 views

### DelauneyMesh in 4d and higher

Is there any way to find the DelauneyMesh in 4D (or higher)? Its documentation implies that it should be possible "A Delaunay mesh consists of intervals (in 1D), ...
239 views

### How to get 3D building data in map functions?

Most modern mapping APIs have 3D model data for city buildings built-in. For example: Is there some way to get this functionality in the Geography related functions? I believe ...
128 views

### Is BooleanRegion limited to only the most trivial cases?

Consider these four regions: regions = Disk[#, 1] & /@ Tuples[{0, 4/5}, {2}] Graphics[{FaceForm[Opacity[0.2]], EdgeForm[Black], regions}] I was looking to ...
90 views

### ReflectionTransform gives different colors

Consider this example of the cow cow = ExampleData[{"Geometry3D", "Cow"}, "GraphicsComplex"]; p = {0, 0, -0.25} Compare the rotation and reflection ...
224 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 ...
303 views

### Is there a 3D Voronoi function in Mathematica?

I use Mathematica v11.1. I made a vase by rotating the graph with Mathematica. ...
496 views

### Extending Bresenham's algorithm for subpixel rendering

Original Bresenham's line drawing algorithm it limited to drawing lines between two integer pixel positions and does not allow subpixel rendering. However with my reformulation of this algorithm as a ...
440 views

### 4 circular arcs, how plot the minimal surface?

By using Sjoerd de Vries code for circular arcs: ...
270 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 ...
208 views

### Ideas for visualizing the shape of a random walk

Context: In the context of (3D) random walks or polymer chains, a useful quantity for capturing and characterizing the shape of the walk or the conformation of the polymer in space is the gyration ... 140 views

### Delaunaymesh boundary effects

I have generated a Delaunay mesh region from the seeds, shown like following: This is a zoomed-in crop image, showing the bottom left corner. The black dots are the seeds. The continuous black lines ...
91 views

### Better discretization for intersections of algebraic surfaces

I am looking for better, preferably analytical approaches to discretize intersections of algebraic surfaces. When surfaces are not identical, these solutions are either curves or points. An extremely ...
167 views

### RegionIntersection and area on GeoPosition polygons

I am trying to write a simple procedure to find the percentage of a large property falls in each surrounding ZIP code. A problem that I am encountering is the fact that RegionIntegration[] and Area[] ...
136 views

### Convexity Coefficient Calculation

I would like to probabiistically estimate the convexity coefficient of a MeshRegion, described as - Given a region $\mathscr{K}$, calculate the probability that ...
670 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 ...
40 views

### Inconsistence in calculating zero geometric area

First, let us see disk ...
104 views

### Placing shapes along a square spiral

Proposed code example is inspired by the main idea of this challenge. Wolfram Language provides great opportunities in computational geometry. But not all of them are equal in terms of speed and ...
88 views

### 3D BoundaryMeshRegion Minkowski difference via RegionErosion Failure

I need to be able to produce Minkowski difference of an arbitrary BoundaryMeshRegion and a cylinder. ...
59 views

### GeometricScene doesn't quite work in v13.0.1

I used GeometricScene in v12.x quite a bit in some project and although the feature was experimental it was reliable before. I recently upgraded to v13.0.1 and had ...
108 views

### Inner polygon approximation

Suppose you want to perform an inner approximation of a planar semialgebraic set by a finite set of polygons. The following is a quick way to yield an approximation but I am not convinced that it is ...
58 views

### GeometricScene extremely slow or cannot complete

I would like to find instances of the following dodecahedral wheel generalized to the situation where the red squares become rhombuses. I tried this using RandomInstance[GeometricScene], but ...
134 views

### Calculate the intersection points of a line and a parametrically defined 3D surface

Thanks to Henrik Schumacher for advice to simplify the sample code: I would be grateful for any pointers on the following issue. A line from an external point intersects the surface at 2 points (...
65 views

### Minimal "triangulation"

I have a list of 9 points in $\mathbb{R}^4,$ and I'd like to know the "minimal triangulation" of the convex hull of these points, i.e. the minimal number of 4-dim simplices such that their union gives ...
417 views

### Calculating Gaussian Curvature for an irregular surface

Below is an irregular surface generated from large data and plotted with ListSurfacePlot3D from this data file using columns {3,4,2}. I would like to calculate the ...
149 views

### ConvexHullMesh fails for collinear points

I've got a List of PointLists, of which some contain only collinear points. I now want to obtain all ConvexHullMeshes of my PointLists. For more than two ...
125 views

### Computing symbolic surface normal of a surface point on a semialgebraic set

Consider a semialgebraic set; such as reg below: ...
71 views

### How to speed up geometric Resolve query involving $\exists$ and $\forall$?

I would want to test connectedness of semialgebraic sets with naive code like this: ...
230 views

### Implementation of Lubaehevsky-Stillinger Algorithm to pack hard spheres

To generate a model of a polycrystalline material with specified grain size distribution (e.g coming from a Monte Carlo Grain Growth simulation) the Paper "Effects of grain size distribution and ...
397 views

### Von Neumann's method to generate points uniformly distributed on a region of a n-sphere surface

I am trying to generate points uniformly distributed on a region of a single n-sphere surface (all angles in hyperspheric coordinates are between 0 and Pi/2). I decided to use von Neumann's method ...
153 views

### projecting a RegionProduct into 3D space

Apparently, RegionProduct should allow you to generate convolution-generated shapes. For instance, take a 1D curve and a sphere, and the region product I would ...
1 vote
69 views

### Subtract ParametricRegions from each other

I have 2 surfaces defined parametrically that overlap. I want to subtract the helical surface from the cylindrical surface to obtain a mesh of just the blue surface in the image. The parameter bounds ...
1 vote
62 views

### Angle sum at center of a skewed quadrilateral

The center of a discrete quadrilateral on a positive, flat or negative curved surface should make angles sum at center point 2 less than, equal to or more than $360^{\circ}$ respectively, making them ...
1 vote
68 views

### Grouping vectors into groups of 3 by attribute

Three groups are given, each with eight $3 \times3$-vectors: ...
1 vote
77 views

### Determine if intersection of Polygon and HalfLine is non-empty

I have a concrete example: ...
1 vote
69 views

### RandomInstance of GeometricScene producing unexpected result

Consider the following scene as an example: ...
1 vote
155 views

### Find the intersection coordinate of a line and a 3D surface defined by a contour plot

I have two points, for instance {1, 1, 1} and {10, 11, 15} that connected to form a line. I also have an enclosed surface region ...
1 vote