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.
101
questions with no upvoted or accepted answers
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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 ...
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10
votes
0
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238
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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 ...
- 32.9k
7
votes
0
answers
142
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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 ...
- 807
7
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181
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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 ...
- 35.5k
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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 ...
- 3,923
7
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581
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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 ...
- 971
6
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0
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78
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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 ...
- 11.8k
6
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356
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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 ...
- 3,683
6
votes
1
answer
853
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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 ...
- 61
6
votes
0
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777
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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:
...
- 407
5
votes
0
answers
65
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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 ...
- 221
5
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184
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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):
...
- 1,593
5
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140
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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), ...
- 4,197
5
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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 ...
- 31.2k
5
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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 ...
- 233k
5
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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 ...
- 27.4k
5
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224
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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 ...
- 1,800
4
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303
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Is there a 3D Voronoi function in Mathematica?
I use Mathematica v11.1.
I made a vase by rotating the graph with Mathematica.
...
- 1,520
4
votes
0
answers
496
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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 ...
- 61.5k
4
votes
0
answers
440
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4 circular arcs, how plot the minimal surface?
By using Sjoerd de Vries code for circular arcs:
...
- 1,149
4
votes
0
answers
270
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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 ...
- 63
3
votes
0
answers
208
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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 ...
user52181
3
votes
0
answers
140
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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 ...
- 185
3
votes
0
answers
91
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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 ...
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3
votes
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answers
167
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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[] ...
3
votes
0
answers
136
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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 ...
- 1,800
3
votes
0
answers
670
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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 ...
- 2,593
2
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answers
40
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2
votes
0
answers
104
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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 ...
- 1,197
2
votes
0
answers
88
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3D BoundaryMeshRegion Minkowski difference via RegionErosion Failure
I need to be able to produce Minkowski difference of an arbitrary BoundaryMeshRegion and a cylinder.
...
- 345
2
votes
0
answers
59
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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 ...
- 5,209
2
votes
0
answers
108
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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 ...
- 467
2
votes
0
answers
58
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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 ...
- 51
2
votes
0
answers
134
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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 (...
2
votes
0
answers
65
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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 ...
- 21
2
votes
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answers
417
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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 ...
- 215
2
votes
0
answers
149
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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 ...
- 1,067
2
votes
0
answers
125
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Computing symbolic surface normal of a surface point on a semialgebraic set
Consider a semialgebraic set; such as reg below:
...
- 18.7k
2
votes
0
answers
71
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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:
...
- 18.7k
2
votes
0
answers
230
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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 ...
- 2,861
2
votes
0
answers
397
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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 ...
- 195
2
votes
0
answers
153
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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 ...
- 743
1
vote
0
answers
69
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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 ...
- 155
1
vote
0
answers
62
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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 ...
- 2,992
1
vote
0
answers
68
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Grouping vectors into groups of 3 by attribute
Three groups are given, each with eight $3 \times3$-vectors:
...
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1
vote
0
answers
77
views
1
vote
0
answers
69
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RandomInstance of GeometricScene producing unexpected result
Consider the following scene as an example:
...
- 9,113
1
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0
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155
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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 ...
- 437
1
vote
0
answers
62
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Why does ConvexHullMesh give inconsistent output stuctures?
I know much of the stuff in ConvexHullMesh needs some TLC convexhullmesh-inconsistency
But, can anyone see why this would produce inconsistent output:
Case 1 (expected behavior):
...
- 3,968
1
vote
0
answers
49
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An apparent bug in Geometry`ConvexHull2
I was replacing some usages of Geometry`ConvexHull2 with ConvexHullMesh and found one of my tests failing. It turned out the ...
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