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.
700
questions
3
votes
1
answer
135
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How do I calculate volume of a polyhedron knowing a list of vertices of polyhedron?
I have a list of vertices
a = {1/2, 1/2, 0};
b = {-1/2, 1/2, 0};
c = {-1/2, -1/2, 0};
e = {-1/4, 1/4, Sqrt[15]/4};
f = {1/4, -1/4, Sqrt[15]/4};
I want to find ...
- 1,945
4
votes
1
answer
69
views
Incorrect result of ConvexRegionQ
Studying that important command of Mathematica in 13.2 on Windows 10, I obtain for both
...
5
votes
2
answers
205
views
How to determine whether a point is within a multidimensional degenerate convex hull? [duplicate]
There are two set of points
...
- 471
2
votes
2
answers
220
views
How to avoid poles in contour integration?
I have two sets of points and need to construct a contour (for contour integration) that
encloses all singularities given in points2 , but avoids enclosing ...
- 7,558
3
votes
2
answers
181
views
Why is SignedRegionDistance always returning zeroes?
I have a simple parabolic region:
reg = ImplicitRegion[
x <= 1/2 && y <= Sqrt[1/2 - x]/2, {{x, 0, 1}, {y, 0, 1}}]
It appears to be behaving ...
- 3,632
1
vote
2
answers
148
views
How to get the centroid of a geographical region? (or: the center of mass of Croatia is in Bosnia and Herzegovina, but where exactly?) [duplicate]
How can I get Mathematica to calculate the centroid of an extended geographical region (say, a country) in a way which (i) fully respects the spherical nature of the Earth, and (ii) involves a minimal ...
- 10.1k
1
vote
0
answers
57
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 ...
- 2,972
4
votes
3
answers
153
views
Simplifying an expression to a sensible conic section polynomial
I have an expression which represents an intersection of the unit sphere and a cone, projected to two-dimensional plane:
...
- 18.4k
18
votes
4
answers
2k
views
How to exactly calculate the volume?
Let us consider the intersection of four cylinders of the unit radius along the big diagonals of the cube $[-10,10]^3$ and the cylinder of the unit radius with the $z$-axis as its axis. More exactly,
<...
9
votes
1
answer
356
views
How can I detect the number of crossings in a layout of a graph?
This question was inspired by the game Planarity in which a player tries to position the vertices so that no two lines cross. As I move the vertices, the change in the number of crossings is detected ...
- 1,617
2
votes
0
answers
100
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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 ...
- 859
2
votes
1
answer
177
views
Bugs with computational geometry: versions 12.2 vs 13.2
Updated
System Info: HONOR laptop AMD Ryzen 5 4600H 3Hz 6 cores 16GB Memory,
Windows 10 Pro 64 bit with updates.
Mathematica Info: Versions 12.2 and 13.2, both on the same laptop.
Examples:
...
- 859
0
votes
0
answers
105
views
Problem with WindingPolygon
Bug introduced in 12.2 or earlier and fixed in 13.1 or earlier.
I would like to slightly modify the standard example:
...
- 859
0
votes
1
answer
113
views
RegionIntersection runs for a very long time and then aborts without returning a result
Is there a good strategy to speed up RegionIntersection computations like the one below:
...
- 4,957
2
votes
0
answers
82
views
3D BoundaryMeshRegion Minkowski difference via RegionErosion Failure
I need to be able to produce Minkowski difference of an arbitrary BoundaryMeshRegion and a cylinder.
...
- 333
1
vote
2
answers
78
views
Another way to find coordinates of two remain vertices knowing given two vertices?
Let be given the polyhedron ABCD with $AB = 4 \sqrt{3}$, $AC=1$, $BC=\sqrt{41}$, $AD=\sqrt{17}$, $CD=4$, and $BD=5$. I am trying to find coordinates of two vertices ...
- 1,945
3
votes
2
answers
304
views
Two squares in the unit square
A square of side one contains two squares of sides $a$ and $b$ having non-overlapping interiors. How to prove the inequality $a+b≤1$ with Mathematica?
The same question in three dimensions and higher ...
4
votes
2
answers
114
views
How to find intersection points of $n$ $n$-spheres reliably and efficiently when $n$ is large
I have positions and radii of $n$ $n$-dimensional hyperspheres and want to find their intersection points efficiently. A very-straight-forward solution seems quite reliable:
...
- 18.4k
2
votes
1
answer
109
views
Plot3D plotting serrated edge
I want to plot the upper casket of a sphere in 3D using its parametrisation as $s(x,y) = \sqrt{1-x^2-y^2}$. Although this show be straight forward with Plot3D, I am running into an issue I find very ...
11
votes
2
answers
370
views
Mark all Points in a triangle that have a certain property
I want to mark all points inside of a triangle having the following property:
I can center a line segment of length $c$ on the point so that the line segment is entirely contained inside the triangle.
...
- 217
5
votes
1
answer
194
views
What is the volume of the intersection of four cylinders of equally radius equally spaced?
I saw that question at the certain forum and answered it with help of
Mathematica 13.1 in such a way. The angles between the unit vectors
...
5
votes
3
answers
175
views
Parellel-To-Plane Version of RegionDistance
RegionDistance basically calculates distance between points P and Q=RegionNearest[Reg,P]:
I need to find a way to find function ...
- 333
6
votes
2
answers
285
views
Extract 2D quad mesh from 3D hexahedral mesh
I would like to extract 2D mesh of outer surface of 3D meshed object.
Let's say I have 3D mesh data from here and I import the data into Mathematica.
...
- 611
4
votes
1
answer
103
views
How to make a density plot on Ellipsoid[] surface?
Suppose I have the ellipsoid below and a set of points that I know rest on its boundary, which we can visualize:
...
- 1,583
3
votes
1
answer
207
views
Generating a non-convex polyhedron from polygons and normals
I am working on developing "directional offset" module, which requires pretty tricky mesh generation: offset values vary in different directions.
Suppose I have list of points and polygons, ...
- 333
5
votes
2
answers
262
views
Finding Mesh Cell Normals
I need to find a normal pointing outside for every face / cell of a closed Mesh Region.
How can I do this?
Here's what I have now - mesh + mesh cells centers and I'm stuck and puzzled.
There's ...
- 333
5
votes
1
answer
128
views
Random point configuration from the Poincare disk model gives division by zero problem near boundary
I am trying to select points uniformly at random from the Poincare disk model of hyperbolic geometry:
...
- 1,713
0
votes
0
answers
80
views
Difference between a region and its convex hull
I have a volume enclosing a certain region. The region is non-convex, and I calculate its convex hull with the built-in Mathematica function. I want to know the difference between the region and its ...
- 135
3
votes
2
answers
399
views
Volume of the intersection and union of two spheres
I'd like to calculate the volume of the intersection and the union of
...
4
votes
2
answers
225
views
Easiest way to obtain MeshRegion from CountryData
What is the easiest way to obtain MeshRegion objects from CountryData that I can use in geographic computations?
For example, ...
- 36.9k
0
votes
0
answers
160
views
Why is regioncentroid not giving correct results?
I am trying to calculate and plot the x-axis of a volume centroid for the region between zx-plane and a function squared $u(t,x,z)$ from time $t=15$ to $25$. The function is a numerical solution to a ...
- 43
18
votes
5
answers
1k
views
Divide a geometric region by (many) lines
Given a shape (e.g., a rectangle, a circle, etc.), how to divide it by $n$ randomly chosen lines. It is trivial to plot those lines (see figure below), using code like
...
- 479
5
votes
1
answer
254
views
Unable to obtain all boundary points on a convex hull using ConvexHullRegion
I'm using an old function which uses ConvexHull from the obsolete ComputationalGeometry package. I understand this is ...
- 2,292
4
votes
1
answer
141
views
How to find boundary of the intersection of two mesh regions in CW or CCW?
I have two lists of points as follow and they're not fixed.
...
- 2,832
8
votes
1
answer
272
views
How to union 3D region to calculate volume?
I have a Teapot likes:
region = RepairMesh[ExampleData[{"Geometry3D", "UtahTeapot"}, "MeshRegion"]]
I want to calculate the volume ...
- 25.6k
5
votes
1
answer
215
views
How to combine several surfaces into a solid and compute its volume?
plot1 is taken from the BSplineSurface document. I add two Disk ...
- 338
2
votes
0
answers
54
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 ...
- 5,159
2
votes
1
answer
144
views
Understanding GeometricScene [closed]
I tried to expand a simple geometric scene:
RandomInstance[GeometricScene[{a, b, c }, { Triangle[{a, b, c}]}], 1]
works fine and shows the triangle.
But if ...
- 44.6k
2
votes
1
answer
70
views
Minimize relating a geometric test
I want to find a circle with a center and a radius that includes all given points, like a circumscribed circle for the points.
points data:
https://www.dropbox.com/s/0unlv1vbngopu38/new_ref.txt?dl=0
...
- 745
5
votes
5
answers
597
views
Normal equation of plane through a point and line
I need to find the normal vector of the form Ax+By+C=0 of the plane that includes the point (6.82,1,5.56) and the line (7.82,6.82,6.56) +t(6,12,-6), with A=1.
Of course, this is easy to do by hand, ...
- 137
3
votes
1
answer
67
views
How to use ConvexOptimization on a piecewise function?
I define a simple piecewise convex function, but ConvexOptimization does not take it as a valid input:
...
- 332
3
votes
1
answer
116
views
How to use ConvexOptimization on a function constructed from data?
Given the following data points sampled from a convex function, how could I construct a convex function that can be minimized using ConvexOptimization?
...
- 332
0
votes
0
answers
67
views
RegionCentroid giving different result on Polygon and ConvexHullMesh
I have the following 5 vertices:
...
- 85
13
votes
2
answers
454
views
GeometricTest doesn't work in ellipse
Bug introduced in 13.0 or earlier and fixed in 13.1.0
Let me look at a circle case:
...
- 25.6k
5
votes
0
answers
63
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 ...
- 203
1
vote
2
answers
106
views
why does the MomentOfInertia behave differently for ConvexHullMesh and ConvexHullRegion
I have a list of points of a convex polyhedron for which I need to compute the eigenvectors of the Moment of Inertia matrix. But, it seems like the built-in ...
- 8,760
4
votes
1
answer
211
views
Is it possible to improve a code related with iterative closest point (ICP) algorithm?
I am trying to write a code related with ICP algorithm.
The purpose of the code is matching a target data with a reference data by translational operation in XYZ axes (3-degree-of-freedom (DOF) ...
- 157
1
vote
1
answer
98
views
Evaluate area of random region covered by disks
If I cover a square of side $L$ with $n$ unit disks at random (the disks may overlap the boundary), is there a standard way to evaluate the total covered area $A$?
I am looking to observe the density $...
- 1,713
13
votes
4
answers
478
views
Group points which on several straight lines
I have some points, they are distributed on three straight lines, how to group points on the same line? I have tried FindCurvePath, but I got the wrong result. I ...
- 5,550
5
votes
1
answer
139
views
Avoiding Concave Polygons
In a vertex model, vertices in a lattice are modelled by a set of ODEs. A T1 transition is the following: when a certain edge becomes small enough (given a threshold), two cells stop being connected, ...
- 4,233