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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Creating a Random T-Spline Instead of a B-Spline

I want to be able to create a function so that instead of BSplineSurface[pts], it would be TSplineSurface[pts,error]. I think it ...
Teg Louis's user avatar
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3 votes
2 answers
146 views

How to discretize a thin prism

I have a very thin prism that I want to discretize using DiscretizeRegion: ...
Cassini's user avatar
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4 votes
1 answer
111 views

How to get finer discretization of 3D polytope?

For some purposes I need detailed mesh models of 2D and 3D shapes. No problem with 2D, so for Rectangle[] we get for example ...
lesobrod's user avatar
  • 1,501
4 votes
3 answers
453 views

Efficiently fill an ellipse with a k-many random ellipses

So, I can create a circle filled with circles of the same radius that gives this example picture: with this code: ...
Teg Louis's user avatar
  • 636
4 votes
2 answers
216 views

Making geometries with Mathematica for use in Ansys

I am trying to model deformations caused by identical, solid half-ball bearings on a thin, solid cylindrical plate in Ansys. But drawing the geometries is much easier in Mathematica, especially if I ...
Teg Louis's user avatar
  • 636
4 votes
0 answers
127 views

How can I tell Mathematica create Heronian triangles in 2D like Maple'post?

I see this post for the generation of triangles in a plane, for which the lengths of all sides, the area and radius of the inscribed circle are integers. In addition, all vertices must have different ...
minhthien_2016's user avatar
9 votes
2 answers
268 views

Envelopment of space curves

In their answers to Creating sculptural forms The respondents showed how to envelop space curves with a net-like structure. I used kglr's answer to create the following function: ...
eldo's user avatar
  • 61.9k
2 votes
4 answers
287 views

Find vertex coordinates of a triangle with sides 6, 25, 29 in 3D

An Integer triangle is a triangle all of whose side lengths are integers. I am trying to find coordinates of the vertices of triangle $OAB$ having side lengths 6, 25, 29. I suppose $O(0,0,0)$ and $A(6,...
Laurenso's user avatar
  • 1,032
2 votes
1 answer
113 views

How can I compute the maximum value of a ConditionalExpression?

If we use GeometricSolveValues in version 14.0, we can use this code to get a ConditionalExpression expr: ...
yode's user avatar
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0 votes
0 answers
61 views

How to get the boundary points from ConcaveHullMesh in 3D?

I am trying to visualize the boundary points of a quadratic polynomial that has only real roots where I treat the coefficients as coordinate values. But I am having a problem visualizing them because ...
Teg Louis's user avatar
  • 636
2 votes
0 answers
47 views

Alternatives for `GradientFittedMesh` and `ReconstructionMesh` in older versions

Are there similar functions to GradientFittedMesh and ReconstructionMesh, which were introduced in v13, for generating mesh ...
Ulrich Neumann's user avatar
13 votes
2 answers
431 views

Colouring the "leaves" (self-intersections) of parametric curves

I want to emphasize the self-intersections ("leaves") of parametric curves by applying a pattern or color to them. Using cvgmt's answer to this question: how-to-separate-the-regions-enclosed-...
eldo's user avatar
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3 votes
3 answers
273 views

Gaussian curvature of a point cloud surface

Having a set of triplets like dsurf={{x1,y1,z1},{x2,y2,z2},...} whose interpolation defines an open surface (as shown by ...
Daniel Castro's user avatar
0 votes
1 answer
179 views

Finding Contours in Photo to Create a Topographical Map

I am setting up a special table to simulate the scenario in this problem in this problem, but instead of finding the geodesics, I want to create a topographical map using the contours. Here is a ...
Teg Louis's user avatar
  • 636
7 votes
4 answers
323 views

Minimal surface bounded between turns of helix

I'm curious to find the shape of a surface bounded between the rungs of a helix, ie the shape of the cloth stretched between the rungs of this child's play tunnel. I'm wondering if we could find it ...
Ariana Fenris's user avatar
0 votes
0 answers
84 views

Speeding up RegionIntersection of multiple sets of rectangles

There is a set of disjoint rectangles shadow that change position over time. I want to find their intersection with another set of small rectangles ...
wowo snail's user avatar
19 votes
1 answer
2k views

Efficiently Mowing Grass with Mathematica

Recently, I was mowing my yard and was thinking about how to use the least amount of time/fuel and how to simulate. Mowing a yard that is shaped as a convex polygon is not difficult, you can just make ...
Teg Louis's user avatar
  • 636
1 vote
2 answers
124 views

What are some quick methods for calculating hyperbolic equations?

Given that the hyperbola passes through three of the four points (m1, m2, m3, m4), find the equation for the hyperbola These four points are like this ...
csn899's user avatar
  • 3,635
0 votes
0 answers
71 views

Finding the Complete Silhouette Area Formula given a Convex Polyhedron

Like always, I am probably over complicating this and there is a much simpler way to derive a general formula using built-in Mathematica functions, think about it differently, or a faster way to solve ...
Teg Louis's user avatar
  • 636
2 votes
2 answers
265 views

Packing unequal spheres into minimal cuboid

There are several non-overlapping spheres in 3D. How to find a cuboid Cuboid[{a,b,c}] containing these spheres with minimal ...
user64494's user avatar
  • 25.7k
0 votes
0 answers
63 views

Weird behaviour of TransformedRegion and GeometricTransformation

What I would like to do is to take some polyhedra (such as Cuboids, Prisms, and ...
Liam Baker's user avatar
0 votes
0 answers
86 views

Solving the clothing problem with Mathematica

Given a surface $\mathbf{r}:\mathbb{R}\rightarrow \mathbb{R}^3$, the Chebyshev clothing problem consists in finding a parametrization $(u,v)$ such that \begin{align} \left|\frac{\partial \mathbf{r}}{\...
Daniel Castro's user avatar
1 vote
2 answers
137 views

How would you use Mathematica to extract a metric tensor from a metric formula? [duplicate]

I'm trying to follow an explanation for extracting a metric tensor from a metric formula and having trouble following the mathematical explanation. I'm sure I would understand it better if written in ...
The Shepard's user avatar
10 votes
2 answers
535 views

Tomographic Reconstruction of a Convex Polyhedron from its Silhouettes

So, I can construct a random polyhedron and find its 3 silhouettes onto the 3 standard planes. For example, ...
Teg Louis's user avatar
  • 636
0 votes
1 answer
40 views

Transition to a new basis with rotation of one of the axes [closed]

The lengths of the basis vectors e1 and e2 of the general Cartesian coordinate system on the plane are equal to 4 and 2, respectively, and the angle between the basis vectors is 120°. Relative to this ...
Сергей Малышев's user avatar
1 vote
2 answers
258 views

How to find a densest configuration of several non-overlapping unit disks? [closed]

Let us consider three non-overlapping unit disks in the plane. I'd like to find a configuration of these disks s.t. the area of the convex hull of these disks is smallest. This is related to the ...
user64494's user avatar
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7 votes
4 answers
958 views

Converting an Unicode's image into polygon data for an SVG

So, I have the the Chinese character 熙, which I can easily turn into an image: img=Rasterize[Text[Style[FromCharacterCode[{29081}], FontSize -> 300]]] which ...
Teg Louis's user avatar
  • 636
0 votes
2 answers
85 views

How to make a function that outputs a mesh region object or some other geometric object that represents a cake number?

The lazy caterer's sequence, more formally known as the central polygonal numbers, describes the maximum number of pieces of a disk (a pancake or pizza is usually used to describe the situation) that ...
Peter Burbery's user avatar
0 votes
1 answer
70 views

How do I find the circumsphere of any spatial geometry? [closed]

How do I find the circumscribed sphere of any spatial geometry? I want to: automatically generate its circumscribed sphere in the original three-dimensional graphics, label its center position, label ...
csn899's user avatar
  • 3,635
4 votes
2 answers
314 views

How to create a random belt polygon or belt polyhedron?

A zonogon is a convex polygon that is made up of parallel sides. Generating a random zonogon in Mathematica can be found here. A natural generalization of zonogons is called belt polygons. A belt ...
Teg Louis's user avatar
  • 636
1 vote
1 answer
40 views

Maintaining form of Manipulate to find the formula area of a projected cuboid

I am experimentally trying to solve this problem about the projected area of a cuboid. I sense patterns when I run the below code, but it is difficult for me to compare them. Here is the code: ...
Teg Louis's user avatar
  • 636
2 votes
0 answers
42 views

Inconsistence in calculating zero geometric area

First, let us see disk ...
matheorem's user avatar
  • 17.1k
4 votes
4 answers
380 views

How can I calculate the volume of spatial geometry?

In the square prism ABCD A1B1C1D1, AB=2, A1B1=1, AA1=Sqrt [2], what is the volume of this prism? It is easy to calculate its volume using the volume formula: ...
csn899's user avatar
  • 3,635
0 votes
1 answer
67 views

Define triple Integral tetrahedron truncated by oblique plane

I am struggling on defining the integration limits of a triple integral of an oblique truncated tetrahedron. Let's get more into the details: I have a standard tetrahedron in a ...
thef's user avatar
  • 43
4 votes
3 answers
283 views

Moment of Inertia for Hexahedron region

I've been going crazy about a problem that I think it has no solution, since I found nothing on the Internet about it. I would like to compute the tensor of inertia of a region. The region is the ...
thef's user avatar
  • 43
3 votes
1 answer
238 views

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 ...
minhthien_2016's user avatar
4 votes
1 answer
76 views

Incorrect result of ConvexRegionQ

Studying that important command of Mathematica in 13.2 on Windows 10, I obtain for both ...
user64494's user avatar
  • 25.7k
5 votes
2 answers
230 views

How to determine whether a point is within a multidimensional degenerate convex hull? [duplicate]

There are two set of points ...
lapcal's user avatar
  • 531
2 votes
2 answers
264 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 ...
Yaroslav Bulatov's user avatar
3 votes
2 answers
191 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 ...
Craig Carter's user avatar
  • 4,250
1 vote
2 answers
244 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 ...
Emilio Pisanty's user avatar
1 vote
0 answers
64 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 ...
Narasimham's user avatar
  • 3,138
4 votes
3 answers
176 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: ...
kirma's user avatar
  • 19k
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, <...
user64494's user avatar
  • 25.7k
9 votes
1 answer
417 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 ...
licheng's user avatar
  • 2,019
3 votes
0 answers
107 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 ...
lesobrod's user avatar
  • 1,501
2 votes
1 answer
193 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: ...
lesobrod's user avatar
  • 1,501
0 votes
0 answers
119 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: ...
lesobrod's user avatar
  • 1,501
0 votes
1 answer
124 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: ...
Shredderroy's user avatar
  • 5,239
2 votes
0 answers
95 views

3D BoundaryMeshRegion Minkowski difference via RegionErosion Failure

I need to be able to produce Minkowski difference of an arbitrary BoundaryMeshRegion and a cylinder. ...
Anton's user avatar
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