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.
760
questions
3
votes
1
answer
193
views
GeometricScene not working when too many polygons are given
I'm trying to create the following geometric scene:
...
- 5,473
3
votes
1
answer
159
views
How can I draw triangles within a triangle if I know their perimeters?
I am trying to draw this picture with perimeters of the triangles in a larger triangle. I don't know how to start.
- 1,118
1
vote
1
answer
111
views
How to get a triangle with so that centroid, orthocenter, center of circumcenter and center of incircle are integers
I want to create some triangle so that centroid, orthocenter, center of circumcenter and center of incircle are integers. I tried
...
- 1,265
0
votes
0
answers
39
views
Some functions keep on running endlessly on xTensor, xAct
I was trying to do some calculations to prove a few equations of the following paper https://arxiv.org/pdf/2004.08362 named "Derivation of regularized field equations for the Einstein-Gauss-...
7
votes
3
answers
321
views
How can I select all pair of two points A and B has integer coordinates and length of AB is also integer?
I have sphere $(x-1)^2 + (y-2)^2 + (z-3)^2 = 81$. To select two points $A$, $B$ on sphere so that coordinates of $A$, $B$ are six different integer numbers and $AB = 18$, $xyz \neq 0$ I tried.
...
- 1,265
4
votes
0
answers
191
views
Face-based discrete directional derivative on triangular mesh
For a scalar function $f$ defined on the faces of a triangulated surface $M$, and a vector field $\mathbf{F}$ on its tangent space, is there a built-in or simple way to get the derivative of $f$ in ...
- 609
0
votes
0
answers
74
views
Box Scans in a Cartoon Warehouse
I used to be a package handler and was very slow at first. Part of the job was to find the appropriate barcode and then scan it.
I sped up a lot after realizing that if I grab opposite corners, then ...
- 114
3
votes
1
answer
84
views
How to Implement Progressive Cell Coloring in a General Mesh or Tiling?
Here are some examples of what I am talking about using Voronoi for simplicity:
Given:
That can be colored depending on which cell is randomly chosen:
I feel like there would be a better name for ...
- 114
15
votes
3
answers
1k
views
Edna Andrade's Black Dragon: Winding Around Control Points
Edna Andrade
Edna Andrade (1917-2008) is now recognized as an early leader in the Op Art movement. She lived and worked in Philadelphia for the majority of her career after first moving to the city ...
- 82.6k
10
votes
3
answers
385
views
Recreating Louise Bourgeois' Insomnia Spirals (Fugue #12)
Louise Bourgeois
Louise Bourgeois (1911 - 2010) was a French-American artist. Although
she is best known for her large-scale sculptures, she was also a
prolific painter and drawer.
"The spiral ...
- 82.6k
1
vote
1
answer
97
views
Animating a Polygonal Chain Worm's Gait
Here is an example polygonal chain worm:
that was created with the code:
...
- 114
18
votes
1
answer
1k
views
How to draw a number of circles inscribed in a square so that the sum of the radii of the circle is greatest?
I have a square with length of side is $a$. How to draw a number of circles inscribed in a square so that the sum of the radii of the circle is greatest? In the below picture is six circles inscribed ...
- 4,317
1
vote
0
answers
71
views
Straightening out rumpled striped bedsheets
I was motivated to investigate this from an seeing a Greg's Hurst answer for a different question. I was curious how to find out what the sheet would look like when flattened with proper size and all ...
- 114
20
votes
4
answers
2k
views
Reproducing Ómar Rayo's "Fresh Fog" Painting
Ómar Rayo
Ómar Rayo (1928 - 2010) was a Colombian painter best known for his
op-art paintings. He completed his first drawing studies at an
academy in Buenos Aires. In 1960 he received a Guggenheim ...
- 82.6k
12
votes
2
answers
841
views
Frank Stella's Protractor Series - can we reproduce Lac Laronge IV?
Frank Stella
Frank Stella, one of the most fanous contemporary American artists, died on May 4 at the age of 87 at his home in Manhattan. I learnt this from our colleague Yarchik, who, a few days ago, ...
- 82.6k
4
votes
1
answer
127
views
Strategy to speed up two polygons (or region) intersection
Basically, I want to compare the overlap between two polygons (or regions).
First, I have a reference particle ring that can form a simple polygon, but this type of ring is very thin and long, and its ...
- 71
4
votes
3
answers
433
views
How can I find distance between two skew lines?
In this code, I want to calculate distance between two lines SC and AB.
...
- 4,317
18
votes
4
answers
1k
views
Can we reproduce Antonio Asis circle interferences?
Antonio Asis
Antonio Asis (1932 - 2019) was an Argentine artist and one of the main exponents of kinetic art and op art. Asis was born in Buenos Aires. At the age of 14 he enrolled at the National ...
- 82.6k
1
vote
1
answer
149
views
Find the polar plane of the ellipsoid and integrate the Ellipsoid cap
I am working on writing a code to find the polar plane of an ellipse, and subsequently calculate the cap formed by subtending the point $p$ (red) onto a random ellipse.
I think I have managed to ...
- 633
20
votes
5
answers
1k
views
Bridget Riley - Movement in Squares and Circles
Bridget Riley
Bridget Riley (born 1931 in London) is an English painter known for her op art paintings. Alongside Victor Vasarely and Vera Molnár, she is one of the best-known representatives of this ...
- 82.6k
1
vote
1
answer
166
views
Robotic Appendages in MMA
I am trying to animate a generalized abstraction of robotic appendages (arms, hands, legs) in Mathematica where the translation is "smooth" in the sense that all of the points except for the ...
- 114
12
votes
1
answer
373
views
Reproducing Ruth Asawa's Wire Sculptures
Ruth Asawa
Ruth Aiko Asawa (1926 - 2013) was an American artist known primarily for her looped-wire sculptures. Born in Norwalk, California Asawa was the daughter of Japanese immigrants. She grew up ...
- 82.6k
21
votes
4
answers
2k
views
Paul Klee's Notebooks: Loops Around Control Points
Paul Klee
Paul Klee (1879 - 1940) was a Swiss-born German artist. His highly individual style was influenced by expressionism, cubism, and surrealism. Klee was a natural draftsman who deeply explored ...
- 82.6k
8
votes
0
answers
290
views
How to Calculate Biharmonic Distance in MMA?
There are many kinds of distances. One of them is Biharmonic Distance where I got the the image below from:
The biharmonic examples are on the left, and the author kept his promise in the paper that ...
- 114
5
votes
1
answer
272
views
Making Adjacency Matrix from Maps
I want to make an adjacency matrix for the world/each country at a specified administrative level. This is very easy to do for countries in Mathematica, but is not straightforward for different ...
- 114
7
votes
1
answer
159
views
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 ...
- 114
3
votes
2
answers
148
views
How to discretize a thin prism
I have a very thin prism that I want to discretize using DiscretizeRegion:
...
- 5,626
4
votes
1
answer
123
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
...
- 1,904
4
votes
3
answers
505
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:
...
- 114
4
votes
2
answers
296
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 ...
- 114
4
votes
0
answers
144
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 ...
- 4,317
9
votes
2
answers
297
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:
...
- 82.6k
2
votes
4
answers
310
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,...
- 1,118
2
votes
1
answer
130
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:
...
- 27.1k
0
votes
0
answers
71
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 ...
- 114
2
votes
0
answers
52
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 ...
- 55.6k
13
votes
2
answers
459
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-...
- 82.6k
3
votes
3
answers
444
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 ...
- 609
1
vote
1
answer
233
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 ...
- 114
7
votes
4
answers
351
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 ...
- 165
0
votes
0
answers
86
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 ...
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 ...
- 114
1
vote
2
answers
140
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
...
- 4,884
0
votes
0
answers
79
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 ...
- 114
2
votes
2
answers
273
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 ...
- 27.9k
0
votes
0
answers
64
views
Weird behaviour of TransformedRegion and GeometricTransformation
What I would like to do is to take some polyhedra (such as Cuboids, Prisms, and ...
- 221
0
votes
0
answers
91
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}}{\...
- 609
1
vote
2
answers
167
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 ...
- 15
10
votes
2
answers
553
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,
...
- 114
0
votes
1
answer
41
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 ...
- 103