# 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
Filter by
Sorted by
Tagged with
193 views

### GeometricScene not working when too many polygons are given

I'm trying to create the following geometric scene: ...
• 5,473
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
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
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-...
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
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 ...
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
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
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
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
97 views

### Animating a Polygonal Chain Worm's Gait

Here is an example polygonal chain worm: that was created with the code: ...
• 114
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
148 views

### How to discretize a thin prism

I have a very thin prism that I want to discretize using DiscretizeRegion: ...
• 5,626
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
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
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
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
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
310 views

1 vote
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 ...