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.
787 questions
2 votes
2 answers
204 views
How should we formulate angle geometry constraints in Mathematica to help the solving system work more efficiently and speed up the solution process?
Quadrilateral $ABCE$ is a parallelogram. Point $D$ lies on segment $AE$. The diagonals of quadrilateral $ABCD$ intersect at point P. If $△ABP∼△CBD$ and $AB<BC$, find the ratio $\frac{AB}{BC}$. The ...
- 345
6 votes
3 answers
454 views
Turning Goldberg Graphs/Skeletons into Goldberg Polyhedrons (possibly skew)
I want to be able to turn the 1-skeletons from the Goldberg Graphs into polyhedrons. An example is to turn this tetrahedral goldberg graph on the left into the polyhedron on the right: which was ...
- 687
5 votes
3 answers
327 views
How to improve the symbolic computation speed for plane geometry with multiple constraint conditions？
This is the simple geometry problem I want to solve: In triangle ABC with side lengths a, b, c respectively, there is a point D on side AB, where AD = d. Find the length of CD. When solving this ...
- 345
3 votes
1 answer
118 views
Is there a built-in function or custom function that can perform symbolic solving under `GeometricScene` constraints？
In the new version of Mathematica, there is a new function called GeometricSolveValues that can solve for unknown geometric quantities in a geometric scene with ...
- 345
5 votes
3 answers
364 views
How does one parallelize WindingPolygon?
Consider this toy model: a list 100,000 simple point sets, and we Map WindingPolygon over it: ...
- 2,072
3 votes
0 answers
183 views
Mathematica demonstration of the expected volume of a random polytope in a ball
Related MSE post I'm trying to make Mathematica demonstration of the paper The expected volume of a random polytope in a ball. In the $d$-dimensional Euclidean space $E^d$ ($d \geq 2$), consider the ...
- 1
6 votes
1 answer
272 views
Finding General Solution for Straight-Line Films between Two Closed Shapes [duplicate]
Given two closed shapes, I want to see if there exists a 'film' between the two shapes and if one exists what they are for various solutions where the film is formed by non-intersecting straight lines ...
- 687
5 votes
3 answers
472 views
Frame of discrete curve
I have a collection of points $p_1,\cdots, p_n$ in 3d that defines a discrete space curve. I wish to compute/approximate the discrete-analog of the Frenet-Serret system/frame without interpolating to ...
- 806