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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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 ...
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Are there any good ways to improve this code so that it can solve the geometry problem？
While using Mathematica to solve the following geometry problem, my computation has been running for a long time without producing any result.
The geometry problem is:
Quadrilateral $ABCE$ is a ...
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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 ...
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Compute the integer hull of a polyhedral set in Mathematica
Computing the integer hull of a polyhedral set creates the smallest convex set (polytope) containing all the integer points within the original polyhedral set.
(? The two convex hulls have the same ...
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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 ...
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Plotting the surface gained by joining every point of a line to every point of another line in 3D space
How can I write code for displaying two lines in 3D space at random and connecting all points of line A with all points of line B and displaying the resulting surface in Mathematica (what would it's ...
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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 ...
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How to improve the accuracy of the coordinates generated by the GeometricScene and RandomInstance functions?
When using the GeometricScene function and RandomInstance function, I noticed that the coordinate precision appears insufficient ...
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How does one parallelize WindingPolygon?
Consider this toy model: a list 100,000 simple point sets, and we Map WindingPolygon over it:
...
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(discrete) Surface parametrization in Mathematica
In Python there are very easy to use and efficient libraries for surface parametrization (for instance igl). I wonder if in Mathematica we have a ready-made implementation.
The parametrization is ...
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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 ...
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Calculating maximal area of constrained SSS triangle
In triangle ABC, the lengths of the three sides are $a$, $b$, $c$, and they satisfy the equation $$3a^2 + 2b^2 + c^2 = 1.$$ I want to find the maximum possible area of the triangle.
Both the ...
user110437
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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 ...
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is it possible to automatically cluster the points constructing iso-surfaces?
I’m working with a hexahedral mesh and analyzing how a level-set function intersects it. Below are the vertices, edges, and facets defining my hexahedron:
...
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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 ...
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