# 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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### Complex infinity at a point and division by zero

Edit: I've found out that the book was written for Mathematica 7, which was a pretty long time ago. It boils down to changes in syntax most probably, but simple renaming to lower lettercase does not ...
50 views

### Triangulations of a convex polygon

I have a piece of code which finds all triangulations of a convex polygon. It is known that a number of such triangulations for a given $n$-gon is is given by ($n-2$)th Catalan Number, so for instance,...
1 vote
81 views

### Problem defining a polygon

I have two polygons that are very similar as: ...
214 views

### Deleting the same lines from a list

Say I have a list of Lines: ...
148 views

### Fill points into a pre-rotated convex Dodecahedron

I am trying to fill a rotated convex polyhedron with points. This functions well in the unrotated case: ...
196 views

### Ideas for visualizing the shape of a random walk

Context: In the context of (3D) random walks or polymer chains, a useful quantity for capturing and characterizing the shape of the walk or the conformation of the polymer in space is the gyration ... 1k views

### Catmull-Clark and Doo-Sabin Subdivision Implementations

I want to work on subdivision surfaces. Unfortunately, I don’t have any source code to start with. I need some Mathematica codes for applying Catmull-Clark and Doo-Sabin methods. I would like to ...
190 views

### Solve: line and rectangle intersections

I have been trying to find the intersections between a rectangle and a line, following the example given in the Solve function: ...
121 views

### Mesh cell count for Voronoi mesh too low

I was trying to solve this question out of interest and thought perhaps creating a Voronoi mesh, cropping it to a circle, and colouring the mesh cells might work. However, if I ask ...
140 views

254 views

### Vertices of a Rotated Polyhedron

I am attempting to geometrically transform a polyhedron (namely rotate and translate the polyhedron in global coordinates) and than find the new vertices. Here is what I have so far, but I am stuck at ...
197 views

### How to write the code for a general B-spline function?

I write the code for B-spline basis and it works very nicely but now I need help to write code for general B-spline functions I would like the code to show the spline segment in this way:
455 views

### How do I verify a vector identity using Mathematica?

I am trying to verify well known Frenet–Serret formulas in general setting using Mathematica. I need to consider a general space curve $r(s)=(x(s),y(s),z(s))$ in $\mathbb{R}^3$ and define its unit ...
405 views

### Speeding up Nearest with multiple distance thresholds

Consider the following example of using Nearest: ...
406 views

### How to make a frustum of a cone

For finite element purposes I need a frustum of a cone with a finite wall thickness, i.e. a tapered pipe. To make a cone is easy ...
429 views

### Finding Intersections Between Arbitrary Surface and A Line

I have a self-intersecting surface H defined as follows: ...
142 views

### Why is RegionIntersection failing on my custom Region?

I load a custom region, specified as BoundaryMeshRegion R = Import["C:\\data\\Profile.stl", "BoundaryMeshRegion"] and I try ...
1 vote
185 views

### ImplicitRegion evaluates the region incorrectly when it must be empty

Consider the following implicit region: ...
711 views

### Relative Neighbourhood Graph

Is there some way to efficiently compute the relative neighbourhood graph on $n$ Euclidean points in $\mathbb{R}^{d}$? Though one can simply define ...
147 views

### Extract Halfspace representation of a ConvexHullMesh

I have computed the convex hull of a set of points in $\mathbb{R}^{n}$ using ConvexHullMesh. This describes a convex polytope $\mathcal{P}$. I was wondering if ...
465 views

### How to evenly distribute points inside a sphere?

SpherePoints[] gives me a fairly even distribution of points on the surface of a sphere. However, following this, I can have a much better distribution (although ...
176 views

### Simplify behavior: assumption as Interval versus assumption as bounds

I am using MMA V11.2 under Linux I am surprised by this: ...
52 views

### Plot variations in geometric sum within prescribed range

I have a simple geometric sum: Sum[a^(j + 1), {j, 1, k}] which evaluates to (a^2*(-1 + a^k))/(-1 + a) ...
1 vote
199 views

### How to get intersection points between "each line" and "multiple circles intersected with that line"?

The following code is used to draw circles; ...
449 views

### How to get size of each polygon of a Voronoi diagram using Shoelace formula?

The following code gets all vertices of all polygons (mesh cells) of VoronoiMesh[pts]: ...