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Results tagged with computational-geometry
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user 53229
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.
9
votes
1
answer
350
views
How to calculate border length between adjacent Voronoi regions?
I have a set of Voronoi cells that I partition into some defined regions. I would like to then calculate the length of the "borders" between these adjacent regions, using the edges of the underlying V …
- 1,643
2
votes
1
answer
299
views
Periodic boundaries for a 3D walk in a Bravais lattice?
I'm using a Bravais lattice, 'face-centered', which is implemented in Mathematica in LatticeData[]. I want to simulate a random walk over neighboring points using periodic boundary conditions, but it …
- 1,643
9
votes
2
answers
2k
views
How to add 'border' to Voronoi diagram
Suppose I have a set of points pts, from which I generate a Voronoi diagram VD:
pts = RandomReal[{-1, 1}, {100, 2}];
VD = Show[VoronoiMesh[pts], Graphics[{Red, Point[pts]}]]
Now, as per the geome …
- 1,643
1
vote
1
answer
114
views
How to modify a particular step length in a 3D random walk?
Suppose I simulate a random walk in 3D using AnglePath3D[]:
nTimeSteps = 5;
myRandomWalk = AnglePath3D[RandomReal[{-360 \[Degree], 360 \[Degree]}, {nTimeSteps, 3}]];
Graphics3D[{{Purple, PointSize[0 …
- 1,643
1
vote
2
answers
174
views
Transfer distribution of points on a sphere to an Ellipsoid[]?
I've seen this cool function, which generates a given distribution of points on the unit sphere, known as Dimroth-Watson distribution:
(* special case; κ = 0 is the uniform distribution *)
dimrothWats …
- 1,643
0
votes
0
answers
42
views
How to reorient a Sphere[] and associated point based on some arbitrary axis?
Suppose I have a unit Sphere[] sitting at the center {0,0,0}, with a point on its "north pole", like this one:
myUnitSphere = Sphere[{0,0,0}];
myUpperPoint = {0, 0, 1};
Graphics3D[{myUnitSphere, Red, …
- 1,643
6
votes
0
answers
194
views
How to obtain the adjacency matrix of morphological components?
I am wondering if there's a simple way to obtain the adjacency matrix of the morphological components of a segmented image. Consider the following example (originally, from this question):
(*Import bi …
- 1,643
0
votes
2
answers
174
views
How to align two ellipsoids along center and long axes?
I'm struggling to understand rotation/translation transforms as applied to things like spheres and ellipsoids. Take the following silly example.
Given this pair of random ellipsoids, how do I find a r …
- 1,643
4
votes
1
answer
133
views
How to make a density plot on Ellipsoid[] surface?
Suppose I have the ellipsoid below and a set of points that I know rest on its boundary, which we can visualize:
myEllipsoid = Ellipsoid[{0.0, 0.0, 0.0}, {0.6, 0.51, 0.51}];
myPts = {{0.593679, -0.07 …
- 1,643
1
vote
1
answer
179
views
How to use VectorAngle[] in AnglePath3D[]?
Suppose I have a specific angle that I calculate from two vectors, in 3D:
center = {0, 0, 0};
v1 = {1, 0, 0};
v2 = {-1, 0.3, 0.3};
Graphics3D[{Thick, Red, Line[{center, v1}], Blue, Line[{center, v2}]} …
- 1,643
4
votes
2
answers
280
views
How to find the MeshConnectivityGraph[] from a list of independent cell mesh regions?
I'm generating a bunch of points inside a BoundaryMeshRegion. Then I generate the Voronoi mesh of the points, and take the intersection of the Voronoi cells into the region. How could I recover the ad …
- 1,643
8
votes
2
answers
850
views
How to visualize a spherical mesh on a squared plane?
I need to visualize the points of a spherical mesh on a squared plane (this question is different than this one, I believe). For instance, let us first generate points pts on a unit sphere. (Original …
- 1,643