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.
723
questions
2
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1
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Region bounded by planes in terms of inequalities
Suppose I have 5 planes that intersect to give a bounded region in 4D.
For example, the planes are
x1==0;
x2==0;
x3==0;
x4==0;
x1+x2+x3+x4==1;
...
- 1,122
3
votes
1
answer
109
views
Convert ConvexHull in a array to Inequality
This question is in continuation with the previous post Convert ConvexHull to Inequality
There are two problems that I faced.
Suppose we have two or more convex hull defined using an array R[i], like ...
- 1,122
7
votes
1
answer
355
views
Convert ConvexHull to Inequality
I have the following convex hull.
P0={0,0,0};
P1={1,0,0};
P2={0,1,0};
P3={0,0,1};
ConvexHullMesh[{P0,P1,P2,P3}]
Now I want the region algebraically as equality ...
- 1,122
0
votes
0
answers
156
views
Surface area of a list of points
I would like to know how I can get the area of the following point list. I am using the following script to make a mesh region and then find the area. However, the area is much larger than the value ...
- 501
1
vote
0
answers
56
views
Image Size change with changing ViewPoint
I have the following code to show the intersection of two convex hulls. The plot has no problem when ViewPoint->Default. But when I try to change the viewpoint manually by holding and dragging the ...
- 1,122
1
vote
1
answer
108
views
How to label vertex of a 3D convex hull?
I have the following code to plot a 3d convex hull with 4 corners only.
...
- 1,122
4
votes
3
answers
106
views
A DistanceFunction for use with a mouse in a DynamicModule
I need to have a mouse cursor that identifies points that are close to the mouse position on a graphics plot. The difficulty is that the scaling of the plot makes this difficult. I think I am missing ...
- 16.1k
7
votes
1
answer
319
views
RandomPoint inside mesh for walk-on-spheres Monte Carlo PDE solver
I'm trying to understand a Monte-Carlo Laplace/Poisson PDE solver:
http://www.cs.cmu.edu/~kmcrane/Projects/MonteCarloGeometryProcessing/paper.pdf
This method inspired by random-walks and ray-tracing ...
- 23.7k
5
votes
0
answers
140
views
DelauneyMesh in 4d and higher
Is there any way to find the DelauneyMesh in 4D (or higher)? Its documentation implies that it should be possible "A Delaunay mesh consists of intervals (in 1D), ...
- 4,197
1
vote
0
answers
127
views
Periodic Voronoi Mesh in a box
Is it possible to generate a periodic Voronoi Mesh inside a rectangular domain? I would also like to obtain the coordinates of each cell separately so that I can perform further operations on each ...
- 41
7
votes
4
answers
1k
views
Find smallest distance from a point to a Bézier curve
I wish to find the smallest distance from a point to a curved defined via a Bézier function. I want to do this automatically. For particular cases it is not to difficult. Here is a minimum working ...
- 16.1k
9
votes
2
answers
1k
views
How to add 'border' to Voronoi diagram
Suppose I have a set of points pts, from which I generate a Voronoi diagram VD:
...
- 1,593
4
votes
2
answers
440
views
Finding shadow area of a 3D object
Given a 3D object, how could one find the area of the shadow? In effect, this is a measure of optical cross section. The ultimate goal would be a table showing latitude, longitude, and, optical cross ...
- 1,050
2
votes
2
answers
91
views
How to speed up finding region centroid and plot3d
I have the following code to make 3D of 9 regions.
...
- 1,122
1
vote
0
answers
123
views
How to find intersection of higher dimensional convex hull?
I have often used ConvexHullMesh to obtain a convex hull for 2-d and 3-d points. But when I try to find it for 4-D points I encounter error even for simple cases.
<...
- 1,122
1
vote
1
answer
149
views
Represent a Concave Mesh Volume
I programmatically generate a shape, where the top surface is defined by a series of polygons. I generate all the points of the polygon.
...
- 4,262
2
votes
1
answer
275
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 ...
- 1,593
0
votes
0
answers
348
views
Projecting a 3D mesh region to 2D
How do I project a 3D MeshRegion to a 2D MeshRegion (or equivalent for a BoundaryMeshRegion). This question is similar to ...
- 4,197
6
votes
2
answers
414
views
1
vote
1
answer
88
views
0
votes
0
answers
60
views
Convex Hull Mess Axis Label
P0={0,0};
P1={1,0};
P2={-1,0};
R[1]=ConvexHullMesh[{P0,P1,P3},Axes->True ]
I use this code to draw the convex hull but I want to also label the ...
- 1,122
3
votes
1
answer
151
views
How can I calculate volume of such a MeshRegion Object
The Data is here:
meshData
===
PolygonData is here
...
- 8,557
1
vote
0
answers
103
views
How to use Mathematica to find the coordinates of 7 points?
Could anyone please help me with using Mathematica to find the coordinates of 7 equally spaced points on the unit sphere $S^3$ in $\mathbb{R}^4$? Thanks a lot!
- 11
0
votes
0
answers
59
views
Torus Hex Mesh - Need Unique Hex Dimensions
I'm looking to laser cut a bunch of hexagons and assemble them into a torus (using hot glue or tape). How do I get the dimensions of the individual unique hexagons? I've seen Create a torus with a ...
7
votes
2
answers
249
views
Penalty function on discrete mesh using Laplace-Beltrami operator?
Context
I am interested in extending to the ill-condionned regime the inversion of linear equations
arising from inverting differential equations which have been solved via 0-splines over a mesh ...
- 22.6k
0
votes
1
answer
57
views
Finding an instance of a parametric equation that intersects given points
So I have this equation for a circle centered at the origin that has some orientation in 3D space.
...
- 395
2
votes
1
answer
180
views
Mathematica Won't Recognize a MeshRegion
I've implemented the code in the top answer of this question on the Plateau problem in differential geometry, and it works with the example shown in Example 1, so there is nothing wrong with the code. ...
- 193
6
votes
1
answer
149
views
Minimization problem and Voronoi Mesh
I have a random convex mesh $Q$, made of $n$ polygons, and I want to test how close it is to a Voronoi tessellation. In other words, I'm looking for generators (seeds) $\{(x_i,y_i)\}_{1\leq i\leq n}$.
...
- 4,167
4
votes
2
answers
267
views
Why can't an annulus be mapped as a rectangle
The following code is used to map an annulus to a rectangle:
...
6
votes
1
answer
162
views
Checking if a Graph forms a Mesh
Given a random graph, I want to define a function MeshGraphQ that tests if the graph is a lattice (or mesh) graph. Here, I don't need the tiling to be regular. ...
- 4,167
8
votes
2
answers
815
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 ...
- 1,593
3
votes
1
answer
119
views
Efficiently finding spheres furthers apart along and perpendicular to a given direction
Setting
I am dealing with a box of spheres, all having the same radius and inserted into a finite box size without any overlaps. Along a given direction $\mathbf v$, I am trying to find:
(a) The two ...
user52181
-1
votes
1
answer
243
views
How to wrap any function/curver around a circle? [closed]
I have a function defined as $y=f(x)$ which i want to wrap around a circle, to get a transformed function $r=f(ϕ)$. It is important that the length of the wrapped curve stay's the same. For two ϕ ...
2
votes
1
answer
74
views
unbounded Voronoi iteration with finite and non-equal point radii
I would like to create a cool differential line growth animation based on this great tutorial.
The only missing part is the relax node, but I couldn't find any pointers on the web how to implement ...
- 150
9
votes
1
answer
311
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 ...
- 1,593
2
votes
1
answer
826
views
Retrieving boundary points of concave hull (or alpha shape) in 3D
I am trying to find the boundary points of some concave 3D region which is described by a list of points. If the region were convex I would take the convex hull and simply extract the coordinates ...
- 4,197
18
votes
1
answer
677
views
Making a graph or network interactively over an image
Given an image, is it possible to manually draw a graph over it? For example, taking the following image:
I want to manually pick the vertices and draw the edges in a "Paint-like" manner to get, for ...
- 4,167
8
votes
1
answer
546
views
Getting cell edges from a picture
I would like to write a program that, given a picture of an epithelium (2D cell array), for example
automatically detects the cell edges and returns the corresponding lattice. Illustratively,
...
- 4,167
6
votes
1
answer
158
views
Algorithms used for DelaunayMesh
Is it possible to find what algorithms are used for Delanunay triangulations?
- 1,335
5
votes
2
answers
175
views
VoronoiMesh as a Graph
I want to draw the following graph
using VoronoiMesh. For example, since
...
- 4,167
6
votes
1
answer
170
views
Updating a graph under ODE dynamics (vertex model)
Consider the following graph, which is obtained from a VoronoiMesh
...
- 4,167
0
votes
1
answer
116
views
How to plot parametric time dependent plot with different parameters taking average of time?
I am trying to plot the solution given in the code with respect to "delc". Now the problem is that it can be plot for a particular value of "t" like t=10,20,50,60,.. upto 100 but what i need is mean ...
- 83
4
votes
1
answer
214
views
Where to get the detailed code of MMA for grid mesh
I know DelaunayMesh can triangulate the specified area, but I can't see the code and partition idea of this built-in function. I want to know how to get the source ...
4
votes
2
answers
266
views
Rectilinear polygon
It is possible to generate a random Rectilinear Polygon (without holes)
in WL? I found this option, but without any possibility to ask for a Rectilinear Polygon.
...
- 1,989
7
votes
1
answer
121
views
5
votes
0
answers
239
views
How to get 3D building data in map functions?
Most modern mapping APIs have 3D model data for city buildings built-in. For example:
Is there some way to get this functionality in the Geography related functions?
I believe ...
- 31.2k
1
vote
1
answer
147
views
How to get the overlap's percentage that occurs between 2 circles or among more than 2 circles?
The following code draws the following circles;
...
- 199
1
vote
1
answer
131
views
Computing cross section area between cylinder and disk
I am creating a cylinder, whose center disk is placed at position vector v1 and whose orientation is given by the disk's normal vector ...
user52181
3
votes
5
answers
826
views
Computing the intersection area of two disks in 3D
Closely related to this question about highlighting intersection of two disks, I am trying to figure out if one can do so similarly for disks embedded in $3D$ (e.g. in a bounding box). The difference ...
user52181
4
votes
2
answers
283
views
Hafnian of a matrix
Is there a Mathematica built-in function for the calculation of the Hafnian of a matrix? I am interested in the function as it appears naturally in the calculation of moments of a multivariate ...
- 165