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.
701
questions
0
votes
2
answers
135
views
2
votes
6
answers
411
views
Graph/Construct (John) ellipsoids circumscribing and inscribing a certain 3D convex set
A famous theorem JohnEllipsoids of Fritz John informs us that associated with a convex body are circumscribed and inscribed ellipsoids of minimal and maximal volumes.
Now, a body--argued to be convex ...
- 2,315
1
vote
1
answer
154
views
Maximum area of projection of cuboid onto plane
For didactic purposes I solve with Mathematica the following problem
(see Vasilyev's box on p. 17): when the area of
the projection of a rotating cuboid in the three-dimensional space with coordinates ...
2
votes
2
answers
159
views
Get 3D surface grown by constant distance
There is a nice example of how to generate an isometric visualisation of surfaces which are at a constant distance from a given region.
All these examples are just working on one single region. If one ...
- 2,801
2
votes
2
answers
420
views
Exporting a FEM mesh from a parametric surface
How is it possible to export a mesh for suitable finite element analysis (such as Abaqus) from a parametric surface expressions? I'm working on this kind of surface:
...
- 41
2
votes
1
answer
193
views
Create concentric circles with numbers inside
Hello there if you can give me a hand
I want to create and export to pdf the following figure, which if you realize forms the multiplication table. The idea is to be able to control the central number ...
- 215
4
votes
2
answers
385
views
Cube cutting problem
Show[Graphics3D[{Cuboid[]}],
ContourPlot3D[{x==1/3,y==1/4,z==1/5},{x,-0.2,1.2},{y,-0.2,1.2},{z,-0.2,1.2}]]
Three planes divide the unit cube into 8 small cubes, ...
- 5,550
0
votes
0
answers
66
views
Does Mathematica have a built-in n-dimensional hypervolume indicator?
Mathematica has so many functions hidden away in obscure packages that I thought I'd ask before starting to code one myself.
Thanks in advance.
- 4,957
6
votes
4
answers
433
views
Speed up the intersection of the diagonals of a regular polygon
I need to calculate all the intersection points of the diagonals of a regular polygon, following code is really slow, when n=15, it take about 30sec. I also tried using ...
- 5,550
1
vote
1
answer
179
views
Checking Membership in Boundary of Conical Hull
I want to check whether a given point is also a member of the edges of a given conical hull.
For example, I have:
...
0
votes
0
answers
59
views
Increase precision of ConvexHullMesh
I want to generate a set of equations for all planes in the convex hull as specified in this question. The problem is that the generated set of equations don't correctly cover all the points. I run a ...
- 133
4
votes
1
answer
191
views
Find intersection points of arbitrary BSpline curve
I'm researching some computational geometry and am trying to find a method of determining the {x,y} intersection of a circle and BSplineCurve for further processing.
...
- 1,076
1
vote
2
answers
200
views
How to find the shortest distance between two regions?
I need to find the shortest distance between the two regions and the two points of the shortest distance, but the following code cannot achieve this requirement:
...
0
votes
0
answers
54
views
Dump Curvature Information for 3d Models
Is anyone aware of any utility to generate and dump Principal, Gaussian and Mean Curvatures for a 3D Model or a set of points? I have reserched following tools -
meshlab
cloudcompare
They are able to ...
- 109
2
votes
1
answer
187
views
For an enclosed surface region, how to find the furthest point on that surface to another point that is not on that surface?
I have an enclosed 3D surface (a distorted sphere surface region, which is got by finding an enclosed contour of a 3D volumetric data, and apply RegionBoundary[BoundaryDiscretizeGraphics[ ]] to get ...
- 437
1
vote
0
answers
150
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Find the intersection coordinate of a line and a 3D surface defined by a contour plot
I have two points, for instance {1, 1, 1} and {10, 11, 15} that connected to form a line. I also have an enclosed surface region ...
- 437
6
votes
2
answers
681
views
How to fill in interior in a mesh region
Say I have a mesh region which encloses a region. How do I get a mesh region where this region is filled? Take for example the meshregion below:
...
- 4,055
3
votes
2
answers
188
views
Finding plane equations of planes in a convex hull
I'm new to mathematica and I need to get the equations for the set of planes which are part of a convex hull that I have calculated using ConvexHullMesh. It is a ...
- 133
7
votes
2
answers
634
views
Finding the intersection(s) of a 3D parametric surface and a line
I have some 3D parametric curve par and some line line.
I want to find parameters u,v and t for the intersection points of par and line.
I tried to do that with NSolve in many different ways and ...
- 511
1
vote
0
answers
62
views
Why does ConvexHullMesh give inconsistent output stuctures?
I know much of the stuff in ConvexHullMesh needs some TLC convexhullmesh-inconsistency
But, can anyone see why this would produce inconsistent output:
Case 1 (expected behavior):
...
- 3,632
1
vote
1
answer
106
views
How to modify a particular step length in a 3D random walk?
Suppose I simulate a random walk in 3D using AnglePath3D[]:
...
- 1,583
0
votes
0
answers
38
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:
...
- 1,583
4
votes
1
answer
105
views
VoronoiMesh with boundary edges removed
I would like to create a Voronoi diagram without the boundary edges highlighted.
This code
gVD = VoronoiMesh[X, MeshCellStyle -> {{1, All} -> {Thick, Red}}]
...
- 4,639
4
votes
1
answer
161
views
Drawing a "realistic" VoronoiMesh
Consider a set of points generated via Lloyd's relaxation algorithm
...
- 4,233
1
vote
0
answers
49
views
An apparent bug in Geometry`ConvexHull2
I was replacing some usages of Geometry`ConvexHull2 with ConvexHullMesh and found one of my tests failing. It turned out the ...
- 7,143
2
votes
1
answer
95
views
Generating points inside convexhullmesh
How could I generate these points
hexagon={{0, Sqrt[3]/2}, {1/2, Sqrt[3]}, {3/2, Sqrt[3]}, {2, Sqrt[3]/2}, {3/2,
0}, {1/2, 0}}
following this rule
...
- 427
1
vote
2
answers
127
views
How to Parallel submit nested do loop
This is the first time I'm trying to parallel compute something on Mathematica. So this question might be silly.
I have a nested Do loop of the form:
...
- 1,092
3
votes
1
answer
140
views
Hyper Tetrahedron in terms of inequalities
The command Tetrahedron[] seems to work fine for the 3-d case. But how can we get hyper-tetrahedron for 4-d case in terms of inequality? Take for example the points:
...
- 1,092
2
votes
1
answer
145
views
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;
...
- 1,092
3
votes
1
answer
99
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 ...
- 1,092
7
votes
1
answer
323
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 ...
- 1,092
0
votes
0
answers
142
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 ...
- 1,092
1
vote
1
answer
102
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.
...
- 1,092
4
votes
3
answers
103
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 ...
- 15.7k
7
votes
1
answer
282
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 ...
- 22.9k
5
votes
0
answers
110
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), ...
- 4,055
1
vote
0
answers
124
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 ...
- 15.7k
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:
...
- 1,583
4
votes
2
answers
403
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 ...
- 1,000
2
votes
2
answers
89
views
How to speed up finding region centroid and plot3d
I have the following code to make 3D of 9 regions.
...
- 1,092
1
vote
0
answers
101
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.
<...
- 1,092
1
vote
1
answer
146
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.
...
- 3,986
2
votes
1
answer
260
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 ...
- 1,583
0
votes
0
answers
311
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 ...
- 4,055
6
votes
2
answers
395
views
1
vote
1
answer
83
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 ...
- 1,092
3
votes
1
answer
126
views
How can I calculate volume of such a MeshRegion Object
The Data is here:
meshData
===
PolygonData is here
...
- 8,459