The study of efficient algorithms and data structures to solve various problems involving point sets, line segments, polygons, polyhedra, simplices, etc.
4
votes
2answers
48 views
Library for closest point on a polyhedron
I need to compute a closest point on a nonconvex polyhedron to a given point in 3D space. I need a simple algorithm or library. I search in CGAL but did not find a suitable function and the package is ...
5
votes
3answers
100 views
Closest interior point on integer grid to a vertex of a convex polyhedron
I have a 3 dimensional convex polyhedron whose vertex coordinates are rational. For one of these vertices, I would like to find the nearest integer grid point (under the Euclidean metric) that is ...
2
votes
0answers
42 views
Dissipation and symplectic manifolds
I'm working on an API for simulation of port-Hamiltonian systems. As far as I understand it, a Hamiltonian system is symplectic if it is power conserving, and so including resistive elements would ...
7
votes
1answer
95 views
How to calculate the area of intersection between a 3D volume and a 2D plane
Hello if anyone can offer insight on how to solve my problem that would be great!
I am looking to calculate the area of intersection between a 3D volume and a 2D plane.
3D volume: defined by 6 points ...
4
votes
1answer
71 views
How to treat hexahedral element with shifted hanging node?
When using the Hexpress grid generator one gets hexahedral cells, possibly with hanging nodes. Because of a smoothing step, the hanging nodes can be shifted: they are not necessarily on the straight ...
4
votes
3answers
105 views
Backward stable projection and normalization of a vector
Given a machine precision unit vector $n$, and an arbitrary vector $v$, I want an unconditionally backward stable method to compute
$$f(v) = \frac{v-nn'v}{\left|v-nn'v\right|}$$
In other words, ...
3
votes
0answers
36 views
exact area resampling
I do image processing, and right now I need to resample some images taken from slightly different perspectives so I can match up features. The pixel intensities have scientific significance, so I want ...
2
votes
1answer
37 views
Error in Maple's CellDecomposition Command
I have a simple system that I want to process with the CellDecomposition command of Maple. I don't know why Maple is giving an error here! The code is
...
2
votes
0answers
44 views
Conservative field mapping between two topologically disconnected surface meshes
Some background: the Front-Tracking method uses a triangular surface mesh to describe the boundary between two immiscible fluids. To deal with the breakup and coalescence of the fluid interface, ...
5
votes
2answers
102 views
Restrict Voronoï diagram to a polygon
I managed to build the Voronoï diagram of n points using Fortune's algorithm.
This gives me a set of half-edges, some of which being infinite (no starting point and/or no end point).
I'd like to ...
5
votes
1answer
65 views
Ray casting algorithm for multiple disjoint polygons is still valid?
We're dealing with country borders, that is the set of multiple disjoint domains that is made of polygons.
To extract the different point on the map by a given country we've been said to implement ...
2
votes
1answer
80 views
Recovering coordinates by eigendecomposition without double-centering
Suppose an Euclidean distance $D\in\mathbb{R}^{n\times n}$ matrix between a set of $n$ objects is given. To obtain inner-products (which will be further be used to recover coordinates), entries of $D$ ...
4
votes
1answer
684 views
Concave polygon 'hull' finding
I implemented an algorithm to find the alpha shape of a set of points. The alpha shape is a concave hull for a set of points, whose shape depends on a parameter alpha deciding which points make up the ...
1
vote
1answer
60 views
Random placement of euclidean points with constrained inter-point distances in a fixed area
I'd like to place as many random points as possible in a 2D square $S=[0,1]x[0,1]$ such that the euclidean distance $d$ between any two points $d$ is greater than a given value $b$ (b is small). I'm ...
0
votes
0answers
26 views
Where can I find a detailed description of the AABBtree data structure implementation?
googling does not return much results on this. Are there any good descriptions in some book/article somewhere?
I require a fast collision detection algorithm between two sets of unordered Axis ...
