Questions tagged [computational-geometry]
The study of efficient algorithms and data structures to solve various problems involving point sets, line segments, polygons, polyhedra, simplices, etc.
198
questions
2
votes
0answers
29 views
Efficient algorithm to determine the intersection volume of simple convex polyhedra
TLDR: Is there an efficient algorithm to compute the intersection of polyhedra with 8 or fewer vertices?
I have two sets of FEM meshes for one geometry (one exhibiting a skin effect). I have to ...
2
votes
0answers
31 views
Algorithm to join hexahedra and obtain outline volume
I would like to join several hexahedra and obtain an outline volume.
First, I started with 2D implementation. In 2D, there are non-intersecting quadrangles which always touch each other as shown in ...
0
votes
0answers
52 views
How to read data from simply formatted text file (c++)?
Mesh information like points, faces and cells is to be stored into separate files:
e.g. for points file:
# points data: x y z
N_Points 100
x1 y1 z1
x2 y2 z2
...
cell file:
# cells data: ...
29
votes
15answers
8k views
Good examples of “two is easy, three is hard” in computational sciences
I recently encountered a formulation of the meta-phenomenon: "two is easy, three is hard" (phrased this way by Federico Poloni), which can be described, as follows:
When a certain problem is ...
2
votes
0answers
65 views
How can one prove the duality of Voronoi and Delaunay?
Hoping I'm not misunderstanding the concept here, but it is my understanding that Voronoi Diagrams and Delaunay Tesselations are 'dual' to one another, owing to the fact that each' solution makes ...
3
votes
0answers
48 views
Calculating depth mask from different lighting
I have a object which is static, the camera is static and light source is moving. How can the depth mask be calculated ?
Concept is to use - calculate height from shadow length
Lets imagine a have ...
2
votes
0answers
45 views
Cover a polygon with least amount of parallelograms [closed]
I am solving the task that is as follows:
Input: a polygon. Can be any kind of polygon without self intersections. Can be a non-convex and with holes inside.
Goal: to cover it with 2 (at least) or ...
7
votes
1answer
109 views
How to calculate the geodesic curvature of a discrete 3D curve?
I have coordinates of a set of points that form a closed loop that lies in a 3D surface. I know the equation of the surface and I can calculate it's surface normal at any point. I found that for a ...
0
votes
2answers
108 views
Ordering points from X Y coordinates
I have series of points extracted from a regular grid, with their X/Y coordinates. A previous algorithm (that I cannot modified!) output a list of these coordinates, but the ordering of these point is ...
2
votes
2answers
67 views
projective reconstruction from orthogonal views
This is a problem from projective geometry. Suppose I have a vector $z \in R^k$ of unit length $\| z \| =1$ inside a $k$-dimensional hypercube. I don't know its value but do know its projection upto ...
3
votes
1answer
67 views
Smoothness regularisation of a 2D field on a triangular mesh?
I'm working on an inverse problem where the solution is the values of a 2D scalar field at the vertices of a 2D triangular mesh, such that the field can be defined continuously inside the mesh via ...
2
votes
1answer
138 views
A robust algorithm to sort a non-convex polygon vertices
Let v_{0},...,v_{N-1} be N points in a Cartesian xy plane defining the vertices of closed polygon (i.e. v_{N} = v_{0}).
Let P_{0}...
1
vote
1answer
87 views
Node renumbering in a 2D mesh
I have a 2D domain which is discretized using Q4 elements. I have the nodal positions and the element connectivity matrix. I would now like to renumber the nodes in such a way that all the interior ...
1
vote
1answer
98 views
How to generate a face list from vertices?
I have a little background in writing toy finite volume CFD codes. In 2D Cartesian scenarios, I typically take $x_{\min}$, $x_{\max}$, $y_{\min}$, $y_{\max}$, and the number of points in $x$ and $y$ ...
2
votes
0answers
110 views
Efficient root finding algorithm for monotonic function
This is my first time asking a question here, so I may not be asking this in the right place. I am trying to find the roots of a monotonic function with as few function evaluations as possible.
I ...
3
votes
0answers
37 views
Minimum axis aliged bounding box of convex polytope
I need to compute a $n-$dimensional integral with $n<10$ on a convex polytope. Since most numerical integration libraries (e.g. Cuba) expect the function to be integrated defined inside an axis ...
3
votes
1answer
192 views
Smallest circumscribed circle in spherical geometry
I work in Python 3 on astrophysics projects. I need to compute the smallest circumscribed circle of a set of points in the sky (so described by Right Ascension and Declination). I have found a code ...
3
votes
0answers
48 views
Approximate the largest simplex in N-dimensional Delaunay triangulation
I am working on determining the spatial information of a set of $M$ points in $N$-dimensional space. It is well-known that the construction of Delaunay triangulation is expensive in high dimensional ...
1
vote
0answers
44 views
Uniformly sample a point per polytope
I want to uniformly sample a point within each of $10^5$ convex polytopes in each iteration of a solver.
The polytopes in one iteration are completely different from the polytopes in another iteration....
2
votes
0answers
98 views
How to numerically optimize affine transformations?
I need to optimize affine transformations for of a set of triangles using energy function based on the connectivity.
The energy of an edge $e_j$ between triangles $T_a, T_b$ is given by
$$
E_j = \...
0
votes
1answer
90 views
Compute outward normal and surface area for 8 noded brick element in FEA
I have a cube which is divided into 8 small cubes by bisecting each edge, I am trying to find out the surface area of each of the faces and the corresponding outward normals for them. This operation ...
0
votes
1answer
128 views
Connectivity matrix in Finite Element Method in Triangular elements
Imagine a simple triangular base mesh in finite element method with an unknown number of elements (varying by the user). How can connectivity matrix be coded to be generated automatically?
6
votes
1answer
239 views
Putting N hard spheres randomly in given volume
I need to put $N$ spheres with given radius $R$ randomly in a Volume $[-0.5,0.5]^3$, without any overlap of spheres.
If I choose values so that all the spheres will occupy ~57% of the total volume, I ...
1
vote
0answers
172 views
Use of Morton Key to reduce number of grid points
I asked a question on Stack Overflow Performance Issue with VP Trees and Nearest Neighborsand I was not satisfied with the answer and so I thought I would reword my question for this site and post ...
1
vote
2answers
313 views
Uniform dots distribution in a sphere
I'm trying to implement Barnes-Hut algorithm, with a binary tree. My initial conditions are a uniform mass distribution in a sphere with radius $R$. How can I create uniform dots distribution in a ...
2
votes
1answer
134 views
Can the Power Method be used here?
Given a set of $n$ points on which a triangulation is performed, it is possible to construct coefficients $\lambda_{ij}>0$ such that each point $x_i$ is a convex combination of the points connected ...
2
votes
0answers
67 views
Simultaneous update to barycenters
Suppose a tiling is given in 2D (an embedding of a planar triangulated graph), with all faces convex.
Now suppose one moves each point, one by one, to the barycenter of its neighbors. I think that ...
4
votes
0answers
82 views
What Derivative-free optimization method should I use when my initial guess is very good?
I am trying to minimize a function where my initial guess is quite close to the minimum.
I'm trying to minimize
$$f(q) = \text{angle}(qw_1q*, v_1) + \text{angle}(qw_2q*, v_2) + \text{angle}(qw_3q*, ...
4
votes
2answers
494 views
3D contour mesh computation
I have the value of a function in three dimensions, $f(x, y, z)$, which varies smoothly.
I would like to compute a 3D mesh where $f(x, y, z)$ has a particular value.
Are there algorithms to do this? ...
5
votes
1answer
171 views
Integrating/Implementing NURBS-related calculations
Recently, I started to develop some codes that use NURBS (general things I intend to use/already using: spline generation, interpolation, grids, isolines, closest-point find, and many others), both ...
2
votes
1answer
63 views
Polygon approximation with a circle
There is an article describing how to detect a pupil from an eye photo.
A.-H. Javadi, Z. Hakimi, M. Barati, V. Walsh, and L. Tcheang, "SET: a pupil detection method using sinusoidal approximation," ...
3
votes
0answers
76 views
Fast Algorithms for the Simplicial Decomposition of a Convex Polytope in N-Dimensions
I'm in the process of constructing an algorithm which computes the Voronoi diagram of a set of points, but I now need a method to decompose each Voronoi cell into simplices. The information we have is:...
1
vote
0answers
54 views
Efficient initial identification of solid or liquid domains for a block structured Cartesian grid generation system
INTRO
Within the last 5 days I was able to generate a block structured Cartesian grid
generation system with a combination of Fortran,C++ and Python.
I am running intersection tests of the ...
0
votes
1answer
112 views
Which free library should I use to perform cutting/clipping operation?
I have a set of points which forms a closed loop, and I want to perform cutting/clipping a 3D model using this loop. I have used VTK but in some cases, it has a "Cannot follow edges" problem.
Is ...
0
votes
1answer
68 views
Gmsh exporting wrong mesh DATA [closed]
so hopefully I'll be using gmsh to make meshes out of 2-D cross sections with o thickness. I tried to make a structured mesh with quad elements of a rectangular ...
4
votes
1answer
243 views
Expanding Winding Number algorithm to arcs
I have a problem that I have been attempting to solve for a few days now. I was wondering if I would be able to get some assistance from the community.
In order to detect if a point is in a polygon, ...
3
votes
1answer
174 views
Compute mesh of the projection of a 3D surface triangulation
Given a triangulated surface in $\Bbb{R}^3$ we can simply project it on a plane. This will result in a family of triangles which do not form a mesh of the projection for the following reasons:
each ...
7
votes
2answers
1k views
Efficiently finding all (x,y,z) points within certain distance of point P
I am using Python, and I have a Pandas dataframe with hundreds of thousands, if not millions, of $(x,y,z)$ coordinates. I am looking to find an efficient method to index the original dataframe so that ...
0
votes
1answer
54 views
Detect all “visible” points on a triangulated surface
I have a triangulated surface that I want to work with. In order to optimize certain quantities related to this surface I want to find all points which are accessible from a given direction. To be ...
2
votes
2answers
109 views
Algorithm to construct all distances of a system described by $3N-6$ distances
A non-linear molecule has $3N-6$ degrees of freedom ($N$ is the number of atoms; ignoring translation and rotation). Therefore, a set of $3N-6$ distances and/or angles is enough, to describe the whole ...
4
votes
1answer
130 views
Delaunay triangulation for datasets with four or more co-circular points
I am working on a library that requires subdivision of polygons into triangles. The polygons are divided into triangles by (more or less) random points that are inside them. In general, the approach ...
2
votes
2answers
131 views
Find connected circles
I have a problem as follows:
We have a set of circles (we know the radius r and the center point c in Rd of each circle)
We ...
6
votes
2answers
154 views
Generating set of points on a surface defined by constraint
I'm writing a differential geometry library, and one minor convenience I'd like to offer is to generate a set of points on a surface given by a constraint. For example, for a sphere,
$$x^2+y^2+z^2-r^...
0
votes
1answer
149 views
Linear Least-Squares Point-to-Plane ICP degenerative case
I'm trying to implement Linear Least-Squares Optimization for Point-to-Plane ICP Surface Registration
Paper describes linear approximation for point to plane distance for rigid ICP. This approach is ...
0
votes
3answers
99 views
Is it valid to assume the center of a bounding sphere to be also the center of the bounding box?
Computing an axis aligned bounding box of a point set is trivial. Computing a bounding sphere of a point set is also trivial when the center is known. Computing the center of the bounding sphere is ...
3
votes
4answers
454 views
find grid points inside the parallelogram defined by an origin and two vectors
I hope someone knows an efficient computational approach to the following 2D problem:
Given two vectors $\mathbf{A}$ and $\mathbf{B}$, find all grid points that lie within the parallelogram spanned ...
6
votes
4answers
2k views
Generate a set of orthogonal vectors to a given vector
I am looking for an alternative and robust alternative to Gram-Schmidt orthogonalization, but with one constraint:
I have a unit vector $\mathbf{v}_1 \in \mathbb{R}^d \,\text{s.t.} \,\|\mathbf{v}_1^T\...
1
vote
2answers
151 views
Sign of integer determinant 4 by 4
I'm in the context of this publication: http://www.gilbertbernstein.com/resources/booleans2009.pdf
I applied quantization to my point coordinates: All coordinates are integer lying in [0, 2 power 20]....
1
vote
1answer
68 views
Sources for verified Voronoi and power diagrams
In the course of trying to implement algorithms for Voronoi and Laguerre diagrams, I realized I needed to verify if my implementation is working correctly using a point (or circle) configuration with ...
2
votes
2answers
486 views
Algorithms to extract trajectory lines out of 3D point clouds
I am looking for different approaches to extract 3D polylines out of Point Clouds.
We are able to create these point clouds out of different data sources of real world surveys (LIDAR, RADAR, etc...) ...
