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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.

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1answer
51 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 ...
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0answers
30 views

Finding the Proportions of and Programatically Representing Topological Disks

I am currently in the process of writing an internal software package that will be used for computational geometry research. I am interested in being able to programatically generate isotoxal ...
2
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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
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1answer
65 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
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1answer
110 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}...
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1answer
73 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
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1answer
86 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 $y$ ...
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0answers
103 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 ...
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0answers
30 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 ...
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0answers
101 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
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0answers
47 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 ...
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0answers
43 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....
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0answers
76 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 = \...
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1answer
85 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 ...
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1answer
100 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
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1answer
222 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 ...
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0answers
158 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
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2answers
160 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
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1answer
124 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 ...
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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
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0answers
78 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
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2answers
474 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? ...
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1answer
152 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
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1answer
59 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," ...
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0answers
74 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:...
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0answers
46 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 ...
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1answer
110 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
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1answer
58 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
207 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
135 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
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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
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1answer
53 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
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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
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1answer
120 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
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2answers
112 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 ...
7
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2answers
139 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^...
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1answer
119 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 ...
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3answers
67 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
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4answers
343 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
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4answers
1k 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\...
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2answers
142 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]....
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1answer
61 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 ...
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1answer
331 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...) ...
0
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1answer
75 views

What is the expected value of area of intersection of a circle and a rectangle

$r$: cicle C1's radius $w$,$h$: rectangle R1's edges: $x=w$, $y=h$, $x=0$, $y=0$ $(w>2r, h>2r)$ $S(x,y)$: area of ...
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0answers
35 views

Algorithms for computing winding numbers of 2-sphere maps

I have a question concerning computational geometry which arises in the simulation of fields with topological defects, and I'd like to know whether there's an efficient algorithm (or any algorithm) to ...
1
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1answer
62 views

Optimally “morph” one set of points into another

Given two sets of (two-dimensional) points, say, $A=\{a_1,a_2,\ldots,a_{n_a}\}$ and (you guessed it) $B=\{b_1,b_2,\ldots,b_{n_b}\}$, and $d^2_{i,j}=\mid a_i-b_j\mid^{\ 2}$ the "matrix" (not ...
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1answer
53 views

Efficient search strategy in a monotonic boolean function wherein the probability of solution location is known apriori

A boolean-valued monotonic function is defined in the set of positive integers, $\mathcal Z$. $$f(n) = \begin{cases} 0, &n_{min}\le n < n\ast\\1, &n\ast\le n\le n_{max} \end{cases} ; n \in ...
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1answer
67 views

Distirbution of Points along a Line

I am facing the following problem: Given is a line of length $L$ which I want to split into $N$ segments. The lengths of the first $(s_1)$ and last segment $(s_N)$ are given. You can assume that the ...
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0answers
25 views

Use custom defined metric(not matrix) in Javaplex

I'm about to get started trying to use Javaplex for the first time for some application in topological data analysis (TDA) and I want to use a custom defined metric. From looking over the documents, I ...
0
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1answer
109 views

From edge-vertex connectivty to face-vertex connectivity?

I am working on mesh generation and optimization and encountered this problem. For example, in the figure below, we have the edge-vertex connectivity: 0-1 1-4 4-5 2-5 3-2 0-3 1-2 1-6 7-6 4-7 ...