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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Desmos saying there are too many variables [closed]

I wasn't sure if this is a Computational Science SE question or a Stack Overflow question but I think it's more of this one. I wanted to make a graph where I can rotate a hyperbola (not parabola or ...
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How do I find the portion of a cell/voxel lying within a defined surface?

We have a 3-dimensional grid of voxels (or cells), with individual voxels being of volume $dx\,dy\,dz$ where $dx=dy=dz=1$. A cone-like surface is defined by some function, $z = f(x, y)$, which in ...
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Detecting degenerate triangles with very thin structures

Between the two ears in the following bunny images, there are some degenerate triangles I want to detect. It looks like a volume-less thin slits. If the question is not clear, please let me know.
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Systematically outputting sign vectors of restricted hyperplane arrangement

(I previously asked this question on Sage's dedicated Q&A site, but got no response, so I figured it would be worth trying here.) I have a way of constructing hyperplane arrangements in Sage, ...
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46 views

How to determine the Jacobian Ratio for triangle element?

I am trying to implement an algorithm to find the Jacobian ratio for each triangle in mesh as a part of mesh quality check. Let's say that I have vertices of the triangle: $P_1(x_1, y_1, z_1)$, $P_2(...
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23 views

Simplification of vertices and dihedral angle relations of a polygonal chain

I am trying to understand the generation of Cartesian coordinates of polygonal system or poly line with fixed bond angles and fixed link lengths. I assumed the bond angle to be the same and link ...
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Packing spheres inside a geometry

I am looking for packing spheres (can be monodisperse or polydisperse with known radii distribtuions) inside a geometry. I am sure this is a well explored scientific problem with applications in ...
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Is the similar subdivision of a delaunay mesh still delaunay?

I have a delaunay triangulation for a 2d box with say an airfoil inside. If I uniformly refine this mesh by subdividing each triangle in the mesh into 4 triangles by halving each edge, is the ...
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67 views

How to divide points on a 3D complex surface into two regions based on a closed curve defined on this surface?

My problem seems simple but I can't find an algorithm that will do that for me for any 3D complex surface. I have a really complex shape 3D surface and a closed curve on it defined by some points (...
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34 views

Produce vertex displacements from volumetric shrinkage data on unstructured meshes

I was wondering what would be an efficient way to produce compatible displacements for mesh nodes/vertices if the computed data is volume shrinkage of each element/cell in the unstructured mesh? ...
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How to approach geographic data interpolation by distance?

let's say I have a set of geographic locations (lat, lng) resulting from a query. Those locations have some kind of internal ranking, my set is sorted by this number in a descending order. Now I'm ...
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How to find the nearest point inside a list in a given direction

Being $\bar{\mathbf{x}} \in \mathbb{R}^3$ a point and $S =\{\mathbf{x}\}_{i=1}^N \in \mathbb{R}^3$ a sample of N points. I am looking for a simple algorithm to determine the nearest point in $S$ in ...
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Maximum and Minimum distance from query point within bounding box

I'm reading an article regarding approximating sums using KD-trees (similar to FMM). As part of the effort I'm trying to make sense of this article , which is cited. I'm having trouble understanding ...
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Find shortest path around a cylinder represented by 3d triangular mesh

Suppose I have a 3d triangular mesh with the topology of a finite cylinder. Let $C$ be a vertex on that mesh. How can I find the shortest path from $C$ to itself that goes around the cylinder? By ...
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Derivatives over a Finite Element mesh

I have a data extracted from Comsol on some node points and I know the coordinates of each node. Does anyone know how Comsol calculate the partial derivative from the values at each node and also ...
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Dividing Point Cloud into voxels

I am reading a paper on implementing convolution neural network for a 3D point cloud. In this paper, they are dividing the point cloud into voxels. Is there any easy way to do it using point cloud ...
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Check if two points are symmetrics/asymmetrics

I am working on an Android app which lets a group of children draw whatever they want in a specific area. I need to check if the lines and figure that they draw are symmetric. The problem is that ...
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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 ...
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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 ...
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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: ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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127 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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2answers
74 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 ...
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70 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 ...
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1answer
303 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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118 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 ...
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1answer
169 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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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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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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1answer
302 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 ...
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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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49 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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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
98 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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433 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?
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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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187 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 ...
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2answers
939 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 ...
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1answer
160 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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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 ...
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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*, ...
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2answers
523 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
225 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 ...
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1answer
68 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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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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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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