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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Translate a 3D point along a heading

I need to translate a point (P1) in 3D a certain amount, call it stepSize, along a vector described by a heading composed of ...
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1answer
20 views

Speedier alternative to “skimage.morphology._pnpoly import points_inside_poly”?

I am using scikit-image's points_inside_poly function, and in my code I am calling it enough times that it takes up about 50% of ...
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1answer
51 views

Integer simplification of irrational inequality

I'm doing work in computational geometry where the robustness of the algorithm is important. On two separate occasions now have I come across a scenario where I compare the numerical size of two ...
2
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1answer
62 views

Unwrap cylinder to plane in Paraview

I want to extract the data from the boundary surface of a cylinder (in a .vtu file) and plot it onto a plane, where the coordinates are theta (rotation angle) and ...
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0answers
31 views

Algorithm for merging mesh with cad file

I am writing the pre processing program for a porosity based cfd project we just started. Basically I have a 3 dimensional mesh made of cubes and I need to import a STL file over it, and calculate how ...
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58 views

difference of polytopes in $\mathbb{R}^n$

Is checking the equivalence of two convex polytopes $p^{s}$ and $p^{t}$ NP-hard? $p^{s}= CH\{ \cup <p^{s,a_1},...., p^{s,a_m}> \} $ // CH is convex hull computed on union of a polynomial ...
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28 views

Algorithm for porosity based CFD mesh

I am writing the pre-processing program for a porosity based CFD project. I have a mesh made of cubes, and need to import an object (a stl file: triangular mesh, not solid) over it. The cubes will ...
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12 views

Any software that can symmetrize input sets?

Is there any software that contains symmetrization techniques ex. polarization, Steiner Symmetrization etc. I suppose not. Which software would you suggest for rigid transformations? Thank you
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25 views

Convex hull and cartesian Product

Under which conditions, the cartesian product of some closed and bounded polytopes is equivalent to their convex hull?
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38 views

How do you mesh and re-mesh a surface (2-manifold) in 4D?

For ease of explanation, suppose that you began with a two-dimensional surface in (x1, x2, x3, x4)-space, and the surface begins as a flat planar region in the (x1, x2)-plane. The boundaries of this ...
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3answers
78 views

Surface integration over a portion of an ellipsoid

I would like to perform a surface integration over a portion $D$ of an ellipsoid. A plane arbitrarily intersects the ellipsoid forming two sections, of which one is $D$. I do not know how I can ...
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38 views

NURBS surface fitting for a closed region on mesh

I'm developing a tool that allows users to select a closed boundary (a polygon) on the triangle mesh and then from this boundary, generate a NURBS surface fitting the original mesh surface. My idea ...
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1answer
54 views

Number of faces in a 3D multi-type unstructured grid

Given a 3D unstructured grid consisting of mixed types of shapes (hex, tet, ...), is there a method to know how many faces (including boundary faces) are contained in the grid?
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40 views

Mesh with constraints

Is it possible to construct a constrained tetrahedral mesh of a domain using Tetgen or similar software? What I mean by constrained is that there are some nodes or edges that are not free but are ...
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1answer
112 views

area of voronoi cell

I have a Voronoi diagram that I need to calculate the area of each cell. This Voronoi diagram is produced by Voronoi command in MATLAB. To find the vertices of the Voronoi cell I use ...
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2answers
45 views

Fitting a surface to scalar functions given on the edges of a triangulation

Given a triangle mesh $\mathcal{T}$ with vertices $V=\{\mathbf{v}_i\}_{i=1}^n$ in $\mathbb{R}^3$ and triangles $T_{ijk}=[\mathbf{v}_i, \mathbf{v}_j, \mathbf{v}_k]$. For each vertex $\mathbf{v}_i$, I ...
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61 views

About Convex Geometry

A consistency notion in constraint programming: Let $P = (X, D, C)$ be a CSP. Given a set of variables $Y \subseteq X$ with $|Y| = k -1$, a locally consistent instantiation $I$ on $Y$ is ...
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2answers
101 views

K-nearest neighbours search in subspaces of a high-dimensional space

I'm looking for a good way to partition a large, fairly high-dimensional dataset in order to perform fast kNN searches not just in the full $N$-dimensional space, but also in lower-dimensional ...
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1answer
61 views

Algorithm to equalize the area of random tessellation of various polygons

I am looking for an algorithm that I can apply for a random tessellation of polygons with different areas. The algorithm can relax the geometry of the polygons to a condition that all of them would ...
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97 views

Plane constraints in R3

I have multiple plane constraints in $\mathbb{R}^3$ of the form: $$n_i \cdot x \ge \delta_i$$ Where $n_i$ is the $i$th plane normal (in form (x, y, z)), $x$ is a point in space, and $\delta_i$ is ...
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54 views

How to model waterflow when only a couple of sample points available

Figure below depicts a cross section of a creek for which I am trying to measure the water flow for that section. What we have as inputs are a bunch of sample points on the river. For each sample ...
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1answer
169 views

Best incremental multidimensional Delaunay tessellation algorithm

I'm looking for a specific type of Delaunay tessellation algorithm. The algorithm should be: incremental so that I can add new sites inside known simplexes (i.e. no searching for the right simplex ...
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1answer
120 views

Finding closed equipotential surfaces on a 3D grid

In short, I'm looking for either: (1) Publications or other sources dealing with contour/isosurface finding algorithms, so that I can write my own implementation (and parallelize as best I can), or ...
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1answer
58 views

The closed form solution of a point on a plane

Given a plane in 3D Euclidean space is $\pi$: $ax+by+cz+d=0$ and a point $P$:$(X,Y,Z)\in \mathbb{R}^3$. Find a point $Q:(X^*,Y^*,Z^*)\in \pi$ such that: $$Q= ...
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1answer
66 views

Extract 3D lower hull from convex hull

For my problem I need to extract the lower convex hull of a set of 3D points (X,Y,Z). In Matlab, one can find the convex hull using the convhull function as follows: K = convhull(X,Y,Z). Could ...
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31 views

Auto labeling algorithm [closed]

I have a set of points (2D space), and for every point there's a label (like city names on a map). I want to find a real-time algorithm that allows labels to avoid overlapping, moving them from their ...
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2answers
81 views

How can I generate shell elements to a mesh

I have a program that generates mesh for given 3d models. The generated mesh must use quadrangle elements. It is required to add "shell elements generation capabilities". The requirement is as ...
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1answer
69 views

how to do geometry clean up in paraview? [closed]

I have a vtk file which has a bunch of points, I would like to delete a few points because, those distort my geometry (basic geometry clean up), is there a way I can do it in paraview? I just want to ...
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52 views

Creating ruled surfaces bounded by Bsplines and how to obtain intersections

I'm just learning gmsh from the tutorial, and I have some questions regarding gmsh geometry design, I have two Bsplines with common start and end points that are not coplanar to each other. A ruled ...
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1answer
66 views

Inclined plate capacitor grid/ mesh

You can calculate the electric potential over every point in a defined space by solving Laplace's equation. To do this in a computer program you set up an 2-d array/ matrix and loop the internal ...
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1answer
542 views

Vertical and horizontal segments intersection (Line Sweep)

Introduction: I have a vertical segment S That i want to move across a plane (Left --> Right), and find intersections with horizontal lines. Problem : The problem which i am having is the ...
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1answer
99 views

Line segment straddle

What is exactly the definition of "Straddle"? Can you please explain what do they mean exactly or a sketch? A segment P1P2 Straddles a line if point P1 lies on the one side of the line and point P2 ...
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47 views

How can i find the coordination number with voro++?

Could anybody please help with voro++ cause i am new to this software?My problem is how can i find the coordination number of an atom ,cause i checked it for a bcc lattice and it gave me 24 for all ...
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4answers
161 views

Computational science contests. Why arent there any?

I was wondering why there are no online or offline computational science contests? At least I couldn't find much by googling. I mean, like a topcoder for computational sciences. I assume one reason is ...
2
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1answer
62 views

Equal Area Sampling on Curved Surface:

I have a quantity $\beta(\mathbf{x}) \in \mathbb{R}$ that I wish to compute on a curved, smooth surface defined by $\{\mathbf{x}: \Gamma(\mathbf{x})=0\} \subset \mathbb{R}^{3}$. (This surface is ...
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0answers
52 views

Environment for implementing/testing Computer Graphics algorithms [closed]

I need to code up a computer graphics algorithm for Surface Registration. Briefly surface registration is the process of finding "optimal" one-one correspondence between surfaces, where the meaning ...
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3answers
485 views

Volume of 3D convex hull of small point sets all on the hull

I have a question that is similar to this one asked before except in 3D, and I only need the volume, not the actual shape of the hull. More precisely, I'm given a small set of points (say, 10-15) in ...
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0answers
148 views

MATLAB Detection of the point where regions meet

A totally beginner here. I've read all the coordinates of nodes of a face from the corresponding file into an [X Y Z] array and displayed as a mesh. The top-most node of the nose i.e. the tip of the ...
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3answers
227 views

N-dimensional Delaunay Tesselation Software Libraries

I have a set of known points/nodes irregularly spaced in N-Dimensional space (N>=2), and I would like a way to generate the Delaunay triangulation of these points, and return the corresponding ...
2
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1answer
339 views

Fast nearest neighbor search, Latitude Longitude

Is there a fast nearest neighbor search algorithm that generates the nearest neighbors, not based on Euclidean distances but based on geographic distances over a set of latitudes/longitudes. The fast ...
3
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1answer
306 views

Minimal surface solution in Python

Note: this question was also posted in StackOverflow and math.stackexchange. I have a set of 3D points defining a 3D contour, as shown below. The points in this contour lie in their best-fit plane ...
3
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1answer
168 views

Compute spatial second derivatives in Isogeometric analysis

Motivation: In isogeometric analysis, state variables(e.g. displacement) are defined in the parametric domain, which can be mapped to the physical domain by $\boldsymbol{\xi}\mapsto \boldsymbol{x}$ ...
4
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1answer
61 views

Fastest method for evaluating the limit of the sign of a polynomial

Consider a multivariate polynomial $f(x) = f(x_1, \ldots, x_n)$ with maximum degree $d$. Following the linear symbolic perturbation scheme described in Seidel 1998, I want to evaluate the limit ...
4
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2answers
79 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 ...
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3answers
179 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 ...
3
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0answers
54 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 ...
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1answer
229 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 ...
3
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1answer
98 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 ...
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3answers
187 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
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0answers
58 views

exact area resampling [closed]

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 ...