The study of efficient algorithms and data structures to solve various problems involving point sets, line segments, polygons, polyhedra, simplices, etc.

learn more… | top users | synonyms

3
votes
1answer
40 views

Fitting a rectangle to a point set

I have an ordered list of (2d-)points that are forming a (not axis aligned) rectangle and I'd like to recover that rectangle. Approximations like a minimal enclosing rectangle can't be used so that ...
2
votes
2answers
151 views

Fitting orthogonal planes to a point set

I have a set of 3d points to which I want to fit two planes. I know the assignment of points to the planes so I don't need any RANSAC or similar. Currently, I'm using a PCA-based approach to fit two ...
1
vote
0answers
24 views

Detecting and joining series of line segments that run along each other

Given: Several circular series of map GPS coordinates for several bus routes. The GPS coordinates are not all equal when they run along the same road. The number of GPS coordinates for a single bus ...
0
votes
0answers
19 views

Interior nodes of a closed graph?

Does anybody know if any graph partitioner library such as Metis, Scotch, or Zoltan can (besides splitting a domain), differentiate between internal (i) and boundary (b) nodes?
1
vote
0answers
40 views

Center of mass in systems with periodic boundary conditions

I have a question about the calculation of center of mass (COM) in systems with periodic boundary conditions. There is a method introduced here: ...
1
vote
1answer
91 views

Calculate the area and perimeter of a hand-drawn shape

I need to know whether my idea for my final year project could be achieved or not. If its achievable please guide me with the relevant language and other frameworks. The idea I have a piece of paper ...
2
votes
0answers
79 views

intersection between polygon. Algorithm to check it

I'm working on an algorithm which should check if two polygons, described by their vertex coordinates, are: one inside the other, are intersecting or are separated image below describe this three ...
3
votes
2answers
78 views

Matrix free finite elements method for visualization in process tomography

I am Computer Scientist and now I am interested in matrix multiplication on GPUs. My research are focused on matrix free finite elements method where I multiply sparse matrix. Sparse matrix could ...
1
vote
0answers
39 views

Area of convex n-dimensional polytope

I am looking for an efficient algorithm to calculate the surface area of an irregular N-dimensional polytope. I have a description of this polytope both as coordinates of the vertices as as linear ...
2
votes
1answer
32 views

Rank constrained SDP

I would like to optimize a function of the following form: \begin{equation} \sum_{i,j=1}^N c_{i,j} \mathbf{x}_i \cdot \mathbf{x}_j, \end{equation} where $\mathbf{x}_i \in \mathbf{R}^d$. Is it possible ...
1
vote
2answers
103 views

Mathematical programming formulation of triangle intersection

Given variables $a_1$, $b_1$, $c_1$ and $a_2$, $b_2$, $c_2$ representing the vertices of two plane triangles, how might one specify the requirement for the two triangles to intersect as an objective ...
4
votes
2answers
217 views

How to determine whether two cylinders intersect or not?

Considering any two cylinders, defined as: the center of their bottoms $A_i$, the radius of their bottom $R_i$, the unit vector $W_i$ of their axis direction, and the length $L_i$ of the cylinders, ...
2
votes
1answer
148 views

Comparison of convex hulls [closed]

Consider a set of polytopes $P_i : i=1,2,...,k$ each of which has a structure as $P_i:= \{(x_{i1},x_{i2},..., x_{in})\; |\; x_{ij} \in [a_{ij}, b_{ij}] \subseteq [0,1]\}\;\; \text{for all}\;\; ...
4
votes
3answers
138 views

Point inside curved finite element

I like to create interpolation functions for second order finite element meshes. For elements with straight edges all is good, but some of my elements may have curved edges as shown in the figure: ...
3
votes
5answers
155 views

Distance between points

I am wondering how can I solve following problem. Arrange randomly $n$ points inside a square of side $a$ under the condition that the distance between any two points may not be smaller than 1. I ...
2
votes
1answer
117 views

Monte Carlo Double Integration Implementation

Am implementing a monte carlo integration routine to compute this double integral in eqn 0.3 of page 2 of this paper 'Mobius energy of knots and unknots', Annals of Mathematics, ...
6
votes
2answers
184 views

Selecting most scattered points from a set of points

Is there any (efficient) algorithm to select subset of $M$ points from a set of $N$ points ($M < N$) such that they "cover" most area (over all possible subsets of size $M$)? I assume the points ...
1
vote
2answers
56 views

Wrapping grid of points around curvature of an infinitely long cylinder [closed]

I have an infinitely long cylinder defined using radius a point in 3d Axis defined using a 3d vector I have a set of points with 3d coordinates placed in a grid. I want to wrap this grid of ...
1
vote
2answers
196 views

Ideas on how to search nearby geospatial data fast

I am looking at a very simple problem, but can't quite find the best solution. I need to accept a lat/lon coordinate and based on that coordinate find all the points within roughly ~1km (accuracy is ...
0
votes
0answers
55 views

Bijection between polyhedrals

Does there exist a bijection between a general axis-parallel polytope in $\mathbb{R}^n$ and a polytope embedded in a unit hypercube in $\mathbb{R}^n$? This means that the bijection must preserve the ...
3
votes
0answers
66 views

How to sample points in hyperbolic space?

Hyperbolic space in the Poincaré upper half space model looks like ordinary $\Bbb R^n$ but with the notion of angle and distance distorted in a relatively simple way. In Euclidean space I can sample a ...
3
votes
0answers
71 views

Shape measure for C-shaped objects

There are many well defined measures for many basic geometrical objects such as rectangularity (area coverage of minimum bounding rectangle), triangularity (area coverage of minimum enclosing ...
1
vote
1answer
99 views

Find area of a polygon. In C and Obj C.

I've been given an assignment: Create a console application (using C and Obj C) that will calculate area of a random polygon. The application should process input data as a .txt file with a list of ...
4
votes
1answer
53 views

Estimating the local compression/expansion ratio for a transformation on a point cloud

Let's say we have an unorganized point cloud P1 with N points, each with coordinates {x,y,z}. We apply non-rigid transformation to P1 (translation + rotation + warping), to obtain point cloud P2. ...
5
votes
2answers
222 views

applications of computational geometry in fields such as CFD?

Out of curiosity, I was recently trying to search what skills are required to be successful as developer in scientific computing field (e.g. CFD or similar). And to do so, I was going to through ...
2
votes
0answers
49 views

interpolate the circle going through three points using splines

It is known from Geometry that any 3 points determine a circle. This is the problem of Appolonius Programming solutions try to approximate using Bezier curves. Can you not draw conics as Bezier ...
1
vote
0answers
138 views

Equilateral triangle based mesh generation by intersection

In work I am currently working on I need to mesh some structure with equilateral triangles to study it using a kind of discrete element method known as spring networks or Lattice model. To mesh the ...
0
votes
2answers
79 views

Minimizing the edge length of a polygon preserving its angles

I am trying to minimize the edge lengths of a polygon while keeping the angles the same. I can achieve this geometrically (iteratively), however, I am looking for some related papers that can solve ...
0
votes
1answer
47 views

Exit point of a ray shot through the earth from another location on the earth?

I have a little computational geometry project I'm struggling with for a non-commercial "art" installation. It is driving me crazy and I'd happily pay for an implementable algorithm/solution ...
2
votes
0answers
50 views

Bracket Algebra, Straightening Algorithm

My apologies if the question is simple. I need to write a code for straightening algorithm. Which includes defining bracket algebra. I tried to write it in CoCoA-5, but it wasn't possible because ...
3
votes
1answer
75 views

How to Check a Hyper-Cube for Defects

I would greatly appreciate some help/references on solving the following problem: You are in charge of searching through a n-dimensional hyper-cube $[0,1]^n$ to make sure that it does not contain ...
0
votes
0answers
111 views

Help with the definition of constraints for a joint optimization problem

A trajectory is piecewise defined by the following polynomial form: $$ f(t) = a + bt+ct^{2}+dt^{3}+et^{4}+ft^{5}+gt^{6}+ht^{7}+it^{8}+jt^{9} $$ for every single segment composing the trajectory (the ...
0
votes
3answers
100 views

Meshing of polygons

I need to generate a sequence of increasingly denser high-quality triangular meshes for some pentagons in MATLAB. I want to supply as my input The coordinates of the 5 vertices of the pentagon ...
0
votes
1answer
139 views

Convex Polygon Intersection

Determining the intersection of two convex polygons is one of the fundamental problems in computational geometry . I'm asking for an algorithm having: INPUT: Given two convex polygons P and Q in 2D ...
1
vote
2answers
108 views

How to determine the support/influence domain for irregularly distributed nodes in the Element-Free Galekin Method?

EDIT (26-12-14):In the Belytschko's EFG code, the domain of influence for uniform distributed node can be calculated using the code below; my question is how to calculate xspac and yspac when the ...
1
vote
2answers
789 views

Determine unit outward normal vector for a curve

It is necessary for me to find the unit outward normal vector for the curve: $$\gamma=(x(t),y(t)) $$ where $$x(t)=\cos(t)−0.5\cos(3t)$$ and $$y(t)=\sin(t)+\sin(7t)+\sin(3t)$$ I know how to find ...
3
votes
2answers
169 views

How to determine a node is outside or inside a curve

Let $$x=0.5\cos(t)-0.3\cos(3t)$$ $$y=1.2+0.6\sin(t)-0.07\sin(3t)+0.2\sin(7t)$$ How could I know an arbitrary point is inside or outside of this curve? Also, another ...
0
votes
0answers
47 views

Checking if convex polytope is nonempty

I am currently running a linear program with MATLAB to determine, by the exitflag of linprog, if two rotated and shifted hypercubes have nonempty intersection. I wondered if this is a waste of time, ...
3
votes
1answer
70 views

Riemann surfaces: computing $f(z) = \int_0^z \frac{dx}{\sqrt{P(x)}}$

I am trying to validate that the Schwartz-Christoffel mapping does indeed take the upper-half plane $\mathbb{H} = \{ z: \mathrm{Re}(z) > 0\}$ to a polygon. This involves integrals of functions ...
3
votes
1answer
77 views

Computing the (non-convex) boundary of a set of paths between two points

I have a set of paths between two fixed points (marked in red below). Each of these paths consists of an ordered series of $\{x, y\}$ points (marked in blue). I am trying to find the ordered set of ...
2
votes
2answers
141 views

Finding nearest neighbors using Jaccard distance for positive, real-valued vectors

Say we have $x_i, \ldots, x_n \in R ^ D$ with positive, real components and use Jaccard distance $d(x_i, x_j) = 1 - \frac{\sum_{d = 1}^D\min(x_i^d, x_j^d)}{\sum_{d = 1}^D\max(x_i^d, x_j^d)}$ to find ...
6
votes
2answers
459 views

A method to determine whether a point can be contained within a circle with no neighbouring points

I have been working on a particularly challenging problem and was hoping for some guidance. Here is my problem. I have a point cloud containing millions of points. For each point in the set, I need to ...
2
votes
1answer
231 views

What is the exact formulation of compressible Euler equation of gas dynamics in polar coordinates with artificial diffusion in 2D?

The interested equation is advection-diffusion equation. One of the canonical example is Navier-Stokes equations. However, I would like to let the coefficient of diffusion constant goes to zero, ...
2
votes
1answer
400 views

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 ...
1
vote
1answer
108 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 ...
1
vote
1answer
59 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
votes
1answer
488 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 ...
1
vote
0answers
70 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 ...
0
votes
1answer
73 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 ...
5
votes
1answer
96 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 ...