# 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.

187 questions
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### Closed-form Jacobian of se3 element w.r.t. 6-dof motion

Let $A$ and $B$ be two rigid transformations in 3D space that transform things from global to local coordinates. Let their relative transformation be expressed by $W=A*B^{-1}$. $W$ can also be ...
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### 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: I ...
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### 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 ...
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### 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, http://www.math.ucsb....
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### 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 ...
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### 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 points ...
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### 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 ...
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### 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 ...
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### 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 triangle)...
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### 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 ...
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### 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. ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 (...
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### 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 ...
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 ...