# Tagged Questions

The study of computer algorithms which admit geometric descriptions, and geometric problems arising in association with such algorithms. The two major classes of problems are (a) efficient design of algorithms and data classes using geometric concepts and (b) representation and modelling of curves ...

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### 'Unrolling' the neighbourhood of a space curve

I have a space curve $\gamma : \mathbb{R} \longrightarrow \mathbb{R}^3$, sampled at $n$ discrete points. I have implemented an algorithm that gives me an approximation to $\gamma$'s tangent, normal ...
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### Computing with graphs in surfaces

I am currently working on a research project involving a polynomial defined for graphs in surfaces, similar to the Tutte polynomial, except with terms accounting for the embedding. At the moment, it ...
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### Calculation of the fundamental group from triangulations

Is there - say, for a triangulable surface - a concrete algorithm how to calculate the fundamental group of the surface from a given triangulation, seen as a graph (of its 1-skeleton), given as an ...
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### For which coverings by “geometrically nice” sets does the nerve admit “Vietoris-Rips-like” approximations?

It is well known that the nerve (or Čech complex) of a covering by metric balls is nicely approximated by the Vietoris-Rips complex. Being a flag complex on its 1-simplices, the latter is ...
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### Turning radius of a vehicle

What's the minimum turning radius of a vehicle, rectangular in shape, with length l units and width w units? One key point to consider, would be that, the inclination of the front wheels can be ...
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### How can I find a maximal inscribed ellipsoid to a *concave* set of points, in 3D?

I have a set of points which describe the surface of an irregular, natural (i.e., occurs in nature) object. This point set is not necessarily convex, and contains occasional indentations so parts of ...
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### Circle Packing Algorithm

I have question related to circle-packing. The problem is to find the circle of minimum radius enclosing four non-overlapping circles of arbitrary radius. I have to write a program in C for this ...
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### Detecting Planes through Point Cloud

Having a point cloud say (10000 points) which are randomly dispersed in 3D unit cube, the question is how to find planes within the cube that include more points with an acceptable tolerance (user ...
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### Formal proof for detection of intersections for constrained segments [duplicate]

Possible Duplicate: Formal proof for detection of intersections for constrained segments Hi I need to come up with a formal proof for the following statement: Given an arbitrary count of ...
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### What are the techniques one can used for rule based plane generation?

I've asked the question here at gamedev SE, but the response wasn't too encouraging. So I try to reask again, from a slightly difference perspective. I have a terrain, which is defined by mesh. And ...
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### The $n$-shortest lattice vectors problem in $\mathcal{R}^2$

I am looking for an algorithm to compute the $n$ shortest lattice vectors in $\mathcal{R}^2$. The problem statement is as follows: Given a lattice $L: \{ m \vec{u}+n\vec{v} \} \in \mathcal{R}^2$, a ...
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### What does “identity map $id$” mean?

What does "identity map $id$" mean in this context? Two metrics $d_1$ and $d_2$ on $X$ are said to be Lipschitz equivalent if the identity map $id\colon (X,d_1)\to (X,d_2)$ is bilipschitz.
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### Connecting all points on a plane with shortest path possible

I want to connect N nodes, so all are connected, by connecting each node to their closest neighbors. An image of what I'm looking for is below. Currently I solve it like this: I add a random node to ...
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### How to find the third coordinate of a right triangle given 2 coordinates and lengths of each side

p2 |\ |b\ | \ A| \C | \ |c___a\ p1 B p3 If given point p1 & p2, side A & B how would you find point p3? I know given this information you ...
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### What is inside and outside of complex polygon?

I am reading this paper http://arxiv.org/pdf/1207.3502.pdf Given a complex polygon. Its edges may intersect. The algorithm finds out if given point is inside of polygon or not. It draws a line from ...