# 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 ...

121 views

### Shortest path in a maze

There is a maze, which is nothing but made of $2$ parallel polylines, which looks like a zig-zag road. We have to find the shortest path between the entrance and exit. Any ideas on how to proceed? ...
149 views

44 views

### '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 ...
98 views

### 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 ...
167 views

### 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 ...
56 views

### 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 ...
958 views

### 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 ...
165 views

### 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 ...
751 views

### 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 ...
642 views

### 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 ...
54 views

### 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 ...
51 views

### 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 ...
178 views

### 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 ...
684 views

### 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.
75 views