# Questions tagged [geometry]

Geometry is a branch of mathematics. Geometry studies the spatial relationships and forms of objects, as well as other relationships and forms, similar to the spatial in its structure.

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### Pixel-To-Angle Transformation in Camera Image

I'm trying to localize points I see in a camera image in terms of azimuth and elevation and match points between shots. Individual shots should differ only in rotation around the camera's center (...
3answers
347 views

### Monte Carlo approximation of PI

I'm trying to understand how to compute the value of Pi by means of the Monte Carlo simulation. I have a circle inside a square where the sides of the square are tangent to the circle. As data I have ...
2answers
129 views

### A sufficient number of distances to recover relative positions of n points

On several places I found different claims on a sufficient number of distances to recover relative positions of $n$ points in $d$-dimensional space. For instance, work from http://www.dimitris-...
1answer
1k views

### Application of an orthogonal matrix to a 3D configuration of point

Suppose a 3D configuration of points is given, $X\in\mathbb{R}^{n\times 3}$, and a matrix $Q\in\mathbb{3\times 2}$, with orthonormal columns. Now, suppose a mapping to 2D is obtained as $$Y=XQ.$$ ...
2answers
250 views

### Algorithm to compute the intersection of meshlines with a boundary

I need a program or an algorithm that computes the intersection of a mesh and a boundary. The mesh is structured orthogonal in nature and the boundary is a circle (for example). This will be used ...
3answers
296 views

### How to fill a 2D set over a cartesian lattice with as few rectangles as possible?

Suppose I have a black and white image (composed of binary pixel values in a 2D cartesian array) that contains an irregular, nonconvex shape. Let's further suppose that the shape is one connected ...
3answers
698 views

### Surface Mesh Library

I'm thinking a bit about the Front Tracking method used for simulation of Two phase flow with sharp interfaces. The literature tells me that the main issue is the surface mesh representation (...
1answer
429 views

### Testing a simple polygon for monotonicity in linear time question

I'm looking for the algorithm of Preparata and Supowit for testing a simple polygon for monotonicity in linear time. I've found it referenced in many textbooks but I can't find the algorithm itself. ...
2answers
1k views

### Looking for a library or algorithms to perfom clipping 3D unstructured meshes by a set of surfaces

We have a 3D (volume) unstructured, possibly hybrid, degenerative irregular mesh data structure that we are capable of generating (mostly composed of hexahedra and general polyhedra, using a mix of ...