# 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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### Finding points inside cells of power (generalized Voronoi) diagram

Suppose we have a set of points $p_1,\ldots,p_n\in\mathbb R^d$ as well as a set of weights $w_1,\ldots,w_n\in\mathbb R$. Recall that the power cell associated to the pair $(p_k,w_k)$ is given by: \...
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### Calculating depth mask from different lighting

I have a object which is static, the camera is static and light source is moving. How can the depth mask be calculated ? Concept is to use - calculate height from shadow length Lets imagine a have ...
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### Algorithm to determine if two polygons intersect

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 ...
69 views

### Simultaneous update to barycenters

Suppose a tiling is given in 2D (an embedding of a planar triangulated graph), with all faces convex. Now suppose one moves each point, one by one, to the barycenter of its neighbors. I think that ...
58 views

### Geometric interpretation of lemma

I am currently studying eigenvalue problems. I already worked through the Minimax-principles, seen why $\lambda_{h, m} \geq \lambda_m$, when comparing the eigenvalues of a discretization and the ...
27 views

### Simplification of vertices and dihedral angle relations of a polygonal chain

I am trying to understand the generation of Cartesian coordinates of polygonal system or poly line with fixed bond angles and fixed link lengths. I assumed the bond angle to be the same and link ...
48 views

### Space covering optimization

I have the following problem: In the space $E=\{1, 2, \dots, N_x\} \times \{1, 2, \dots, N_y\}$, I want to define $N_R$ rectangles $R_k=\{x_k^0, \dots, x_k^1\}\times\{y_k^0, \dots, y_k^1\}$ which ...
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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 ...
36 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 ...
93 views

### Principal Components Analysis Not Behaving as I Expect it to

I have a bunch of points in $\mathbb{R}^3$ that I would like to translate and rotate so that their center is at the origin and the variance along the $x$ and $y$ axes are maximal (greedy, and in that ...
180 views

### Is it possible to generalize the two view Sampson error to multiple view cases in computer vision?

In multiple view geometry of computer vision, there is a geometric error called Sampson error which is very useful in the nonlinear estimation of fundamental matrix....
I find myself having difficulties to get a concrete coordinate representation of the contangent lift of the configuration space of a mechnanical system. Setupwise, we have a vector field $X \in TQ$ ...