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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The closed form solution of a point on a plane

Given a plane in 3D Euclidean space is $\pi$: $ax+by+cz+d=0$ and a point $P$:$(X,Y,Z)\in \mathbb{R}^3$. Find a point $Q:(X^*,Y^*,Z^*)\in \pi$ such that: $$Q= ...
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39 views

Geographic distance between two regions

I am currently trying to calculate the geographic distance between two regions as I want to correlate it with their similarity of another aspect (e.g., similarity in word usage). Currently, I have ...
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24 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 ...
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1answer
62 views

Inclined plate capacitor grid/ mesh

You can calculate the electric potential over every point in a defined space by solving Laplace's equation. To do this in a computer program you set up an 2-d array/ matrix and loop the internal ...
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Environment for implementing/testing Computer Graphics algorithms [closed]

I need to code up a computer graphics algorithm for Surface Registration. Briefly surface registration is the process of finding "optimal" one-one correspondence between surfaces, where the meaning ...
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1answer
291 views

Minimal surface solution in Python

Note: this question was also posted in StackOverflow and math.stackexchange. I have a set of 3D points defining a 3D contour, as shown below. The points in this contour lie in their best-fit plane ...
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0answers
153 views

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 ...
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2answers
207 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 ...
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2answers
88 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 ...
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239 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 $$Y=XQ.$$ ...
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2answers
202 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 ...
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3answers
221 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 ...
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378 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 ...
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1answer
225 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. ...
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458 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 ...