# 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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### Approximating the boundary between two sets of points (in 2D): Fitting a region

Given two sets of points $p_{\text{in},i}$ and $p_{\text{out},j}$ inside and outside of what I intuitively call a "region", I would like to estimate and describe the boundary of this region. ...
151 views

### Computation of the tensor of curvature on surface mesh

Is there a formula which enables the computation the tensor of curvature knowing the following at each vertex and cell of a triangulated mesh: Normal vector Two arbitrary vectors in the tangent space ...
97 views

### Metric Space for Direction Cosine Matrix?

I work in the medical field. Sometime we receives MR images that have been acquired along the same direction, however when looking up the direction cosine matrix, the values are slightly different (up ...
60 views

### Calculating versors of a plane from the normal versor

I'm trying to calculate the 2 perpendicular versors (unit vectors), $\vec{n_1}$ and $\vec{n_2}$, that define a plane whose normal versor (unit vector) is $\vec{n_n}$. For example, assuming that the ...
109 views

### Algorithm to merge two polygons (using connectivities)?

I am struggling with implementing an algorithm that does one simple thing: Consider two polygons (one can just draw any two polygons and number their vertices), whose connectivities in a node list are:...
75 views

### Is there a source/cookbook of equations that approximate geometric shapes?

I'm numerically modelling flows around various geometric 2D shapes. Is there a good source/cookbook of equations that approximate these? Some examples are Rectangle: $(x-a)^n+(y-b)^n < r^n$ where ...
1k views

### Generate random smooth 2D closed curves

I would like to know how can I generate a collection of random 2D closed smooth curves. I thought about generating a random 3D surface with random peaks, and then intersecting the Z=0 plane with it, ...
262 views

### What are some algorithms to calculate the width of an arbitrary polygon when a bounding box approximation is inaccurate

What are some alternative algorithms to creating a bounding box for finding the max width of a concave, simple winding polygon, like the one in the below image? I prefer solutions that are more ...
273 views

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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 ...
485 views

### How can I find a line segment with the most intersections along with the coordinates of the intersection points?

There are $n$ points in a 2-D plane and each is given by its $x$ and $y$ coordinates. They are stored in an array in an ascending order with respect to $x$. All points are connected together by line ...
314 views

### Does some form of documentation of GMSH exist?

I am looking to implement GMSh into a simualtor that I am going to create. I am looking to integrate the geo, mesh, and post processor modules. However, looking online, it appears the documentation ...
387 views