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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How to correctly discretize volume elements in different geometries?
I am solving a reaction-diffusion problem in one dimension for a catalyst particle to get the internal effectiveness factor ($\eta$),as given below:
$$ \eta = \frac{\int_0^{V_p}{R_i\ dV}}{R_i^{surf}\...
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What exactly is a "unit-torus"?
I've seen references to the "unit torus" in papers such as this (Start of Sec 3.3, page 5). So, what exactly is a unit torus? Is it just a square or cube in d-dimensions with periodic ...
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How do you build a polyharmonic discrete system?
Polyharmonic equations, to my understanding, are defined as:
$$\Delta ^k u = 0$$
i.e. one repeatedly applies the laplace operator to the function a certain number of times and the result must be 0.
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Computing discrete laplacian matrix for mesh fairing
I asked this question on the math stack exchange and got an answer, but I am just as utterly confused as before. My fundamental goal is to actually construct the matrix, that is, a series of steps I ...
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Constructing generalized Laplacian matrix?
I am staring intently at this paper by Botsch and Kobbelt.
In particular, I want to make the matrix specified in equation 5. I am trying to understand the specific computations I must instruct a ...
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How to find the formula of a projected circle in a pencil of conics structure?
Hi this is my first question on the platform so feel free to comment if I have a mistake regarding the question.
I'm working on an ellipse detection scheme in which I have markers consisted of 3 ...
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Algorithm for 1-dimensional minimal surfaces
Consider a set of points. For simplicity, let's say that those are 2D points (although the problem works in higher dimensions as well). The goal is to find the minimum possible length of a connected 1-...
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Partial derivatives for triangular meshes (in 3D)
A grid offers an obvious definition for the partial derivatives at a grid point, given
$x$ the value of a point $p$ in an $n$ dimensional grid, the forward partial derivative that point for coordinate ...
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Finding maximums in mesh of graph?
I have a triangle mesh which is an approximation of a smooth graph. i.e. a scalar function of $xy$.
I am interested in finding extrema. One naive way I did it was to look at some number of points ...
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Suggestions for libraries that can numerically compute geodesics from a given Riemannian metric?
I am dealing with a non-trivial Riemannian metric $H$ defined on a particular subset of Euclidean space ($E \subset \mathbb{R}^n$). I was able to show the Riemannian manifold $(E,H)$ is geodesically ...
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Computing numerical derivatives
I am trying to create a sweeping surface, for which I need the frenet frame of a curve. I am trying to compute this for arbitrary curves but for testing I am just using the parametric unit half circle....
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Open source implementations of the medial axis transform for vector shapes
Are there any open source implementations of the medial axis transform for vector shapes?
I have searched without finding any useful results. It seems that CGAL library doesn't have it implemented nor ...
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Difference between Numeric, Combinatorial, and Geometric Computing
In the paper [1], author has discussed a distinction between the 3 types of computations: numeric, combinatorial, and geometric. The author says that Geometric computation is one that has elements of ...
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Min supporting line of a set of points
I am following along Rourke's book and I am trying to do the excercies mentioned in this SO post:
Min supporting line for a set of points
Design an algorithm to find a line 𝐿 that:
has all the ...
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Minimum distance from point to surface
I’m looking for code that is well-suited to solving a fairly simple minimization problem:
I have a reference point $\mathbf p$ in 3D space, and I want to minimize $\|\mathbf x - \mathbf p\|^2$ subject ...
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