Questions tagged [computational-geometry]
The study of efficient algorithms and data structures to solve various problems involving point sets, line segments, polygons, polyhedra, simplices, etc.
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(Isoparametric) Mapping of physical coordinates to their equivalent parametric coordinates on a reference element
I have some experiece with finite element methods (FEM), in general. However, I mainly worked with Cartesian grids -- i.e. using orthogonal (non-curved) elements.
Recently, I became interested in a ...
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Efficiently detect overlaying ellipses in distorted images
I'm currently facing the problem of efficiently detecting (special) ellipses in edge images. These images are given (i.e. previous image processing is impossible) and contain quite some noise. I need ...
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Population of the coefficient matrix of a linear system Ax=b stemming from the finite differences of an arbitrary geometry
I've been looking into solving a linear system $$Ax=b$$ where $A\in\mathbb{R}$ is the sparse coefficient matrix of size $K\times K$, $b\in\mathbb{R}$ is the right-hand side (i.e., the source term) of ...
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Find a set of positions of a rectangle of fixed size, which would "cover" a curve on a plane
I have a curve on a plane, and a rectangle with one side much longer than the other (let's say it is a "thick segment). I need to find a set of positions of the rectangle which would include all ...
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Cover a 3D surface with 2D rectangles of fixed size, allowing overlap
I have a 3D surface, defined as collection of points in a 3D evenly spaced mesh. I have a rectangle of fixed size (height x width), and I need to find a collection of rectangles positions in the 3D ...
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Need help with the python code: Calculating Madelung constant CsCl crystal structure
Need help with the code to estimate the Madelung constant for CsCl lattice:
Cs at (0,0,0)
Cl at (0.5, 0.5, 0.5)
Answer: Converged value I am getting is 0.465. ...
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Role of rotation's pivot point in optimization?
In this paper, the authors describe how to use locally rigid transformations (sampled on nodes in space) to deform mesh vertices. In the paper, rotations are relative to the pivot point, which ...
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Order in a subset
Lets consider a range of "K" binary digit numbers. In that range, we want to take a subset of those values which have (<="n" consecutive 0s) AND (<="n" consecutive ...
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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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Optimization: Find minimizer along linestring
Given some function f(x) and a set of points A representing a linestring (or polygonal chain), I am searching for the point on ...
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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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Equilibrium position finding with DSM
I've coded a framework that can be used to simulate the dynamic behavior of a system discretized by particles (nodes) that are connected by spring-damper elements. However, I want to compare it to a ...
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Parallel Block-Structured class abstraction for FDM
I’m currently developing a FDM/FVM (using contravariant coordinates) code using Fortran and Co-Arrays (SIMD, in general), and so far I have all sparse matrix (BiCGStab, working on AMG) solvers and ...
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