# 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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### 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 ...
148 views

### 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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1 vote
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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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1 vote
108 views

### 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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1 vote
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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 ...
49 views

### 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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1 vote
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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 ...
60 views

### 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-...
38 views

### 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 ...
29 views

### 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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1 vote
288 views

### 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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### Adding stability to MPM simulation?

I am writing a 2D implementation of MLS-MPM, I have fluids working perfetly fine, solids technically work as well, at low time steps. This is the fluid simulation at a large time step: https://i.stack....
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### Selecting most points from a set of points with distance constraint

I am looking for an algorithm to select the largest subset of $M$ points from a set of $N$ points ($M < N$) such that no point is within a certain minimal distance d to any other point in $M$? I ...
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1 vote
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### How to find fundamental matrix based on other fundamental matrix and camera movement?

I am trying to speed up some multi-camera system that relies on calculation of fundamental matrices between each camera pair. Please notice the following is pseudocode. ...
• 121
780 views

### How to find the smallest ellipse covering a given fraction of a set of points?

I have a set of points $P$ and want to find the ellipse with the smallest area that covers at least a fraction $f$ of these points. How can I do this? These questions ask the same thing, but folks ...
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46 views

### Find tuples of points from multiple sets

Given n sets of points in general position in dimension 2 (n typically small, 2-6), can one find tuples of points, one from each of the sets, which are close in some sense (the closest, mutual ...
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### How do I find the minimum-area ellipse that encloses a set of points?

I have a set of points that resembles more of an ellipse than a circle. I implemented the optimization formulation below and the solution gives a circle. I tried with various initial values, still to ...
172 views

### The implicit form of a NURBS curve

I am trying to evaluate and analyse a NURBS curve to generate a mechanism. I understand that the general form of a NURBS curve is commonly written as a parametric equation in the form of $f_{par}(t)$. ...
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### 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 ...
141 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 ...
78 views

### Dividing a continuous domain into small squares; how to perform storage and querying?

I recently had a software engineering interview and was asked a series of questions that was a bit outside of knowledge realm, and I feel like there's some scientific computing principles here (I took ...
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### Extracting a mid-plane for thick shell analysis

I have a complex part that contains features of the form shown in the figure below. Because of the cost of 3D finite element simulation of the part, I want to try an analysis with 2D thick shells. ...
141 views

### Getting euclidean distance between vector A and C without anyway of retrieving them when their distances with a common vector B is known

Motivation: My plan is to get the overall euclidean distance matrix for all the vectors in N number of dataset. Each dataset is basically an array of n-dimensional points. For e.g: A dataset can be ...
1 vote
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### How to determine the orientation of convex/concave hexahedra?

I am writing a code that checks the orientation of a list of vertices (along with face connectivity) describing both convex and concave hexahedra. The face connectivity table stores the list of vertex ...
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### Algorithm to convert STL files to STEP files

My goal is to learn the algorithms that allow to convert STL files to STEP files. I am struggling to find learning materials. Can you suggest here research papers, books, open source code about this ...
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1 vote
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### Dyadic operations, fourth order tensors and Tensor algebra

I am trying to understand the dyadic operation for a while since I am interested in Elasticity problems. I believe an intuitive understanding (rather than assuming) will give me good problem solving ...
79 views

### How to distinguish primary hosts (stars) and orbiting satellites (planets) and tertiary bodies (moons) by their mass and trajectory?

I posted this question in the astronomy stackexchange. There are no responses, and it was suggested that I pose the question here. The "too long, didn't read" was taken from a comment, and ...
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783 views

### Jacobian Matrix of 2D element mapped to 3D

Note: I previously posted this question to MathStackExchange, but got no attention there. So I'm rewritting and trying over here. Problem summary Given a common¹ set of shape functions defined at ...
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### Parametric surface in 3D

I want to create a mesh for a 3D surface with coordinates defined by a parametric function. Is it possible to define this mesh using Gmsh? If it is not possible, what free software do you recommend me?...
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