All Questions
334 questions
-1
votes
1
answer
68
views
Convergence of FEM on curved boundaries, and inhomogenous boundary data
In a smooth domain in $\mathbb{R}^{2}$ or $\mathbb{R}^{3}$ let's consider $-\Delta u = f$ with $u=g$ on a part of the boundary and $\partial_\nu u = w$ on another part of the boundary, which is far ...
- 259
1
vote
0
answers
171
views
From 3D to 2D with a STL file
I would like to do a 2D projection from a 3D geometry saved in a stl file and know the distance between the two projected planes. In order to explain better the concept I will start with an almost ...
- 109
2
votes
0
answers
92
views
How to accelerate the computing of implicit finite difference method for heat conduction between two solids
Edit on May 3rd: I have found the problem. Because the difference of between $k_1$ and $k_2$ is huge, a very small time step need to be chosen so that the right green part can "feel" the ...
- 21
2
votes
0
answers
89
views
Geodesic approximation algorithms for minimal geodesic curvature
Introduction
I am building an application in which, given a surface and a pair of points on it, an analytic expression of some geodesic arc between them is needed, preferably the one with the shortest ...
- 121
3
votes
0
answers
70
views
Change in Variables applied to biharmonic equation
Background
I want to solve the following biharmonic equation:
$$\frac{ \partial^4 s }{ {\partial \xi}^4 }+\frac{ \partial^4 s }{ {\partial \xi}^2{\partial t}^2 }+\frac{ \partial^4 s }{ {\partial t}^4 }...
- 31
2
votes
2
answers
172
views
How to find fundamental matrix based on other fundamental matrix and camera movement?
I am trying to speed up some multi-camera system that relies on calculation of fundamental matrices between each camera pair.
Please notice the following is pseudocode. ...
- 121
2
votes
0
answers
294
views
Rosenthal equation for multi track
Rosenthal's equation lets one calculate the temperature profile of a moving point heat source analytically for thin and thick plates. For simplicity I use the equation for thick plates defined as:
$$T-...
- 840
9
votes
1
answer
893
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 ...
- 4,021
0
votes
0
answers
50
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 ...
- 101
14
votes
2
answers
4k
views
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 ...
- 143
1
vote
1
answer
2k
views
How to solve heat equation in spherical coordinates with finite differences?
I have a problem dealing with heat transfer which is spherically symmetrical. I was thinking it should be possible to solve this as a 1d problem in spherical coordinates using the radius only.
...
- 111
3
votes
0
answers
206
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 $f_{par}(t)$.
...
- 31
4
votes
2
answers
402
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
...
- 65
-1
votes
2
answers
154
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 ...
- 3
2
votes
1
answer
85
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 ...
- 143
2
votes
0
answers
76
views
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.
...
0
votes
0
answers
145
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 ...
- 11
1
vote
0
answers
87
views
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 ...
- 233
0
votes
1
answer
438
views
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 ...
- 103
1
vote
2
answers
1k
views
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 ...
0
votes
0
answers
80
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 ...
- 11
3
votes
0
answers
924
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 ...
- 39
0
votes
1
answer
210
views
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?...
- 527
4
votes
1
answer
139
views
Solving geodesics on triangular meshes gives negative distances
I have implemented the heat method for geodesics:
https://www.cs.cmu.edu/~kmcrane/Projects/HeatMethod/paperCACM.pdf
When I run it I am getting a solution that, visually, seems correct:
In this image, ...
- 379
3
votes
0
answers
109
views
Why is bounding a surface with a capsule is better than with a cylinder to detect intersections?
In this article:
https://www.geometrictools.com/Documentation/IntersectionOfCylinders.pdf
the writer says: "If you plan on using cylinders
for bounding volumes in a real-time graphics engine—...
- 81
0
votes
1
answer
214
views
Incorporating heat flux into Laplace Equation
I need to find the temperature distribution of a square plate using the Laplace equation by using FDM:
$$ \frac{d^2T}{dx^2} + \frac{d^2T}{dy^2} = 0$$
But there is a heat flux entering from the top ...
- 145
1
vote
1
answer
181
views
Calculate the arc length of a Steinmetz curve numerically
I'd like to know the length made by the intersection curve of two orthogonal cylinders of different radii a and b where a > b >0.
I came across this post that provides a solution with an ...
3
votes
1
answer
111
views
Good rectangular covering of an SDF
I have a 2D SDF describing my shape, but it's fine to think of it as a black/white image (black="inside" white="outside").
I want to generate a small set of rectangles (say, 8 of ...
- 131
2
votes
2
answers
468
views
Two-dimensional heat equation with Neumann boundary conditions: any hope to find an analytical solution?
I am looking for references showing how to analytically solve the heat equation with Neumann boundary conditions in two dimensions.
So far, I have found the problem solved analytically in one ...
- 61
5
votes
1
answer
2k
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:...
- 155
1
vote
0
answers
60
views
Largest triangle that contains a point
Given the location of $n$ points on a 2D plane ($P_1, P_2, \ldots, P_n$); and the location of a special point $X$.
Find three points $P_i,P_j,P_k$ ($i \neq j \neq k$) such that point $X$ is inside the ...
0
votes
0
answers
63
views
Storing and retrieving two-dimensional and three-dimensional data
I work on computational geometry.
A huge number of two-dimensional and three-dimensional data are found in my project. Coordinates of polygon and polyhedrons vertices consisted of two-dimensional and ...
- 11
0
votes
3
answers
156
views
Problem of half-planes intersection
Consider the half-planes $\{x \leqslant 2\}$ and $\{x+y \leqslant 3\}$. These two half-planes are coded with the R package 'rcdd' as follows:
...
- 283
5
votes
3
answers
2k
views
How to determine if 2 rays intersect?
We are given the 2D coordinates of 2 points: the first point is where the ray starts and it goes through the second point. We are given another ray in the same way. How do we determine if they have a ...
- 151
0
votes
0
answers
29
views
Minimal covering of rectangle with fixed, overlapping rectangles
A finite set $R$ of fixed, axis aligned 2-D rectangles $r_i=\left\{x_{0i},y_{0i},W_i,H_i \right\}$ is given. These rectangles are potentially overlapping. Given a new axis aligned rectangle $t$, I ...
- 301
2
votes
2
answers
219
views
Heat equation in non-dimensional form behaving differently than in usual format
Starting from
$$
c_p \frac{\partial u }{\partial t} = k \nabla^2 u
$$
in a one dimensional domain [0,1] where $c_p$ and $k$ are modeling two different materials:
$$
k =
\begin{cases}
1 ~\text{if} ~x &...
- 601
0
votes
0
answers
56
views
Hi I am trying to model a 2D Lug angle using Gmsh 4.6. How can I combine transfinite quad and regular full quad meshes in the following geo file?
I need transfinite mesh a small section of the bolt hole to insert a crack. However, The transfinite mesh and regular full quad mesh seem being incompatible and throwing errors. How can I combine ...
1
vote
2
answers
811
views
How to use the Thomas-Algorithm to the Heat-diffusion-equation correctly
My post is structured in four parts:
I give you some information about the context my principal questions refer to.
I will tell you what I believe to know about the Thomas Algorithm. If I am wrong ...
- 11
0
votes
0
answers
226
views
Producing Voronoi diagram in three dimensional
A Voronoi diagram is a kind of tesselation that divided the medium into polygons in 2D and polyhedrons in 3D.
Although there are many algorithms to construct a Voronoi diagram, some of them are faster ...
- 11
1
vote
0
answers
278
views
Fortune algorithm for voronoi diagram
Although there are many algorithms to construct Voronoi diagram, some of them are faster than others. Based on my knowledge Fortune algorithm is fastest for construct Voronoi diagram either in two ...
- 11
3
votes
3
answers
739
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 ...
- 131
2
votes
3
answers
373
views
For traditional FEM and FVM, why can't we use mesh to represent geometry and use the mesh which represent the geometry to do the computation directly?
Isogeometric analysis [1] has the advantage of integrating geometric and mesh models using NURBS or Spline. At the same time, I would like to ask a question to my friends: for traditional FEM and FVM, ...
- 115
5
votes
4
answers
370
views
Can the mesh generation methods in FVM and FEM be totally based on the knowledge of the mesh generation theory in computer graphics?
The main references of mesh generation methods in computer graphics (CG) I found are discrete Differential Geometry [1] and a famous book "Polygon Mesh Processing" [2], while the "...
- 115
2
votes
3
answers
553
views
Flux sign and face normal confusion in finite volume method
I implemented a solver for the 2D steady-state heat equation (without heat generation and homogeneous material) $\nabla. (k\nabla T) = 0$, using finite volume method, however, I am having some ...
- 304
3
votes
1
answer
224
views
Project to nearest point on convex polytope
I have a point $y \in \mathbb{R}^d$ and a convex polytope $\mathcal{P}$ given as the intersection of half-spaces:
$$\mathcal{P} = \{x \in \mathbb{R}^d \mid a_1 \cdot x \le b_1, \dots, a_n \cdot x \le ...
- 477
0
votes
0
answers
250
views
Surface mesh from labeled 3D points
I'm trying to figure out how to create a surface mesh from a set of labeled 3D points. The 3D object could be something like part of a cave system or asteroid where there would be parts of the surface ...
7
votes
0
answers
302
views
Finding points inside cells of power (generalized Voronoi) diagram
Suppose we have a set of points $p_1,\ldots,p_n\in\mathbb R^d$ as well as a set of weights $w_1,\ldots,w_n\in\mathbb R$. Recall that the power cell associated to the pair $(p_k,w_k)$ is given by:
$$\...
- 1,433
0
votes
2
answers
151
views
How to minimize $(x-a)^2+(y-b)^2$ subject to $ \sqrt{a}+\sqrt{b}=\sqrt{2}$?
I am not sure if this is on-topic here, but I am trying.
Let $x,y$ be positive real numbers. I am trying to find
$$ \min_{\sqrt{a}+\sqrt{b}=\sqrt{2}}(x-a)^2+(y-b)^2$$
I tried using Mathematica for ...
- 119
0
votes
1
answer
110
views
Applying weak form
I have two dimensional equation and I want to solve it using Finite Element Methods.
$$ \nabla . (\alpha(x,y)\nabla u(x,y)) + \dfrac{\partial u(x,y)}{\partial x}+\dfrac{\partial u(x,y)}{\partial y}+u(...
5
votes
0
answers
84
views
Why does the naive barycentric hodgestar fail?
The discrete exterior calculus is defined first using circumcentric dual cells, because the primal and dual edges are orthogonal and thus the dual cells are convex. This leads to a diagonal hodge star ...
- 617