# 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.

249 questions
Filter by
Sorted by
Tagged with
65 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 $f_{par}(t)$. ...
105 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 ...
59 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 ...
70 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 ...
38 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. ...
122 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 ...
52 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 ...
112 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 ...
162 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 ...
73 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 ...
85 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 ...
55 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?...
112 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, ...
64 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—...
91 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 ...
77 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 ...
92 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:...
36 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 ...
45 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 ...
99 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: ...
272 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 ...
17 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 ...
37 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 ...
48 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 ...
123 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 ...
235 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 ...
209 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  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, ...
204 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  and a famous book "Polygon Mesh Processing" , while the "...
116 views

103 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 ...
98 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(...
61 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 ...
783 views

### Desmos saying there are too many variables [closed]

I wasn't sure if this is a Computational Science SE question or a Stack Overflow question but I think it's more of this one. I wanted to make a graph where I can rotate a hyperbola (not parabola or ...
123 views

### How do I find the portion of a cell/voxel lying within a defined surface?

We have a 3-dimensional grid of voxels (or cells), with individual voxels being of volume $dx\,dy\,dz$ where $dx=dy=dz=1$. A cone-like surface is defined by some function, $z = f(x, y)$, which in ...
114 views

### Detecting degenerate triangles with very thin structures

Between the two ears in the following bunny images, there are some degenerate triangles I want to detect. It looks like a volume-less thin slits. If the question is not clear, please let me know.
58 views

### Systematically outputting sign vectors of restricted hyperplane arrangement

(I previously asked this question on Sage's dedicated Q&A site, but got no response, so I figured it would be worth trying here.) I have a way of constructing hyperplane arrangements in Sage, ...
1k views