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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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—...
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1answer
72 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
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1answer
65 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 ...
4
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1answer
52 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:...
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0answers
28 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 ...
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0answers
39 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 ...
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2answers
71 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:
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3answers
150 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 ...
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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 ...
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27 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 ...
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35 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 ...
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81 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 ...
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3answers
142 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 ...
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3answers
183 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, ...
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4answers
170 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 "...
2
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1answer
77 views
Project to nearest point on convex polyhedron
I have a point $y \in \mathbb{R}^d$ and a convex polyhedron $\mathcal{P}$ given as the intersection of half-spaces:
$$\mathcal{P} = \{x \in \mathbb{R}^d \mid a_1 \cdot x \le b_1, \dots, a_n \cdot x \...
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47 views
Surface mesh from labeled 3D points
I'm trying to figure out how to create a surface mesh from a set of labeled 3D points. The 3D object could be something like part of a cave system or asteroid where there would be parts of the surface ...
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262 views
Finding points inside cells of power (generalized Voronoi) diagram
Suppose we have a set of points $p_1,\ldots,p_n\in\mathbb R^d$ as well as a set of weights $w_1,\ldots,w_n\in\mathbb R$. Recall that the power cell associated to the pair $(p_k,w_k)$ is given by:
$$\...
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2answers
94 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 ...
0
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1answer
93 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(...
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0answers
59 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 ...
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1answer
428 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 ...
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1answer
85 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 ...
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1answer
73 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.
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1answer
50 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, ...
2
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2answers
718 views
How to determine the Jacobian Ratio for triangle element?
I am trying to implement an algorithm to find the Jacobian ratio for each triangle in mesh as a part of mesh quality check.
Let's say that I have vertices of the triangle: $P_1(x_1, y_1, z_1)$, $P_2(...
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0answers
27 views
Simplification of vertices and dihedral angle relations of a polygonal chain
I am trying to understand the generation of Cartesian coordinates of polygonal system or poly line with fixed bond angles and fixed link lengths. I assumed the bond angle to be the same and link ...
3
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2answers
86 views
Packing spheres inside a geometry
I am looking for packing spheres (can be monodisperse or polydisperse with known radii distribtuions) inside a geometry. I am sure this is a well explored scientific problem with applications in ...
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2answers
102 views
Is the similar subdivision of a delaunay mesh still delaunay?
I have a delaunay triangulation for a 2d box with say an airfoil inside. If I uniformly refine this mesh by subdividing each triangle in the mesh into 4 triangles by halving each edge, is the ...
2
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1answer
84 views
How to divide points on a 3D complex surface into two regions based on a closed curve defined on this surface?
My problem seems simple but I can't find an algorithm that will do that for me for any 3D complex surface.
I have a really complex shape 3D surface and a closed curve on it defined by some points (...
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1answer
39 views
Produce vertex displacements from volumetric shrinkage data on unstructured meshes
I was wondering what would be an efficient way to produce compatible displacements for mesh nodes/vertices if the computed data is volume shrinkage of each element/cell in the unstructured mesh?
...
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0answers
71 views
How to approach geographic data interpolation by distance?
let's say I have a set of geographic locations (lat, lng) resulting from a query. Those locations have some kind of internal ranking, my set is sorted by this number in a descending order.
Now I'm ...
0
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1answer
43 views
How to find the nearest point inside a list in a given direction
Being $\bar{\mathbf{x}} \in \mathbb{R}^3$ a point and $S =\{\mathbf{x}\}_{i=1}^N \in \mathbb{R}^3$ a sample of N points. I am looking for a simple algorithm to determine the nearest point in $S$ in ...
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1answer
140 views
Maximum and Minimum distance from query point within bounding box
I'm reading an article regarding approximating sums using KD-trees (similar to FMM).
As part of the effort I'm trying to make sense of this article , which is cited.
I'm having trouble understanding ...
3
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2answers
123 views
Find shortest path around a cylinder represented by 3d triangular mesh
Suppose I have a 3d triangular mesh with the topology of a finite cylinder. Let $C$ be a vertex on that mesh.
How can I find the shortest path from $C$ to itself that goes around the cylinder? By ...
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0answers
73 views
Derivatives over a Finite Element mesh
I have a data extracted from Comsol on some node points and I know the coordinates of each node.
Does anyone know how Comsol calculate the partial derivative from the values at each node and also ...
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0answers
66 views
Dividing Point Cloud into voxels
I am reading a paper on implementing convolution neural network for a 3D point cloud. In this paper, they are dividing the point cloud into voxels. Is there any easy way to do it using point cloud ...
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0answers
30 views
Check if two points are symmetrics/asymmetrics
I am working on an Android app which lets a group of children draw whatever they want in a specific area. I need to check if the lines and figure that they draw are symmetric. The problem is that ...
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0answers
67 views
Efficient algorithm to determine the intersection volume of simple convex polyhedra
TLDR: Is there an efficient algorithm to compute the intersection of polyhedra with 8 or fewer vertices?
I have two sets of FEM meshes for one geometry (one exhibiting a skin effect). I have to ...
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0answers
38 views
Algorithm to join hexahedra and obtain outline volume
I would like to join several hexahedra and obtain an outline volume.
First, I started with 2D implementation. In 2D, there are non-intersecting quadrangles which always touch each other as shown in ...
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0answers
96 views
How to read data from simply formatted text file (c++)?
Mesh information like points, faces and cells is to be stored into separate files:
e.g. for points file:
# points data: x y z
N_Points 100
x1 y1 z1
x2 y2 z2
...
cell file:
# cells data: ...
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18answers
9k views
Good examples of “two is easy, three is hard” in computational sciences
I recently encountered a formulation of the meta-phenomenon: "two is easy, three is hard" (phrased this way by Federico Poloni), which can be described, as follows:
When a certain problem is ...
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1answer
119 views
How can one prove the duality of Voronoi and Delaunay?
Hoping I'm not misunderstanding the concept here, but it is my understanding that Voronoi Diagrams and Delaunay Tesselations are 'dual' to one another, owing to the fact that each' solution makes ...
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0answers
52 views
Calculating depth mask from different lighting
I have a object which is static, the camera is static and light source is moving. How can the depth mask be calculated ?
Concept is to use - calculate height from shadow length
Lets imagine a have ...
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0answers
48 views
Cover a polygon with least amount of parallelograms [closed]
I am solving the task that is as follows:
Input: a polygon. Can be any kind of polygon without self intersections. Can be a non-convex and with holes inside.
Goal: to cover it with 2 (at least) or ...
7
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1answer
527 views
How to calculate the geodesic curvature of a discrete 3D curve?
I have coordinates of a set of points that form a closed loop that lies in a 3D surface. I know the equation of the surface and I can calculate it's surface normal at any point. I found that for a ...
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2answers
144 views
Ordering points from X Y coordinates
I have series of points extracted from a regular grid, with their X/Y coordinates. A previous algorithm (that I cannot modified!) output a list of these coordinates, but the ordering of these point is ...
2
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2answers
84 views
projective reconstruction from orthogonal views
This is a problem from projective geometry. Suppose I have a vector $z \in R^k$ of unit length $\| z \| =1$ inside a $k$-dimensional hypercube. I don't know its value but do know its projection upto ...
3
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1answer
74 views
Smoothness regularisation of a 2D field on a triangular mesh?
I'm working on an inverse problem where the solution is the values of a 2D scalar field at the vertices of a 2D triangular mesh, such that the field can be defined continuously inside the mesh via ...
2
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1answer
659 views
A robust algorithm to sort a non-convex polygon vertices
Let v_{0},...,v_{N-1} be N points in a Cartesian xy plane defining the vertices of closed polygon (i.e. v_{N} = v_{0}).
Let P_{0}...
