# Questions tagged [geometry]

Geometry is a branch of mathematics. Geometry studies the spatial relationships and forms of objects, as well as other relationships and forms, similar to the spatial in its structure.

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• 1,423
1 vote
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### 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 ...
• 119
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### 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 ...
• 2,089
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### Linear algebraic research direction that's not to do with differential equations and physics?

So I've found some interesting linear algebraic research areas that's both pure-ish, with a numerical bent to it, too -- e.g. inverse eigenvalue problems have both interesting theoretical and ...
• 101
72 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 ...
• 139
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### 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 ...
589 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 ...
• 101
109 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 ...
• 203
1k views

### Compute affine transformation between two sets of points

Consider two sets of points $P = (P_1, ...,P_n), \ Q = (Q_1, ..., Q_m)$ included in $\mathbb{R}^3$. I'm looking to compute an optimal affine transformation that "maps" $Q$ to $P$, although the sets ...
• 103
73 views

### Simultaneous update to barycenters

Suppose a tiling is given in 2D (an embedding of a planar triangulated graph), with all faces convex. Now suppose one moves each point, one by one, to the barycenter of its neighbors. I think that ...
• 41
1 vote
55 views

### Space covering optimization

I have the following problem: In the space $E=\{1, 2, \dots, N_x\} \times \{1, 2, \dots, N_y\}$, I want to define $N_R$ rectangles $R_k=\{x_k^0, \dots, x_k^1\}\times\{y_k^0, \dots, y_k^1\}$ which ...
585 views

### Expanding Winding Number algorithm to arcs

I have a problem that I have been attempting to solve for a few days now. I was wondering if I would be able to get some assistance from the community. In order to detect if a point is in a polygon, ...
• 499
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### Vector characterization of cylinder displacements in a box

We have a cylinder of length $l$ (in units of its radius $d,$ as basic unit of length set to $d=1.$) in a box, and we consider an orthonormal Cartesian coordinate system with its origin placed at the ...
• 179
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### Is it valid to assume the center of a bounding sphere to be also the center of the bounding box?

Computing an axis aligned bounding box of a point set is trivial. Computing a bounding sphere of a point set is also trivial when the center is known. Computing the center of the bounding sphere is ...
• 1,463
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### Rotate a vector by a randomly oriented angle

We start off with a unit vector $\mathbf{v}$ randomly oriented in 3D space and we want to generate another unit vector $\mathbf{w}$ so that $$\mathbf{w}\cdot \mathbf{v} = \cos \beta$$ where $\beta$...
1k views

### Commonly-used metrics to quantify the irregularity of a triangular mesh

Say you have a triangular mesh on a flat plane. This has been drawn to eventually solve some problem in mechanics, for example. A mesh of equilateral triangles is the best inasmuch as the distances ...
• 246
1 vote
398 views

• 383
1 vote
81 views

### Distirbution of Points along a Line

I am facing the following problem: Given is a line of length $L$ which I want to split into $N$ segments. The lengths of the first $(s_1)$ and last segment $(s_N)$ are given. You can assume that the ...
• 301
1 vote
264 views

### Gaussian geometry optimisation: molecule is getting dissociated into sub group?

I was trying to optimise CdSe (Cysteine) molecule using a semi-empirical method in Gaussian 09 (and gaussView) for a preliminary study of quantum dots. But it seems as the number of iterations ...
2k views

### Fitting Implicit Surfaces to Oriented Point Sets

I have a question regarding quadric fit to a set of points and corresponding normals (or equivalently, tangents). Fitting quadric surfaces to point data is well explored. Some works are as follows: ...
• 2,249
113 views

I don't think this is a pure math problem, so I post it here. Assume we have two regions in $\mathbb R^n$: $$\lbrace x : a \leq x \leq b \rbrace\\$$ and $$\left\lbrace x : \sum_{i=1}^n |x_i | \... • 189 7 votes 4 answers 692 views ### How can I find a line segment with the most intersections along with the coordinates of the intersection points? There are n points in a 2-D plane and each is given by its x and y coordinates. They are stored in an array in an ascending order with respect to x. All points are connected together by line ... 7 votes 1 answer 325 views ### Does some form of documentation of GMSH exist? I am looking to implement GMSh into a simualtor that I am going to create. I am looking to integrate the geo, mesh, and post processor modules. However, looking online, it appears the documentation ... • 499 2 votes 5 answers 470 views ### Fast comparison of line segments lengths I have two line segments given by their endpoints (a_1,a_2), (b_1,b_2) in R^3 and want to know if they have the same length (up to some error), so that the naive test looks like$$|\, \Vert a_1-...
• 133
I have a 2D triangle which deforms with each vertex moving by some small ($\sin(x) \approx \tan(x) \approx x$) displacement vector. The displacement of any point in the triangle is linearly ...