The study of computer algorithms which admit geometric descriptions, and geometric problems arising in association with such algorithms. The two major classes of problems are (a) efficient design of algorithms and data classes using geometric concepts and (b) representation and modelling of curves ...
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74 views
Approximating Bezier curves
I would like to approximate one cubic Bezier curve with two quadratic ones. In other words, I would like to split a cubic curve at some parameter t and approximate ...
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0answers
96 views
Maximum diameter of a 2D shape
What is the diameter of an arbitrary 2D figure? (Diameter=The longest distance between two points within the 2D figure). What is the most efficient algorithm? Is it an exact one? Specifically, could ...
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1answer
105 views
distance between a polytope point and a polytope vertex
How to find distance in between any polytope point to the closest vertex of the polytope (the verteces of the polytope are known)?
How to find a distance from the farest polytope point to the closest ...
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46 views
Plot randomly oriented gaussian kernel
I would like to plot with scipy randomly oriented gaussian kernels. For a gaussian kernel along x and y axis (with an angle 0 w.r.t. coordinate system), I simply plot function
...
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0answers
129 views
Algorithm for intersection between polyline and rectangle?
My problem is simple, and probably obvious from the title itself, but I'll still clarify it a bit:
I have a rectangle and a polyline (array of N connected points). I need an optimal algorithm that ...
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1answer
141 views
Given two sets of vectors, how do I find a change of basis that will convert one set to another?
Given two sets of dimension $n$ vectors
$\lbrace v_1 , v_2 , \ldots , v_m \rbrace$, $\lbrace u_1, u_2, \ldots , u_m \rbrace$,
where $m > n$, is there a computational method (in particular, using ...
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1answer
92 views
Analytic Intersection of Objects Located on a 3D Grid's Vertices
I previously posted this question on stackoverflow, but it's really more of a mathematical question. I have reworked the question for presentation here.
I have a regular 3D unit cubic grid of ...
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163 views
distance to Triangle using barycentric coordinates
So, I'm trying to efficiently calculate the distance of a point to a triangle $d(\omega,T)$ using barycentric coordinates via the method described in this paper A Hybrid GPU Rendering Pipeline for ...
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0answers
75 views
Minimize the number of ellipses to cover a region
Suppose I have n ellipses, $\left\lbrace E_i \right\rbrace_{i=1}^n $; each ellipse, $E_i$, has the same area $A_1$. I want to completely cover a region (assume a rectangle) , $R$, with the least ...
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33 views
Approximating a spheroid using spheres
I seek a way to approximate a spheroid using spheres. I guess this is a classic sphere packing problem? I am dealing mostly with prolate spheroids.
I use the definition given here ...
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0answers
28 views
weighted initial ideal versus lex or graded reverse lex initial ideal
$$
$$
By imposing certain weights $\mathbf{w}$ on the variables, say, of a polynomial ring $k[x_1,\ldots, x_n]$, I read that we may obtain the initial ideal $In_{\mathbf{w}}(I)$ of an ideal $I$ with ...
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40 views
using weight vector in M2
Let $R = k[x_1,\ldots, x_n]$ be a polynomial ring and assume $f_i$ and $g_i$ are homogeneous of degree 2, and $h_j$'s are linear forms.
I would like to show that assuming $A = \{f_i + t g_i, h_j\}$ ...
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0answers
102 views
Difference between Marching Cube Algorithm and Iso-Surfaces?
I have always seen the two ideas together so I am not sure what makes them different...
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0answers
51 views
Sufficient conditions for “2-sphericity” of orientable triangulated 2d surface in 3d space
Let $T$ be finite set of tetrahedrons in $\mathbb{R}^3$. Let $T$ be tetrahedral complex in a sense that if two tetrahedrons intersect, the intersection is a face of both. Let $\partial T$ consist of ...
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0answers
87 views
Decomposition of multidimensional point set
I am trying to use point sets to define the subdivisions of a multidimensional space and use a hash table to store the subvisions. This approach requires decomposing the multidimensional space into ...
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0answers
101 views
polygon inside a polygon
i have several point patches lie on different planar faces. then, I obtained enclosing polygons to represent points so that i have several planar polygons (for example A,B,C,D).
when i examine the ...
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1answer
61 views
Convex Hull in Hierarchy Structure
As a beggining to convex hull algorithms lecturer introduced the structure which it's called "Hierarchy Structure".
Hierarchy Structure: in every given convex hull there is a maximum size convex hull ...
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0answers
71 views
Does a single Gauss-Seidel iteration lead to unique coordinates?
I managed to reduce certain computational problem to the Gauss-Seidel solution of the following linear system: $$Ax=Ly,$$ where $A, L\in\mathbb{R}^{n\times n}$, and $x,y\in\mathbb{R}^{n\times 2}$ are ...
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0answers
78 views
Can 2 parallel lines be discriminated as 'away', 'beside' with respect to 3rd parallel line?
I have nearly parallel several 3D line segments. some line segments locate (blue line) beside to a spefic line segment (black line) and some other (red line) locate away from that line segment. i want ...
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0answers
104 views
“Way” to decide if points are in a rectangle.
Suppose $P_1=(x_1,y_1)$, $P_2=(x_2,y_2)$ are two points.
Also suppose that we have a rectangle which we just know the value of its sides $a$ and $b$.
I am looking for some kind of formulation which ...
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0answers
43 views
Maintaining the line with the 2D iterands
Suppose a linear system is given
$$AX=B,$$
where $A\in\mathbb{R}^{n\times n}$ is a symmetric strictly diagonal matrix, and $X, B\in\mathbb{R}^{n\times 2}$. Therefore, the 2D Jacobi iterative solver is ...
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69 views
Polyhedra generation with computations and permutations.
i'm not a matematician, i'm only a computer programmer that in spare time want to aplly some geometry math with code, so sorry if this place is not the right place where to answer.
I've just found a ...
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1answer
347 views
line projection on top of a plane
If I have a horizontal line (a 3d point and 3d vector with zero z component) and another plane (could be an oblique or a horizontal; i have normal vector of the plane); then how do we get the ...
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2answers
173 views
Computing the minimum distance between two hollow tubes provided a method for computing the minimum distance between finite line segments
Say I have a method of calculating the minimum distance between two finite line segments in three-dimensional space. How might I adapt this method to provide the minimum distance between the surfaces ...
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0answers
52 views
What are algorithms or approaches to find a convex hull on higher dimensions?
I have some background in 2D computational geometry and understand how to find a convex hull in 2D. Now I'm looking at a set of vectors with 20-some components and want to find the convex hull on ...
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49 views
Multidimensional simplex meshing
I'm trying to figure how to make a simplex mesh on orthogonal domain.
Basically it comes to this:
Make (2) triangles of a rectangle
Make (5) tetrahedrons of orthogonal prism (cuboid)
etc.
I don't ...
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0answers
100 views
what kind of formula for spherical 3d tag cloud
I am not an expert in mathematics, I am only a young programmer.
I am trying to construct a spherical tag cloud and I've found this formula:
...
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0answers
65 views
How to interpolate sequential points to obtain functions and/or vectors?
I would like to know how I can interpolate a sequence (time) of points in order to obtain curves as some kind of mathematical functions.
Unfortunately math is not my area so I don't really know the ...
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1answer
155 views
Deriving an expression for an epipolar line
I would like to derive an expression for an Epipolar Line that appears in a right camera (there are two cameras - a left a right one). These cameras are placed in a $(x,y,z)$ vector space. This is a ...
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votes
1answer
59 views
Limiting search space for efficient line matching [closed]
I have 2D line segments extracted from an image. So i know end point coordinates of them. also, i have some reference 2d line segments. Both line segments are now in vector form. comparing to ...
-1
votes
1answer
72 views
How to change XYZ axes system into another 'xy' system
I have $3D$ point set lying on a vertical plane. This plane is not parallel to either $X$ or $Y$ axis but makes an angle (say, $\theta$) to $X$ axis. And also it has some ($+$ or $-$) intercept to the ...
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0answers
37 views
Maximum feasible subsystem problem (MaxFS) in 2 variables [closed]
Topic:
The maximum feasible subsystem problem, which is generally NP-hard [1]
Question:
Are there special algorithms in case of only 2 variables (2D linear constraints)? The problem seems to be a lot ...
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4answers
146 views
The equation of the plane [closed]
In geometry 3D, let $A(1,2,1)$, $B(-2,1,3)$, $C(2,-1,1)$, $D(0,3,1)$ be four points. Write the equation of the planes $(P)$ which passes through the points $A$, $B$ and equidistant from the two points ...
