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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2answers
120 views

Books for Geometry processing

Please suggest some basic books on geometry processing. I want to learn this subject for learning algorithms in 3d mesh generation and graphics. Please suggest me subjects or areas of mathematics i ...
2
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1answer
85 views

Computational geometry

Computational geometry? (Computational geometry) Given a set of n randomly scattered points for even n = 2,4,6,...,50 . Find the maximum number of lines between the pairs of nodes in such a way the ...
2
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1answer
39 views

Fragemented linear feature alignment technique

I am having set of linear features lie on a plane (it does not a matter whether the pane is vertical or horizontal). all linear features are either parallel or othogonal to the vertical axis or ...
2
votes
1answer
46 views

How to estimate orientation errors of an image with respect to known data (line features)

I think this is very simple but for me, it is confusing to figure out a way. Here is my problem. I have been given a 3d line segment list obtained from a field survey. So I know each end point ...
2
votes
2answers
239 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 ...
2
votes
1answer
472 views

Finding points on ellipse

I have ellipse in 2D. I want to compute fixed number of points on this ellipse with constant angular seperation between those points. My first idea was to generate line equations from center of the ...
2
votes
1answer
469 views

Calculating volume of convex polytopes generated by inequalities

I have a set of inequalities, I am looking for a way to compute its volume. More specifically, I would like to compute the ratio of its volume with the volume if some more inequalities were added. I ...
2
votes
1answer
165 views

Finding the intersections of straight lines

Given a set of lines intersecting the quadrant with $x, y>0$, what are the available algorithms for finding the area below all straight lines (including $y$ and $x$ axis)? In other words, methods ...
2
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2answers
135 views

Did I write the right “expressions”?

$9$. Consider the parametric curve $K\subset R^3$ given by $$x = (2 + \cos(2s)) \cos(3s)$$ $$y = (2 + \cos(2s)) \sin(3s)$$ $$z = \sin(2s)$$ a) Express the equations of K as polynomial ...
2
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1answer
102 views

Algorithm for Identifying Convex Kernel

What algorithms currently exist to determine the convex kernel of any low-dimensional set, especially a planar set? Also, if one exists, what research has been done on it and are there any references ...
2
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2answers
315 views

Finding an appropriate axis of rotation for two points such that they can be rotated and translated to overlay a given line

I have two lines with known parametric equations and some number of distinct points along each line. I would like to rotate the points on $L_2$ some number of degrees $\theta$ along one and only one ...
2
votes
1answer
221 views

What is the most accurate method to get intersection point in 3D?

I have been given 3D point data, belonging to different planar segments. Points are not exactly laid on the planes so that I have fitted best planes using least square solutions. Now, I want to find ...
2
votes
1answer
439 views

alpha shapes for polygonal boundary detection - for point cloud data

i am trying to implement alpha shape algorithm but the theories is quite hard to undestand. so, if any one know (or have) pseudo codes to implement alpha shape (2d) algorithm please post us. thanks
2
votes
1answer
204 views

Need line generalization method like Dougles Peuker, that is able to keep turning points along closed polygon boundaries (for 2d or 3d point data)

I have set of point clouds, representing boundaries of different closed polygons. These polygons contains 3d points. But they also can be considered as a 2d case once boundary points are projected to ...
2
votes
2answers
709 views

Fitting data to a portion of an ellipse or conic section

Is there a straightforward algorithm for fitting data to an ellipse or other conic section? The data generally only approximately fits a portion of the ellipse. I am looking for something that doesn't ...
2
votes
1answer
38 views

Bounding Sphere for Two Hyperrectangles

Please see the image for best illustration of the task. I have two hyperrectangles, $\text{R1}$ and $\text{R2}$, whose exact location and size is arbitrary. Now, my task is to construct a bounding ...
2
votes
2answers
64 views

Find polygon with smallest perimeter that encompasses all points

Given a random set of points in 2D space such as: How would one go about finding the smallest perimeter polygon that encompasses all points and has a point as each one of its vertices? For the ...
2
votes
0answers
26 views

Efficient algorithm for calculating hypervolume

Given a $d$-dimensional hyperrectangle that spans from the origin to the integer coordinates $l_1,l_2,l_3,\cdots,l_d$. If $V$ is the hypervolume of the solid formed by all points in the ...
2
votes
0answers
68 views

Similarity of Polyhedra: What is the measure?

When comparing two convex polyhedra, how can one determine if they are geometrically similar. Is there any algorithm to determine if one is the distorted or truncated version of the other? Vertex, ...
2
votes
3answers
48 views

Number of layers in nested convex hull

Find the maximum number of nested convex hull
2
votes
1answer
153 views

Modify the closest-pair algorithm to use the $L_\infty$ distance.

I'm trying to understand the closest pair of points problem. I am beginning to understand the two-dimensional case from a question a user posted some years ago. I'll link it in case someone wants to ...
2
votes
0answers
13 views

Link and its Intersection

Let $K$ be a simplicial complex in $R^2$ such that $|K|$ is a simple polygon with inside. An internal edge $ab \in K$ is an edge such that both of its two endpoints a and b are NOT on the boundary of ...
2
votes
0answers
80 views

How do I most efficiently find the perpendicular distance from a point to the convex hull of a collection of circles?

I have a collection of one or more line segments for which I know the (x,y) coordinates of the endpoints. The segments may or may not be parallel and may or may not intersect. Each segment endpoint ...
2
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0answers
117 views

Best closed convex surface fitting N points in 3D

First. It's easier to understand the problem by describing the application where it arises from. We have a convex body $B$ in $\mathbb{R}^{3}$ and measure points on its surface. The measurements are ...
2
votes
2answers
59 views

How to make sure that a given set of points lie on the boundary of a possible square?

Given a set of integral coordinates , check whether all the points given lie on side of a possible square such that axis of the square so formed lie parallel to both X-axis and Y-axis . Suppose ...
2
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2answers
99 views

Polytope parametrization

How one could parametrize a convex polytope? By parametrization I mean something like in multiple integrals, when to integrate over an area one can integrate over one variable in an interval $[l,r]$ ...
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0answers
83 views

Higher Order Voronoi Diagram of a Poisson Point Process: What do we know?

This question is looking for probabilistic results of the Voronoi diagrams of 2-D space when the points are distributed by a homogeneous Poisson point process. The results can be the distribution of ...
2
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0answers
60 views

Generalization of Minkowski's theorem

I would like to prove a generalized version of the Minkowski's theorem, but I don't quite know how to do it. Here is what I would like to prove: Let $X\subset \mathbb{R}^d$ is convex, symmetric ...
2
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0answers
82 views

Orthogonal 4-cut of a convex polygon

Given a convex polygon with N vertices I need to cut it into four equal area parts with two straight orthogonal cuts. I feel that I have all the necessary pieces to solve this puzzle, but I can't put ...
2
votes
1answer
77 views

A method to test for uniform distribution over a convex polytope

Assuming I have a convex polytope defined as the intersection of $Ax=b$ and $x>0$ and I have a way to sample points from this object, is there a way I can test for uniformity of these sampled ...
2
votes
0answers
128 views

RANSAC line fitting (3d) by line segments (3d)

I am having many 3d line segments. some of them are nearly parallel and some are oriented in to different direction. I want to avoid outliers and to get the best line 3d to represent the given ...
2
votes
0answers
102 views

Calculation of the fundamental group from triangulations

Is there - say, for a triangulable surface - a concrete algorithm how to calculate the fundamental group of the surface from a given triangulation, seen as a graph (of its 1-skeleton), given as an ...
2
votes
0answers
70 views

Finding the smallest nonzero vector perpendicular to $\vec v$ with integer coordinates

Let $\vec v\in\mathbb Q^n$. Is there an efficient algorithm to compute the smallest (in the $\ell_\infty$ norm) nonzero vector $\vec w\in\mathbb Z^n$ such that $\vec v\cdot \vec w=0$? Equivalently, if ...
2
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0answers
373 views

Algorithm for Collection of Shortest Paths in a Grid without any clash at a point of time.

The efficient algorithm needs to be done and proved for the best solution for the given problem: User inputs: (#) Size of the NxN Grid. (N); (#) No. of Paths: Z; (#) Source and Destination ...
2
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1answer
155 views

Showing: point of polytope which maximizes the minimum distance to a vertex is a barycentre?

Let $T_1$ and $T_2$ be two regular $(n-1)$-dimensional simplices with vertices $$(t,0,\ldots,0), (0,t,\ldots, 0),\ldots, (0, 0, \ldots, t),$$ and $$(t-n+1,1,\ldots, 1), (1, t-n+1, \ldots, 1), \ldots, ...
2
votes
0answers
46 views

Terrain tile scale in case of tilted camera

I am working on 3d terrain visualization tool right now. The surface is logically covered with square tiles. This tiling could be visualized as follows: For some reason I have to know scale of a ...
2
votes
1answer
140 views

Fitting a cylinder of known length to the chord between its circular edges s.t. the cylinder's mass near a point is minimized

Let the pair of three-space coordinates $p_1$ & $p_2$ define a chord between the edges of a cylinder of radius $R_c$ and length $L$. The edges here represent the two circular borders between the ...
2
votes
0answers
719 views

Is there a formula for the solid angle at each vertex of tetrahedron?

A tetrahedron has four vertices as much as a triangle has three vertices. A tetrahedron therefore can have four solid angles as much as a triangle can have three angles. I am wondering: Is there a ...
2
votes
0answers
972 views

How to find all intersection points of two splines?

2D-Cubic splines are given in parametric form (X(t), Y(t) and X(s), Y(s)). Every segment has it's own X and Y expression. And I want to find all intersection points. Some segments are intersecting ...
2
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0answers
99 views

find largest cube in lot of cuboids

sorry for my bad English... I've a system consists of many cuboids, many are adjacent to the others. My problem is... I want to find the largest cube in this system (which may consists of many of some ...
2
votes
0answers
448 views

Set of segments a vertical ray intersects

The problem is 10.6a from Computational Geometry: Algorithms and Applications. We want to solve the following query problem: Given a set $S$ of $n$ disjoint line segments in the plane, ...
1
vote
4answers
346 views

What is the name for a maximal convex set of points contained in another set of points?

What is the name for a maximal convex set of points contained in another set of points X? Maximal in terms of inclusion. For the desired set to be unique, X can be restricted to be a simple polygon ...
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3answers
194 views

Finding a point above the line in $O(\log n)$

I am trying to solve the following problem. So far with no success. Let $S$ be a set of $n$ points in the plane. Preprocess $S$ so that, given a (non-vertical) line $l$, one can determine whether ...
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2answers
6k views

How to find the third coordinate of a right triangle given 2 coordinates and lengths of each side

p2 |\ |b\ | \ A| \C | \ |c___a\ p1 B p3 If given point p1 & p2, side A & B how would you find point p3? I know given this information you ...
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2answers
891 views

Is this a wrong solution to the smallest enclosing circle problem?

I have a set of points in $\mathbb{R}^2$ and I need to find the smallest enclosing circle, i.e. the circle with the smallest radius that contains all of the points belonging to the set. I have the ...
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2answers
2k views

Two plane intersection and angle between 2 planes

I am trying to implement my problems in different ways. So, may be though this question has some relation to some other questions, please answer me. We know; Intersection of two planes will be given ...
1
vote
1answer
132 views

Can Centroid Lies on the Edge of a Polygon?

This question is similar to the one here. Now the question is, given a simple polygon with $Area>0$, regardless of whether it is convex or concave and with no opening, can we prove that the ...
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2answers
208 views

Find outline of $N$ points in a plane

If I have $N$ point coordinates $P_i = ( x_i, \, y_i ) $ and I want to draw the outline connecting only the points on the "outside", what is the algorithm to do this? This is what I want to do: ...
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2answers
696 views

superellipsoid: problem in understanding parametric formula

hi i've found this interesting page: superellipse and superellipsoid and i used the formula for one of my computer graphics applications. i used (the most usefull for computer graphics) the parametric ...
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2answers
56 views

Estimating the missing points of a 3D point cloud

Consider a cloud of N points (forming a smooth 3D object), in which n points are missing. Also, consider that there is no prior knowledge about the original shape of the point cloud. The only ...