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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112 views

Convex hull questions

Suppose I am in D-dimensional space, e.g. D=2. What is the minimum number of points to create a valid convex hull? If D = 2, would I need 3 points to create a convex hull (i.e. to form a triangle)? ...
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93 views

Correcting plane parameters with the fixed azimuth angles

I am trying to reconstruct specific 3d objects such as cubes, pyramids and so on. For this, i am using point cloud data and then fitting planar surfaces for the segmented point patches. Planes ...
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1answer
66 views

Understanding the Wolfram Demonstration “Distance of a Point to a Polygon”

I've recently came across a neat Wolfram Demonstration script by Jaime Rangel-Mondragon that calculates the minimum distance from a point to an arbitrary convex or non-convex polygon: ...
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1answer
198 views

Ellipse arcs. Draw a tangent line in the end point or make arc longer?

I read this article: link It describes how to draw ellipse arcs at all from svg. Each ellipse is described with the following params (and I know them): x1, y1, x2, y2 - arc from point (x1, y1) to ...
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2answers
181 views

Finding the largest circle that contains a single point in a set (and no other point)

Given a bounded $A \times B$ rectangle with a set of chosen coordinates, generated for example with the command: ...
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175 views

Formula for intersection of “power” curve and parabola.

EDIT I have edited this question to make it more clear. I have spent quite some time trying to find this on Google, but haven't succeeded. I need the formula(s) to determine the intersection ...
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0answers
28 views

Length of the voronoi diagram

Does there exist an algorithm for computing the length of the voronoi diagram of a set of points or just gives the intersection points of the voronoi diagram?
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0answers
58 views

largest polygon from segments

There is a set of segments. and I want to calculate the area of the largest polygon which can be build using these segments. I try to search it, but I can't find anything. thanks
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1answer
103 views

Graphics clipping: How can repeated half-space clipping fail?

Hi I am currently going through the past exam problems and I am stuck on this clipping problem. Could you give me some hint on how to solve it? If we clip a polygon to a window, it is inadequate ...
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1answer
60 views

Center of Distance

I am given $N$ points in a 2D plane($x$ and $y$ coordinates). I have to find a point in this plane with coordinates $X$ and $Y$ such that: $$\sum_{i=1}^N \max\{|X - A_i|, |Y - B_i|\}\text{ is ...
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2answers
131 views

Checking convexity from outside

Is there any method or algorithm to determine convex (or non-convexity) property of a region from outside (perimeter) ? One way is plotting tangent line in each point of perimeter and discuss how ...
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1answer
156 views

On finding the nondominated set of vectors. How to understand this algorithm?

L et us denote by $x_i(v)$ the $i$th coordinate of $v \in \mathbb{R}^d$. Then $v = \left [ x_1(v), x_2(v), \dots ,x_d(v) \right ]$ We say that a $v \in \mathbb{R}^d$ dominates another vector $w \in ...
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2answers
156 views

How to check if polylines can be untangled?

In a program I'm writing I need to be able to check whether a straight line between two points is homotopic to a polyline between them. For example in the below example the first one is equivalent to ...
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2answers
203 views

Proof of the following: How many $(n-2)$ dimensional faces from a corner of a hypercube

I asked a question earlier regarding the number of $(n-2)$ dimensional faces exiting a corner of an $n$ dimensional hypercube. (For example the number of points in a corner of a square, or the number ...
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0answers
98 views

Optimal bounding boxes selection for $N$ rectangles

Suppose that I have $n$ straight rectangles on a plane $r_i = (x_i,y_i,w_i,h_i)$. Each rectangle has a cost function, its area $A(r_i) = w_i \cdot h_i $. I can also "merge" 2 or more rectangles into ...
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0answers
35 views

Polytime programming

Given a linear system of the form: $$x_r = a$$ $$x_j = b$$ $$c_1x_1 + c_2x_2 ... c_nx_n = n$$ $$x_1 + x_2 + x_3 ... x_n = k $$ $$0 \leq a,b,x_1, x_2, x_3 ... x_n \leq 1$$ $$k \geq 0$$ How quickly ...
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1answer
84 views

Computing with graphs in surfaces

I am currently working on a research project involving a polynomial defined for graphs in surfaces, similar to the Tutte polynomial, except with terms accounting for the embedding. At the moment, it ...
4
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1answer
91 views

Covering all the edges of a hypercube?

Consider an arbitrary $n$- dimensional hypercube: If we select $n - 1$ corners of that hypercube and highlight all $(n - 2)$ dimensional elements that originate from each of the corners is it ...
2
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1answer
69 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 ...
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1answer
1k views

How to find rotation angles along X,Y,Z axes with a known vector to bring the axes to correct situation

I am working with 3d point data. When I checked the data I realized that there is some error on my data and need to do some kind of rotational rectification because the points which should be ...
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0answers
144 views

how to get optimal vector, which is parallel to intersection line of many plane (Least Square way)

My idea is to construct the best optimal 3D line representing the intersection of many 3D planes. (As we know, due to fitting errors or data errors, the fitted planes might not intersect exactly ...
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1answer
242 views

my plane is not vertical, How to update 3D coordinate of point cloud to lie on a 3D vertical plane

I have a bunch of points lying on a vertical plane. In reality this plane should be exactly vertical. But, when I visualize the point cloud, there is a slight inclination (nearly 2 degrees) ...
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1answer
50 views

How can I geometrically (or geographically) group items together?

I'm a programmer, and I'm working on a project that takes a bunch of photos and separates them into groups by their gps coordinates. I have no experience in things like geometric group theory so I'm ...
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1answer
106 views

What is the typical method for sampling uniformly in a convex polytope

The polytope in my case is the intersection of the k-plane $Ax=b$ and $\{x>0\}$ where $A$ is the constraint matrix and $b$ is some solution. I'd like to find a method that is fast and efficient for ...
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0answers
60 views

Checking if a binary vector lies in the affine span of given binary vectors

Let $x_1, \ldots,x_N \in \{0,1\}^D$ be $N$ binary vectors, assumed affinely independent (in the field of reals). Is there an efficient algorithm for determining whether a new binary vector $x_{N+1}$ ...
2
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0answers
100 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 ...
3
votes
3answers
891 views

Finding the major and minor axis vertices for an ellipse given two conjugate diameters?

I've been googling, searching forums and looking in my old algebra/trig books to try to understand how to find the end points to the major and minor axis of an ellipse given the end points of two ...
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1answer
69 views

Generating Vectors under Constraints on 1 and 2 norm

Update: I left out some important information in my previous description... I am actually dealing with a special problem, which is better described as follows: Given user-specified parameters ...
2
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1answer
281 views

Distance between point and plane & orthogonal projection matrix

I am poor in mathematics and want to learn few fundamental ethics to understand some of advanced things; For plane $i$, denote $n_i\in\mathbb{R}^3$ and $o_i\in\mathbb{R}^3$ respectively as its normal ...
4
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1answer
140 views

Potential Division by zero in the construction of NURBS basis functions: how to handle?

Some background context In reading about NURBS I saw the definition that the B-Spline basis functions are defined by a recurrence relation. $N_{i,n} (u)= f_{i,n}(u) N_{i,n-1}(u) + g_{i+1,n}(u) ...
2
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1answer
462 views

Angle between different rays (3d line segments) and computing their angular relationships

I have several positions (say A,B,C,..) and I know their coordinates (3d). From each point, if a certain ray is passing in a way to converge them at a given (known) point (say O). This point O ...
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0answers
84 views

viewing ray geometry - with multiple aerial photographs

I am working with multiple aerial images. My idea is to model 3d objects (only upper parts). I am having known orientation parameters. As I am new to this field so that, I want to clarify few general ...
4
votes
1answer
154 views

Intersection of planes by forming 3d lines

If I have $n$ known planes (known normal vector and a point on a plane) that intersect each other in such a way so as to form closely located 3D lines, then (1). To get a common single 3D line to ...
3
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1answer
159 views

Partitioning a set of rectangles into disjoint subsets each of which consists of disjoint rectangles

Suppose we have a list $R$ of axis-aligned rectangles in the plane. There is the well-known problem of determining the maximum subset of $R$ which consists of disjoint rectangles; this problem is ...
2
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1answer
116 views

incident angles between rays, falling on an oblique plane

I am having really two simple questions, but following two things are confusing me. Question 1 If I know plane parameter (v3) of a given plane (say AB); if a pair of rays are incident at a ...
4
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0answers
121 views

Biggest ball included in an intersection of balls

I would like to prove that for any family of balls $\{B(c_i,r_i)\}_i \subset \mathbb{R}^d$ such that $\{c_1, \dots, c_n\} \subset \bigcap_i B(c_i,r_i) $ and $\forall i, r_i \geq 1$, there exists a ...
1
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1answer
51 views

What do we call the angular arcs between two edges of triangles?

I've been trying to find a geometry library for java which is as high level as describing angles between adjacent sides of triangles given 3 sides. So, what do we call such kind of arcs. In many ...
2
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2answers
107 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
votes
1answer
81 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
votes
1answer
412 views

Circle Packing: Unsolved Problem in Geometry?

Graham and Sloane minimize the second moment of the centres of a number discs in order to maximize their compactness. They use computational geometry techniques to find the optimal packings for ...
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2answers
470 views

Finding the tangents common to two rotated ellipses?

Is there a way to find the four tangents that two rotated ellipses share? I believe that if two ellipses do not intersect and do not contain one another, they will have four tangents in common and I ...
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1answer
583 views

closest pair in N-Dimensional

I have to find the closest pair in n-dimension, and I have problem in the combine steps. I use the divide and conquer.I first choose the median x, and split it into left and right part, and then find ...
1
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2answers
95 views

Approximating Euclidean geometry, restricted to $\mathbb{Q}$

I'm having trouble putting this into a fully coherent question, so I'll give the broad question, then a few bullet points to give you a better idea of what I'm asking. I'm looking for a line of ...
3
votes
1answer
77 views

Linear, Bi-linear or better

I have been writing some code to do some interpolation of 2D data on an irregular grid. So far what I have done is: Triangulate the known points using Delaunay. Find the vertices of the triangles ...
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1answer
113 views

Winding a space curve

Can I find parametric equations for a curve that is winding another curve, which I know -- let's say it's $\vec{f}(t) = (x(t), y(t), z(t)) = \{\sin (t)+2 \sin (2 t), \cos (t)-2 \cos (2 t), -\sin (3 ...
2
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1answer
38 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 ...
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1answer
170 views

Perpendicular to a vector at point on the vector

I am working with a model where I have to calculate a perpendicular to a vector through two points $\mathrm{P_1}$ and $\mathrm{P_2}$ (3d) at point $\mathrm{P_3}$ on the line joining these points. ...
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2answers
106 views

How to find co ordinates of a triangle after increasing the area by a factor of $\alpha$?

i am given with a triangle $\{(x_1,y_1),(x_2,y_2),(x_3,y_3)\}$ and the area need to be increased by a factor $\alpha$. can i anyone let me know formula to find the co ordinates of new triangle? There ...
2
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1answer
184 views

Lloyd's algorithm in normed vector spaces

How do I run Lloyd's algorithm in a normed vector space? The space: L*a*b* color space, finite sRGB segment, $R^3$ The distance metric: CIE94 using L*C*h* information derived from the L*a*b* ...
2
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1answer
44 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 ...