0
votes
0answers
19 views

How to test for a polygon witn n vertices if it's nonintersecting polygon or not?

How can you design an algorithm to know if an n-vertex polygon nonintersecting ? On what criteria is the test going to be
1
vote
0answers
11 views

Mapping optimal sensor placement problem to Art Gallery Problem

I am trying to design an algorithm for optimal sensor placements in a given area. I researched in this domain and found ...
0
votes
2answers
34 views

Room for computational geometry in advanced algorithms course

I am currently putting together an independent study in advanced algorithms and because of my interest in (computational) geometry, wanted to include as many interesting algorithms from this field as ...
1
vote
2answers
110 views

Flood algorithm - find polygon containing a given point.

I have some code that represents a set of a set of interconnected line segments in 2D, in pseudo-code it'd be like this: ...
5
votes
2answers
164 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: ...
1
vote
2answers
122 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 ...
1
vote
1answer
129 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 ...
7
votes
2answers
146 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 ...
0
votes
0answers
50 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 $x_{N+1}$ ...
0
votes
1answer
67 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 ...
3
votes
1answer
113 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 ...
0
votes
1answer
247 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
vote
3answers
76 views

Are there any Heron-like formulas for convex polygons?

Are there any Heron-like formulas for convex polygons ? By Heron-like I mean formulas without angles as arguments and which takes as arguments only lenghts of sides of polygon - that is - we know no ...
1
vote
1answer
119 views

Algorithm Design for Delaunay Triangulation?

I am very much happy after seeing some very good answers in this site. I am trying to design a algorithm for the construction of Delaunay Triangulation using Randomized Incremental Algorithm.(I wont ...
3
votes
0answers
105 views

How can I find a maximal inscribed ellipsoid to a *concave* set of points, in 3D?

I have a set of points which describe the surface of an irregular, natural (i.e., occurs in nature) object. This point set is not necessarily convex, and contains occasional indentations so parts of ...
1
vote
1answer
80 views

Diagonal of a convex polygon such that the obtained cuts have simmilar areas

Let $P$ be a convex polygon represented with a list of vertices specified by some orientation. Consider the following problem Problem. Find in linear time a diagonal of $P$ such that the absolute ...
0
votes
2answers
470 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 ...
0
votes
0answers
193 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 ...
2
votes
1answer
730 views

How many rectangles can fit in a polygon with n-sides?

I am trying to write an algorithm to solve a problem I have. I have a few ideas of what the algorithm might be like but I am posting to see if anyone else has a better more efficient solution or any ...
2
votes
1answer
133 views

Maximizing the number of points covered by a circular disk of fixed radius.

Given a set of points in two dimensional space, and a radius r, what is the algorithm to find a disk of radius r that covers the maximum number of points?
2
votes
1answer
117 views

Test if a given point q is a kernel of polygon P

Point $q$ is a kernel of a polygon $P$ if from $q$ we can see all vertices of $P$. In addition, kernel is a intersection of $N$ half planes formed by edges of polygon. Proofs of the above ...
3
votes
1answer
94 views

Determining position at some point in time

I try to solve the following problem. On $n$ parallel railway tracks $n$ trains are going with constant speeds $v_1$, $v_2$, . . . , $v_n$. At time $t$ = 0 the trains are at positions $k_1$, ...
4
votes
0answers
149 views

Convex hull of balls

The convex hull is defined as the smallest convex set containing a set of points. Now we want to generalize it to a set of balls. If these balls have the same radius, then it can be shown that a ball ...
1
vote
3answers
169 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 ...
0
votes
1answer
435 views

Improving Gift Wrapping Algorithm

I am trying to solve taks 2 from exercise 3.4.1 from Computational Geometry in C by Joseph O'Rourke. The task asks to improve Gift Wrapping Algorithm for building convex hull for the set of points. ...
1
vote
1answer
124 views

Algorithm for Triangulation Dual Tree

I am looking for algorithm for the following problem. Given a list of diagonals of a polygon forming a triangulation, with each diagonal specified by counterclockwise indices of the endpoints, ...
2
votes
1answer
148 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
votes
1answer
667 views

Convex Hull Algorithms

I have an exercise in Computational Geometry. At first all statements look like very obvious and straightforward and this is misleading. All proofs should be very careful and very rigorous. Please ...
1
vote
2answers
139 views

General Proof Of Intersection Of Two Segments

Sorry for a silly question, I am trying to prove the fact of intersection of two segments on the plane. For example, $(d_1,d_2)$ is the first segment, where $d_1$ and $d_2$ are endpoint of the ...
3
votes
0answers
498 views

Circle Packing Algorithm

I have question related to circle-packing. The problem is to find the circle of minimum radius enclosing four non-overlapping circles of arbitrary radius. I have to write a program in C for this ...
3
votes
1answer
224 views

What is the complexity of computing the minimum distance between two convex polyhedra that both have $n$ faces?

EDIT: (in response to what deinst said) sometimes using a sledgehammer for some menial task is rather convenient - especially if it also has the complexity $O(n)$ (which is what my question is about) ...
2
votes
1answer
104 views

Computing the point which is closest to many Planar surfaces

Suppose, i have been given different planes which orients to different direction (i.e. i know only the plane parameter of those planes). If i am able to find out planes (probably more than 3 planes) ...
1
vote
0answers
207 views

Line comparison algorithm advice

Line is array of points (2 or more). I have a plane full of lines. For a given line in plane I need a measure which will tell how much difference there is between this and any other line in plane. I ...
8
votes
2answers
124 views

Efficient method for detecting a convex body in $\mathbb{R}^n$

Let $K_0$ be a bounded convex set in $\mathbf{R}^n$ within which lie two sets $K_1$ and $K_2$. Assume that, $K_1\cup K_2=K_0$ and $K_1\cap K_2=\emptyset$. The boundary between $K_1$ and $K_2$ is ...
1
vote
0answers
72 views

Questions about interpolating translated points from a grid

I would like to do the following transformations on a very low resolution bitmap (64x64 pixels). I am doing this transformation on a computer images, but it has nothing to do with computers, you can ...
1
vote
1answer
83 views

Line segment k-intersection

Could you please help me to design the following algorithm: I have a random-access list of line segments defined by a pair of points $[x^s_i; x^e_i]$. The list is initially unsorted, but of course ...
1
vote
1answer
76 views

Algorithm to compute mesh from intersection of infinite halfspaces

Is there a simple algorithm to compute the convex polyhedron (as a mesh with verticies, edges, and faces) resulting from the intersection of a set of infinite halfspaces? This is essentially a CSG ...
5
votes
2answers
339 views

Algorithm for positioning rectangles of various size into a larger rectangle

I am working on tool for merging smaller textures into one larger for use on Android app. I have $n$ rectangles of given size $(w_k, h_k)$, where $k=1,\ldots,n$ and I need to position them within ...
1
vote
1answer
1k views

Can Cox-de Boor recursion formula apply to B-splines with multiple knots?

We know that Cox-de Boor recursion formula can be used to compute the B-spline basis function. $$ N_l^n(u)=\frac{u-u_{l-1}}{u_{l+n-1}-u_{l-1}}N^{n-1}_l(u)+ ...
5
votes
1answer
194 views

Efficient algorithm for finding how many times a point is inside the triangles formed by given points

Given n 2D points and a special point p, what would be the best way to find how many times p is inside among those $^nC_3$ triangles formed by the n points.
2
votes
2answers
140 views

Convex hull for convex polygons

Is there something tricky about that? Or I should use some of the standard convex hull algorithms ? I mean, I don't see anything different between creating convex hull for a set of points and creating ...
2
votes
3answers
109 views

Formal proof for detection of intersections for constrained segments

They told me it was off-topic at stackoverflow. So I am trying my luck here. Yes, it's a homework, but I'm looking for some guidance (or related literature) instead of complete solutions. Please see ...
3
votes
0answers
50 views

Formal proof for detection of intersections for constrained segments [duplicate]

Possible Duplicate: Formal proof for detection of intersections for constrained segments Hi I need to come up with a formal proof for the following statement: Given an arbitrary count of ...
0
votes
0answers
72 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 ...
2
votes
0answers
407 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, ...
5
votes
1answer
133 views

How to check if a polytope is a smooth Fano polytope?

Question: We say that a convex lattice polytope $P\subset \mathbb{R}^d$ is a smooth Fano polytope if: The origin is contained in the interior of $P$ The vertices of every facet of $P$ are a ...
2
votes
1answer
763 views

Convex hull has the smallest perimeter

How do you show that the convex hull of a given set of points S, always has the minimum perimeter ? By perimeter i mean the length of the boundary of the hull
2
votes
0answers
130 views

The $n$-shortest lattice vectors problem in $\mathcal{R}^2$

I am looking for an algorithm to compute the $n$ shortest lattice vectors in $\mathcal{R}^2$. The problem statement is as follows: Given a lattice $L: \{ m \vec{u}+n\vec{v} \} \in \mathcal{R}^2$, a ...