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 and surfaces.
Questions tagged [computational-geometry]
1221 questions
19
votes
1 answer
Geometry of nose in and nose out parking in parking lots
I would like some computational evidence in favor of my observation that one can park a car in tighter (parking lot) spaces by backing in rather than nose in. I have been doing this successfully for some 15 years, but see few others trying this.…
Will Jagy
- 139,541
19
votes
4 answers
How to union many polygons efficiently
I've asked this question at SO, but only answer I got is a non-answer as far as I can tell, so I would like to try my luck here.
Basically, I'm looking for a better-than-naive algorithm for the constructions of polygons out of union of many…
Graviton
- 2,292
9
votes
1 answer
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 their bounding box. In this case the cost…
Andrey Rubshtein
- 175
9
votes
3 answers
Way to measure the similarity/difference of 2D point clouds
i need a way to measure the similarity or difference of two point clouds? The number of points in each point cloud can be different. The Point clouds are already aligned. By similarity I mean the similarity of the shapes.
I have already tried the…
8
votes
2 answers
"Concave hull" - Possible? Feasible? Deterministic?
So there are several questions regarding how to compute the convex hull of a set of points. However, let's say that on inspection the set of points inscribed a star shape. A Convex hull algorithm would define a pentagon around a five-point star and…
KeithS
- 2,759
6
votes
1 answer
Putting fence around sheep
Convex hull algorithms are well known. However, in my case, the goal is slightly modified:
Given $N$ points in a plane, construct convex polygon with minimal area so that it contains all points, and there is no point that is closer than given…
VividD
- 15,966
6
votes
1 answer
Constructive algorithm for Minkowski's theorem.
There is a theorem of Minkowski that says that given $k$ unit vectors $x_i$ that span $\mathbb{R}^n$ and $k$ positive real numbers $a_i$ such that $\sum_{i=0}^k a_i x_i = 0$ then there exists a unique convex polytope (up to translation) such that…
deinst
- 5,646
5
votes
1 answer
Delaunay-like algorithm to get four sided polygons instead of triangles?
Is there an algorithm similar to the Delaunay triangulation which can organize a set of points into a set of four sided polygons instead of triangles?
5
votes
0 answers
Segment Tree vs Interval Tree
Segment trees and interval trees both answer stabbing queries about line segments. In 1D, they both take $O(n \log{n})$ preprocessing time and $O(\log{n} + A)$ query time where n is the number of line segments and A is the size of the answer.…
starflyer
- 550
5
votes
2 answers
Finding the virtual center of a cloud of points.
Given:
(latitude, longitude) points $P_1, P_2,\ldots, P_n$.
Presumably, all the points should form a dense cloud. However, noise is possible.
Needed:
The virtual center of the points.
For instance, 99% of the points may lie within a circle with…
mark
- 313
4
votes
1 answer
How to predict the tolerance value that will yield a given reduction with the Douglas-Peucker algorithm?
Note: I'm a programmer, not a mathematician - please be gentle. I'm not even really sure how to tag this question; feel free to re-tag as appropriate.
I'm using the Douglas-Peucker algorithm to reduce the number of points in polygons (in a mapping…
Herb Caudill
- 143
4
votes
2 answers
Equality of Voronoi diagram
What can we say about two sets $A$ and $B$ if both of them have the same Voronoi diagram.
First, I thought if the Voronoi diagram are equal so the sets also should be equal, but by definition, Voronoi diagram is determined by distances to a…
com
- 5,612
3
votes
2 answers
Determinant (computational geometry)
Let p=(px,py),q=(qx,qy), and r=(rx,ry).Show that the sign of the determinant
|1 px py|
D=|1 qx qy|
|1 rx ry|
determines whether a point r lies to the left or right of the directed line pq. ( I know that this true, not exactly sure how to…
Cory
- 91
3
votes
2 answers
Finding how many points to which a certain point is connected
This may be a programming issue, not a mathematical one. If so, please let me know so that I can rewrite it specifically for that audience.
Consider a shape with a random border. Each point on its border has an x and y value that is an integer. This…
maxedison
- 175
3
votes
1 answer
Drawing Triangles from a List of Incircles?
I have drawn the incircles of triangles which were generated through a delaunay triangulation but lost the original delaunay mesh. Is it possible to invert the process and draw the triangles back from this list of circles?
Many thanks,
Arthur