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 ...

learn more… | top users | synonyms

1
vote
1answer
76 views

Calculate base and coefficient for power curve through 3 non-linear points

I have a formula that takes a 0-based bounded single dimensional input and transforms it to a specific power curve. EDIT This is single dimensional. There is no $y$. In the image, I'm showing how ...
1
vote
1answer
73 views

3D Convex Hull and The Gift Wrapping Principle

I am currently trying to implement a 3D convex hull algorithm that is based on the paper Convex Hulls of Finite Sets of Points in Two and Three Dimensions by F.P. Preparata and S.J. Hong, but I’ve run ...
1
vote
1answer
63 views

When is a convex polygon inscribable?

Defining the diameter of a convex polygon as the maximum possible distance between all pairs of vertices, can we conclude that the convex polygon is inscribable (i.e has all its sides as chords of a ...
1
vote
1answer
128 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 ...
1
vote
1answer
81 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 ...
1
vote
1answer
232 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 ...
1
vote
1answer
46 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 ...
1
vote
1answer
85 views

angle between steepest gradient of two plane

IF I have two 3d planes such as Oab and Oa'b'. If these two planes intersect a horizontal plane and the intersection of each plane makes AB and A'B' lines. then, Does the angle between AB, A'B' ...
1
vote
2answers
279 views

Determing the distance from a line segment to a point in 3-space

Imagine I have a line segment defined by endpoints $p_1$ and $p_2$, and some 3-space coordinate $q$. Is there a robust (in the sense of never giving divide-by-zero errors) way to quickly determine ...
1
vote
1answer
440 views

How to find the intersection of the area of multiple triangles

I have a couple of questions regarding finding the intersection of triangles. I have a system of 16 projectors that all have slightly different color gamuts. The color gamuts are represented by a ...
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 ...
1
vote
1answer
205 views

Hausdorff Distance Between Convex Polygons

I'm interested in calculating the Hausdorff Distance between 2 polygons (specifically quadrilaterals which are almost rectangles) defined by their vertices. They may overlap. Recall $d_H(A,B) = ...
1
vote
1answer
75 views

How to find out the control function of a cosine wave with sinusoidal input?

I have a system which is sampling at 100Hz. my input is sinusodial. The output is similar to cosine waveforms with varying frequency. I have no clue how to find out the exact formula to put into the ...
1
vote
1answer
64 views

Polygon: Internal Rays

Suppose I have an arbitrary non-self-intersecting polygon. I want to generate a list of points which lie on the edges of this polygon according to the following procedure: I iterate over each edge ...
1
vote
1answer
112 views

Testing polygon monotonicity

I am looking for an idea of an algorithm for the following problem: Give an efficient algorithm to determine whether a polygon P with n vertices is monotone with respect to some line, not ...
1
vote
1answer
122 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, ...
1
vote
1answer
178 views

Computing surface normal, floating point arithmetic

If I have a $n$-gon in $\mathbb{R^3}$, and I want to compute the surface normal, how can I get a value that minimizes error in a floating-point system? For example: Would I gain accuracy by first ...
1
vote
1answer
172 views

Ancient astronomers, planetary conjunctions, and epicycles

How did ancient astronomers predict planetary conjunctions? I know they used a system of epicycles to represent the path of planets, but finding the point and time of alignment of two planets still ...
1
vote
2answers
831 views

Check if point on circle is in between two other points (Java)

I am struggling with the following question. I'd like to check if a point on a circle is between two other points to check if the point is in the boundary. It is easy to calculate when the boundary ...
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
208 views

Cover a polygon using a minimal set of rectangles

Given some polygon and rectangles all of a fixed height and width, how I can calculate the number and placement of the rectangles so that no point within or on the polygon is not contained within at ...
1
vote
1answer
196 views

Intersection of two sectors

Is there algorithm that decide if two sectors intersect? I can transform the sector into polygons and use standard algorithms, but it has some cons. Any other ideas?
1
vote
1answer
457 views

3 line / 3 plane intersection

I am confused on a very simple thing, so I need your clarifications. Here is my doubt: I want to find the intersection point of three straight lines. Alternatively, I can find it by using three ...
1
vote
2answers
205 views

Calculating probabilities on a spherical map

A black and white colored sphere is given. We are looking at a random starting point on the sphere below us, which has a certain color. A random rotation can change the color of the spot below us. ...
1
vote
0answers
31 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 ...
1
vote
1answer
60 views

Find equation of line without using division

I need an algorithm to find equation of a line without using division. Given a line by two points on it, with coordinates: $(x_1, y_1),\ (x_2, y_2)$. We can simply get the line equation by the ...
1
vote
0answers
35 views

How many edges is sufficient to check to prove polyhedron convexity?

Consider the set $\{u_{1}, u_{2}, \ldots, u_{n}\}$ of points on the spere in $\mathbb{R}^{3}$ (i. e. $||u_{i}|| = 1$) and their convex hull C = $Hull(u_{1}, \ldots, u_{n})$. It's obvious that each ...
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 ...
1
vote
0answers
26 views

Geometric accuracy analysis of 2d rectangular models

I have reconstructed set of rectangular objects lie on a 2D plane (for ex. ABCD). All these objects are in a one coordinate system. On the other hand, I have reference models for all of them ...
1
vote
0answers
50 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 ...
1
vote
0answers
32 views

Background required for Computational Geometry

I am hoping to enroll in Computational Geometry course this spring. This was the textbook used for the course in the past. I am trying to figure out if I have required math background for this ...
1
vote
0answers
40 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 ...
1
vote
0answers
66 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 ...
1
vote
1answer
35 views

Convex Combination of Disks

We can define a closed disk $D$ with center $c$ and radius $r$ as the set of points $x$ satisfying $f(x) \le 1$ where $f(x) = \frac1{r^2}\lVert x-c \rVert^2$. Now take two disks $D_0,\,D_1$ with ...
1
vote
0answers
28 views

sweeping edges till they get a given elevation on an oblique plane

I am constructing wireframe model of 3d objects (prisms,..etc.). from a triangular mesh, I have obtained boundary points and fit striaght lines in order to get polygon edges refering to prism ...
1
vote
0answers
160 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 ...
1
vote
0answers
24 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?
1
vote
0answers
56 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
1
vote
0answers
74 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 ...
1
vote
0answers
78 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 ...
1
vote
0answers
52 views

How to estimate error pattern of a set of line segments with respect to given reference segments (2D case)

I am having set of pair of line segments (2D). Though each pair should be coincided on top of each other they are not so. I have been the reference data and then I extracted other line segments ...
1
vote
2answers
62 views

What is the equation stands for in geometry(intuitively)?

I am writing a bilinear interpolation method. This method can be abstract by solve the equation A*x = b, A is a 4x4 matrix below: $A=\begin{pmatrix} 1 &x_1 &y_1 &x_1y_1\\ 1 ...
1
vote
0answers
39 views

problem in dimensionality reduction

I am using multidimensional scaling to plot my data in R. However there is a hierarchy in my dataset which i want to exploit and I am using the delaunay triangulation to visualize the plot. So now I ...
1
vote
0answers
56 views

Integration through a Rotated Square

I have a 2D square S. S is described by s, the side length, theta, the angle it is rotated by, and c, the position of S's center. There is an axis-aligned rectangle R that extends infinitely in the ...
1
vote
0answers
119 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 ...
1
vote
0answers
55 views

Triangulation of a Convex Polygon [duplicate]

Possible Duplicate: Explanation/Intuition behind why $C_n$ counts the number of triangulations of a convex $n+2$-gon? I am interested in counting of how many distinct triangulation are ...
1
vote
0answers
320 views

differentiation of polygons, having cross borders

I have point data set and I segmented the data into different planar objects. after that, using contouring (convex hull), I obtained the boundary points. Please assume all points relevant to one ...
1
vote
1answer
90 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 ...
1
vote
0answers
35 views

How to discuss the maximum Area of Internal rectangular in an irregular region?

How to discuss the maximum Area of Internal rectangular in an irregular region? such as Fan-shape,or the region....
1
vote
0answers
96 views

The orientation of a closed discrete curve embedded in a triangle.

The two triangles $xyz$ and $x^{\prime}y^{\prime}z^{\prime}$, shown below, have opposite orientations. A closed curve $abcd$ is embedded in the first triangle ($abcd$). The vertices of the ...