0
votes
2answers
26 views

Retrieve the initial cubic Bézier curve subdivided in two Bézier curves

I have a cubic Bezier curve subdivided to two cubic Bezier: Assuming that "t_cut" is the t value where this initial Bezier is cut: example of function subdivision(BezierCurve initialCurve, ...
1
vote
1answer
45 views

Merge two or more cubic Bézier curves for optimization

I am looking for an algorithm which can merge several cubic Bezier curves. For instance, I have a lot of cubic Bezier that are joined to form a poly-Bezier curve. The idea is to merge dynamically some ...
0
votes
1answer
22 views

Convex hulls for a finite amount of points

I'm trying to understand what a convex hull intuitively is, and say given for a set of points $(x,y)\in\mathbb{R}^2$ how is it generated from these points? I tried reading the wikipedia article and ...
0
votes
0answers
7 views

Maximum amount of positional offset caused by noisy distance measurements in Quadrilateration

Quadrilateration is a range-based localization technique applied to wireless sensor networks. It is the equivalent method of trilateration in 2D. Assume that, there are four beacons (the sensors ...
0
votes
0answers
10 views

The mathematical road to learning procedural graphic generation

I am trying to get started with procedural generation of computer graphics and animation, but my basic math skills are not enough. Can anyone recommend the courses/topics in mathematics that will get ...
11
votes
3answers
157 views

is there an efficient algorithm for comparing collections of points?

Let's say you have two sets of M points $p_1...p_M$, and $q_1...q_M$, which reside in $\mathbb{R}^N$. Is there an efficient (e.g. polynomial in M and N) algorithm to determine if the point-sets are ...
1
vote
0answers
46 views

Computationnal geometry: vector, basis, point and coordinate system?

I am trying to build a small geometrical library in C++, that is mathematically consistent (not so false). The goal here is to construct two concepts: vectors and points. I am not sure that the ...
1
vote
1answer
35 views

Can convex hulls contain duplicate points?

Given 4 vertices: (-3.2, 0.8), (-3.2, -0.8), (3.2, -0.8), (3.2, 0.8) A function which I did not write, and given vertices, will return the points of a convex hull. Using the points above, it ...
2
votes
1answer
153 views

Vectors Angles from $[0,2\pi]$

Given two vectors $V_1 = (x_1, y_1)$ and $V_2 = (x_2, y_2)$. How to calculate the angles between them in the range of $[0, 2\pi]$? I know the $\cos\theta$ similarity equation could present a $\theta$ ...
0
votes
0answers
57 views

Spherical object with n vertices and no coordinate singularities

I'm programming a tool where I want to track the directions of a unit vector. I want to store the position to which the vector is pointing on a unit ball. Each time the vector points to a position $x$ ...
3
votes
1answer
98 views

Finding the angle of a moving target

I'm developing a submarine game and found a mathematical problem that exceeds my knowledge. A submarine has $x$ and $y$ coordinates in the plane, a speed $v$, and two angles: one indicates the ...
2
votes
3answers
203 views

angle between two intersected plane

If two planes are intersected by making a straight line, like $AB$ then Does the angle between two planes (see figure) always given by the angle between normal vectors ($n_1$ and $n_2$) ?
5
votes
2answers
89 views

Find the most vertical line in a point set in $O(n \log n)$ time

Input: a set of $n$ points in general position in $\mathbb{R}^2$. Output: the pair of points whose slope has the largest magnitude. Time constraint: $O(n \log n)$ or better. Please don't spoil the ...
-1
votes
1answer
77 views

Limiting search space for efficient line matching [closed]

I have 2D line segments extracted from an image. So i know end point coordinates of them. also, i have some reference 2d line segments. Both line segments are now in vector form. comparing to ...
1
vote
1answer
117 views

Fraction values around the vertices of a Loop's subdivision

In Loop's subdivision scheme, what do the variables $\alpha$ and $n$ refer to? Knowing what the variables refer to will help to derive the fractions around the vertices. But, what do these ...
5
votes
2answers
366 views

Distance between a point and a m-dimensional space in n-dimensional space ($m<n$)

I am trying to find a method with a low computational cost to compute the distance of a point $P$ and a space $S$ that is defined by the origin $O$ and $m$ vectors $v_1, v_2, ..., v_m$ in an ...
1
vote
3answers
184 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 ...
1
vote
1answer
188 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 ...
7
votes
1answer
2k views

Calculating Distance of a Point from an Ellipse Border

I'm thinking about using oriented ellipses to represent curves (dents/bumps etc.) in my physics engine, and have a few questions about working with them: What methods are there to finding the ...
0
votes
0answers
61 views

Multidimensional simplex meshing

I'm trying to figure how to make a simplex mesh on orthogonal domain. Basically it comes to this: Make (2) triangles of a rectangle Make (5) tetrahedrons of orthogonal prism (cuboid) etc. I don't ...
4
votes
1answer
70 views

Efficiently deciding if any of a set of cylinders in 3-space intersect

Let's say I have a set $C$ of $N$ cylinders in 3-space, $(c_1, ..., c_N) \in C$, where each cylinder, $c_i$, has an associated radius $r_i$ and two coordinates specifying the endpoints of the line ...
1
vote
1answer
179 views

Characterizing and counting the unique vertices in a geodesic sphere based on a triangulated icosahedron

I have a geodesic sphere generated by triangulated an icosahedron to some frequency $\nu$, with a circumscribing sphere of radius $R_c$. Let's define a 'component' of the geodesic sphere to be a ...
1
vote
1answer
385 views

Deforming a truncated icosahedron into its circumscribing sphere

Imagine that I have a truncated icosahedron consisted of 60 vertices, each of degree $deg(v) = 3$, and fixed edge length $L$. I'd like to assign some constant curvature or bending angle $\theta$ to ...
1
vote
1answer
314 views

why does multiplicatively weighted voronoi diagram (mwvd) with 2 sites create a circle?

I want to understand the structure of a multiplicatively weighted voronoi diagram. I found that the bisector between 2 sites is circle shaped, but couldn't formally ...
3
votes
2answers
283 views

How to get 'rectangular size' of arbitrary circular sector?

Given a circular sector defined by sweeping from a 'start' to a 'stop' angle (see diagram below) and a radius, how do you compute the bounds of the rectangle that fits to the edges of the sector? ...
1
vote
2answers
410 views

shadow simulation from buildings

is it possible to calculate shadow areas of buildings or simulate shadows of buildings in a city, using the heights of these buildings and the sun angle and azimuth? the basic light tracing concept ...
1
vote
1answer
101 views

Problem interpretation - Distance Formula?

If you've got multiple arrays like this: (24,36,28,28,16,27) (38,38,45,57,35,50) every array being 6 integers, each integer in range [0,60] I would like to find the distance between those 2 ...
0
votes
1answer
125 views

What is computational geometry and who should take a course on this subject? [closed]

In mathematics, geometry is the topic I like. Just out of curiosity I would like to know what computational geometry is about. Who studies this subject and why. What are its applications, or is it ...