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Seemingly simple mathematical problem

I'm looking for a solution to a seemingly simple mathematical problem. Please refer to the attached drawing to illustrate the following description.

Given:

- A sphere with radius R = 1

- Two circles on the surface of this sphere, described by two arbitrary vectors A and B as well as two angles alphaA and alphaB (0..PI/2)

To calculate for the following seven cases:

1. Circles lie side by side and do not touch or intersect: - nothing -

2. Circles touch outside in one point: vector coords for this point C

3. Circles intersect each other: vector coords of the two points C1 and C2

4. Circles touch inside in one point: vector coords of this point C

5. Circles lie inside each other and do not touch or intersect: - nothing -

6. Circles are identical, with A = B and alphaA = alphaB: - nothing -

7. Circles are identical, with A = -B and alphaA = alphaB = PI/2: - nothing -

The drawing does show case #3.

In addition to a formal mathematical solution, I'm also looking for its implementation. This implementation should be numerically stable and in form of a function which accepts A, B, alphaA and alphaB as parameters and returns the case number as well as either zero, one or two points of intersection. Delphi would be prefered as programming language, but any similar will do (C, Java, VB etc.).

To clarify:
- This is not home or course work. It's just a puzzle piece I need for a larger software project. I already posted this problem on various math help user boards, but nobody there seems to be able to point to a reasonably simple solution.
- I need just the bare-bone function, as stated in the project description. No gui of any kind is required.
- I already have a "solution" which is rather complex and computational expensive and does so not fit the apparent simplicity of the problem. There just has to be a better solution.

To give a better understanding of the context in which this function will be used:
- Image processing software, that computes certain information by analyzing source images
- Function has to be executed 256 times for every pixel in 5000x4000px source files (approx. 5,000,000,000 times per image) with no room for optimization.
- To achieve reasonable run times, the implementation has to be quite fast. My current implementation takes about 5s for 10,000,000 runs (2010 MacPro). Obviously, I'm looking for an implementation that is faster than that.

Compétences : Mathématiques

Voir plus : vectors programming, vectors point of intersection, vectors in c programming, vector intersect, vector in c language, the r programming language, simple programming language, programming vector, programming language r, problem of points solution, point of intersection, point intersection, on the intersection, number mathematics, m programming language, intersection points, intersection point, intersection of vectors, intersection and, delphi language programming, b programming language, a point of intersection, a intersection b, Sphere, simple language

Concernant l'employeur :
( 4 commentaires ) Leipzig, Germany

N° du projet : #1037141

Décerné à :

doi6

Hi, i have a solution for the intersecting circles which uses only 12 arithmetic and 9 vectorial operations to get the points. I can give you a Delphi solution.

50 $ USD en 3 jours
(0 Commentaires)
2.2

15 freelance ont fait une offre moyenne de 77 $ pour ce travail

navi1974

Hi! Very nice problem! Please check your PMB.

60 $ USD en 2 jours
(10 Commentaires)
6.0
Raghavanps

see private message

75 $ USD en 5 jours
(2 Commentaires)
4.3
JohnBHarris

You have presented an interesting problem - I like the drawing ! I have a Mathematics degree and stacks of experience programming in C/C++/C# so I am confident I can do this. Do you want graphics output - or just a con Plus

75 $ USD en 3 jours
(0 Commentaires)
0.0
topcoder0

I can do it

30 $ USD en 3 jours
(0 Commentaires)
0.0
udaykiranc

Hi, I am a graduating student in International Institute of Information Technology, Hyderabad in India. I participate in many coding competitions. I did so many problems in c & c++. I can do that code in c,c++ or a Plus

30 $ USD en 2 jours
(0 Commentaires)
0.0
hamurapi111

please check your pm

80 $ USD en 2 jours
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0.0
CDspace

Please Check PM

75 $ USD en 2 jours
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0.0
memethief

Please check PM for details.

80 $ USD en 2 jours
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0.0
santoah

Dear, I'm expert in Math and liked this job. I'd already solved the first 3 items. As I'm in a Bussiness trip I don't have access to Delphi (I've it in my personal computer), but I can send you it implemented in Plus

50 $ USD en 1 jour
(1 Commentaire)
1.0
millesaRin

i am a mathematician and having more than 8 years experience in the field of teaching you may contact me thanks

200 $ USD en 5 jours
(0 Commentaires)
0.0
chinmayk

I liked this problem and I have worked on such problems in the past.

50 $ USD en 2 jours
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0.0
zizo0003

Please check your inbox.

60 $ USD en 1 jour
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0.0
ksrslm

I am ready to solve this problem in 2 days

200 $ USD en 5 jours
(0 Commentaires)
0.0
EdwardNigma

On a 1.5 Ghz single core laptop, I am getting 5 seconds for 10,000,000 randomly generated pairs of circles and 55 seconds for 100,000,000. I assume it would run faster on your computer. The function is very simple, not Plus

40 $ USD en 2 jours
(0 Commentaires)
0.0