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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.).

Kỹ năng: Toán học

Xem thêm: vectors point intersection, vectors programming, vector intersect, vector language, simple programming language, programming vector, problem points solution, number mathematics, intersection points, intersection point, intersection vectors, intersection and, delphi language programming, point intersection, sphere, simple language, r seven, problem, problem java, Mathematics problem , mathematics 3, mathematical m, java problem, c1, programming java solution

Về Bên Thuê:
( 4 nhận xét ) Leipzig, Germany

Mã Dự Án: #1037141

Đã trao cho:

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 trong 3 ngày
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2.2

15 freelancer đang chào giá trung bình $77 cho công việc này

navi1974

Hi! Very nice problem! Please check your PMB.

$60 USD trong 2 ngày
(10 Đánh Giá)
6.0
Raghavanps

see private message

$75 USD trong 5 ngày
(2 Đánh Giá)
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 Thêm

$75 USD trong 3 ngày
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0.0
topcoder0

I can do it

$30 USD trong 3 ngày
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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 Thêm

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hamurapi111

please check your pm

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CDspace

Please Check PM

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memethief

Please check PM for details.

$80 USD trong 2 ngày
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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 Thêm

$50 USD trong 1 ngày
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1.0
millesaRin

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

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chinmayk

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

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zizo0003

Please check your inbox.

$60 USD trong 1 ngày
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ksrslm

I am ready to solve this problem in 2 days

$200 USD trong 5 ngày
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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 Thêm

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