faultymoose

10-06-2006, 01:24 AM

Hiya, I'm having a serious dilemma, and my brain is threatening to leave me if I continue to hammer it with this problem:

We have object "N" which is point constrained between three objects, A, B and C, with (normalised) weight values of i, j and k.

Object N's position is found by:

N = Ai + Bj + Ck

Given N, A, B and C... how do we find i, j and k?

I attempted to solve using this equation and I share what follows purely for amusement and out of a masochistic desire to be told my maths is horribly, horribly wrong, SO, anyone seeking to answer my question, please ignore what follows because I don't think this is the road to the solution.

We know that:

i + j + k = 1

Taking the long and arduous road of trying-to-remember-highschool-maths, I substituted i = 1 - j - k into the equation to get:

N = A(1 - j - k) + Bj + Ck

= A - Aj - Ak + Bj + Ck

Not sure if this was helping me or not, I ran some tests substituting values for k until I came up with the further equation:

j = ( N - ( A(1-k) + Ck) ) / (B - A)

I can't remember how to prove an 'estimated' equation so I just kept throwing numbers at it and it kept working, so with the glimmer of scientific discovery (manic psychotic disassociation) I went through a small forest in paper to end up with.... nothing usable.

I have before me pages and pages of mathematical substitution and minimisation and...all

this...number...stuff. The end result?

N = A ( 1 - ( ( N - ( A ( 1 - k ) + Ck ) ) / ( B - A ) ) ) + B ( ( N - ( A ( 1 - k ) + Ck ) ) / ( B - A ) ) + Ck

Just thought I'd share. For those real mathematicians out there, please excuse my heavy handling of your art.

EDIT: I should add that the first couple of pages of my attempt to minimise this equation resulted in the accidental discovery of the groundbreaking mathematical formula:

N = N

We have object "N" which is point constrained between three objects, A, B and C, with (normalised) weight values of i, j and k.

Object N's position is found by:

N = Ai + Bj + Ck

Given N, A, B and C... how do we find i, j and k?

I attempted to solve using this equation and I share what follows purely for amusement and out of a masochistic desire to be told my maths is horribly, horribly wrong, SO, anyone seeking to answer my question, please ignore what follows because I don't think this is the road to the solution.

We know that:

i + j + k = 1

Taking the long and arduous road of trying-to-remember-highschool-maths, I substituted i = 1 - j - k into the equation to get:

N = A(1 - j - k) + Bj + Ck

= A - Aj - Ak + Bj + Ck

Not sure if this was helping me or not, I ran some tests substituting values for k until I came up with the further equation:

j = ( N - ( A(1-k) + Ck) ) / (B - A)

I can't remember how to prove an 'estimated' equation so I just kept throwing numbers at it and it kept working, so with the glimmer of scientific discovery (manic psychotic disassociation) I went through a small forest in paper to end up with.... nothing usable.

I have before me pages and pages of mathematical substitution and minimisation and...all

this...number...stuff. The end result?

N = A ( 1 - ( ( N - ( A ( 1 - k ) + Ck ) ) / ( B - A ) ) ) + B ( ( N - ( A ( 1 - k ) + Ck ) ) / ( B - A ) ) + Ck

Just thought I'd share. For those real mathematicians out there, please excuse my heavy handling of your art.

EDIT: I should add that the first couple of pages of my attempt to minimise this equation resulted in the accidental discovery of the groundbreaking mathematical formula:

N = N