Path: chuka.playstation.co.uk!news
From: "Graeme Evans" <evans@fourny.demon.co.uk>
Newsgroups: scee.yaroze.programming.3d_graphics
Subject: Re: Quirky Maths Prob
Date: Thu, 22 Jan 1998 20:15:57 -0000
Organization: Yaloozer
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I think this is a simultaneous equations problem

What you want to find is the equation of the plane

Z=aX+bY+c

then rearrange it in the form Y=(Z-aX-c)/b

All you need to find are the variables a, b and c.

You have three equations

z1 = ax1 + by1 + c
z2 = ax2 + by2 + c
z3 = ax3 + by3 + c

So you have enough pairs of simultaneous equations to solve for a, b and c

And the answer is;

b = -(-z2*x3+z2*x1+x2*z3-x2*z1+z1*x3-x1*z3)/
(-x2*y3+x2*y1+y2*x3-y2*x1+x1*y3-y1*x3)

a = (z3*y2-z3*y1-y3*z2+y3*z1-z1*y2+y1*z2)/
(-x2*y3+x2*y1+y2*x3-y2*x1+x1*y3-y1*x3)

c = (-y3*x2*z1+z1*y2*x3-z3*y2*x1+y3*z2*x1-y1*z2*x3+z3*x2*y1)/
(-x2*y3+x2*y1+y2*x3-y2*x1+x1*y3-y1*x3)

heh heh

Graeme