Path: chuka.playstation.co.uk!news
From: "Peter Dollochan" <Peter.Dollochan@btinternet.com>
Newsgroups: scee.yaroze.programming.3d_graphics
Subject: Re: Quirky Maths Prob
Date: 22 Jan 1998 23:10:25 GMT
Organization: PlayStation Net Yaroze (SCEE)
Lines: 45
Message-ID: <01bd278b$91620720$683063c3@default>
References: <01bd2751$acaa0620$cc3163c3@default> <6a8935$722@chuka.playstation.co.uk>
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By god man I think you've cracked it, however I just spent the time between

post's limiting the heightfield landscape to 30 & 60 deg angles.But I'll
be sure to include this gem in the next version.

Thank for your help  Pete.

Graeme Evans <evans@fourny.demon.co.uk> wrote in article
<6a8935$722@chuka.playstation.co.uk>...
> 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
> 
> 
>