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List:       mesa3d-dev
Subject:    Re: [Mesa3d-dev] Color Interpolation
From:       Brian Paul <brian.paul () tungstengraphics ! com>
Date:       2005-04-25 15:56:06
Message-ID: 426D1316.8030201 () tungstengraphics ! com
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³¯¥¿­õ(Murphy Chen) wrote:
> In Mesa, color interpolation is calculated as follows:
> 
> /* Y(vMin)<=Y(vMid)<=Y(vMax) */
> 
> const GLfloat area = eMaj.dx * eBot.dy - eBot.dx * eMaj.dy;
> GLfloat oneOverArea = 1.0F / area;
> GLfloat eMaj_dr = (GLfloat) ((ColorTemp) vMax->color[RCOMP] - (ColorTemp) vMin->color[RCOMP]);
> GLfloat eBot_dr = (GLfloat) ((ColorTemp) vMid->color[RCOMP] - (ColorTemp) vMin->color[RCOMP]);
> span.drdx = oneOverArea * (eMaj_dr * eBot.dy - eMaj.dy * eBot_dr);
> span.drdy = oneOverArea * (eMaj.dx * eBot_dr - eMaj_dr * eBot.dx);
> 
> I'd like to know how drdx and drdy is deduced?

They're the partial derivatives of color with respect to x and y.

If you consider Z instead of color, think of a triangle in 3-space.
If you want to determine the change in Z over X and Y you'd plug in X
and X+1 into the plane equation for some Y to get the change in Z.  If
you simplify that arithmetic you'll eventually arrive at expressions
like you see above.

I haven't worked through that arithmetic in a while.  But the cross
product of two edge vectors, normalized according to the area of the
triangle is directly related to the dz/dx and dz/dy terms.

-Brian


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