Josh Seagoe wrote:
> 

> > universal formula for area of triangle:
> >
> > S=sqrt(p*(p-a)*(p-b)*(p-c))
> >
> > where a,b,c are lengths of edges and p is half of perimeter = (a+b+c)/2
> >
> 
> Is that faster than using half the cross product of two of the sides?
> (cosidering vcross is internal...)
> 
> Something like:
> area = vlength(vcross(P1-P2,P3-P2))/2;

I have not looked at their mesh code yet,
but I assume that they are calculating
the normal vectors for the triangles by
just taking the cross product of a pair
of each triangle's "edge vectors".

And if this is the case, then I don't see
the point in first calculating this cross
product, normalize it and then multiply
it by your area expression.

I.e.:

vnormalize(vcross(P1 - P2, P3 - P2))
*vlength(vcross(P1 - P2, P3 - P2))/2

They could just use the cross product
directly:

vcross(P1 - P2, P3 - P2)/2

And they don't even have to divide it
by 2 prior to the summing. Because
every triangle normal will be "double"
length.

The final normalizing of the sum of
all the "weighted" normal vectors will
eliminate it anyway.


Tor Olav

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