Re: [Algorithms] Extracting filtered height data from quadtree terrain.

[Thatcher U. <tu...@tu...>]

On Nov 03, 2002 at 08:52 -0800, Charles Bloom wrote:
> 
> You can make the derivative continuous just by doing bilinear
> but using a "hermite lerp" or "cosine lerp" instead of linear
> lerp of the s,t parameters inside the four points.
> 
> //!	remap (0->1) to (0->1) but with derivative continuity
> inline float fHermiteLerpParameter(const float t)
> {
> 	gAssert( t >= - EPSILON && t <= 1.f + EPSILON );
> 	return (3.f - 2.f*t)*t*t;
> }
> 
> //! even better continuity than Hermite lerp, but slower
> inline float fCosLerpParameter(const float t)
> {
> 	gAssert( t >= - EPSILON && t <= 1.f + EPSILON );
> 	return 0.5f - 0.5f * cosf( t * PI );
> }

That makes the derivative continuous by ramping it to 0 at the
boundaries, correct?  That would make slopes wavy -- might look/act
weird for a heightfield.

Anyway, bicubic interpolation using 4x4 control points is the deluxe
solution here, but if the quadtree is adaptive, I'm not sure of a
correct way to collect the control points.  I'm sure there is one,
I've just never had to do it personally.

-- 
Thatcher Ulrich
http://tulrich.com