// Persistence of Vision Ray Tracer Macro Definition File
// File: 8DInterp.inc
// Vers: 3.1
// Desc: Interpolation routines for the 8th Day Macro Library. 
//       Functions in this file based upon an artile on Perlin Noise at:
//       'The Good-Looking Textured Light-Sourced Bouncy Fun Smart & Stretchy Page'
//       http://freespace.virgin.net/hugo.elias/ 
// Date: January, 2000 
// Auth: Lonnie Ezell

// Single Inclusion
// this attempts to save parsing time by
// limiting this file to being parsed only once
// even when included in multiple files.
#ifndef (ED_INTERP_INC)
#declare ED_INTERP_INC = 1;   
	                 
//------------------------------ Includes ------------------------------//

//------------------------------ Declarations --------------------------//

//------------------------------ Macros --------------------------------//

// Linear Interpolation
// Used for the fastest interpolation, however, results
// may be less than desired.
//
// REQUIRES:	a - first of the numbers to be interpolated between (float)
//					b - second of the numbers to be interpolated between (float)
//             m_x - the ratio to base our interp on. If m_x=0, returns a
//						 If m_x=1 returns b (float between 0 and 1)
//
// RETURNS:    a number between v1 and v2 based upon m_x
#macro ED_LinearInterpolate(a, b, m_x)
	( a * (1 - m_x) + b * m_x )
#end		// ED_LinearInterpolate  


// Cosine Interpolation
// Used for a compromise between speed and results.
//
// REQUIRES:	see Linear Interpolation
//
// RETURNS:    a number between v1 and v2 based upon m_x
#macro ED_CosineInterpolate(a, b, m_x)
	#local ft = m_x * 3.1415927;
	#local f = (1 - cos(ft)) * 0.5;
	( a * (1 - f) + b * f )
#end		// ED_CosineInterpolate  


// Cubic Interpolation
// Provides the best results, though no guarantee they
// will be all that much better than Cosine Interpolation
//
// REQUIRES:   v0 - the point before a (float)
//             v1 - the point a (float)
//             v2 - the point b (float)
//             v3 - the point after b (float)
//             m_x - see Linear Interpolate (float between 0 and 1)	
//
// RETURNS:    a number between v1 and v2 based upon m_x
#macro ED_CubicInterpolate(v0, v1, v2, v3, m_x)
   #local P = (v3 - v2) - (v0 - v1);
   #local Q = (v0 - v1) - P;
   #local R =  v2 - v0;
   
   ( (P * pow(m_x, 3)) + (Q * pow(m_x,2)) + (R * X) + v1 )
#end     // ED_CubicInterpolate
                 
#end		// Single Inclusion Block