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Hermite.cc

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/*
    File:       Hermite.cc

    Function:   

    Author:     Andrew Willmott

    Notes:      
*/

#include "gcl/Hermite.h"


/* This basis takes [x(0),x(1),x'(0),x'(1)] as knot points   
   Each column holds the coefficients of one of the Hermite 
   polynomials. */

static Transform gHermiteMatrix(
     1.0,  0.0,  0.0,  0.0, 
     0.0,  0.0,  1.0,  0.0,
    -3.0,  3.0, -2.0, -1.0,
     2.0, -2.0,  1.0,  1.0
);


/*
    Calculate hermite coefficients.

    t0, y0, ySlope0 are start time, value, and slope.
    t1, y1, ySlope1 are end time, value, and slope.
    t1 had better not equal t0.
        
    For automatic slope control, set 
        ySlope1 = (y2 - y0) / (t2 - t0);
        ySlope0 = (y1 - y-1) / (t1 - t-1);
*/

Void CalcHermiteCoeffs(
        GCLReal     t0,
        GCLReal     t1,
        GCLReal     y0,
        GCLReal     y1,
        GCLReal     ySlope0,
        GCLReal     ySlope1,
        Cubic       &result
    )
{
    result = gHermiteMatrix * 
        Cubic(y0, y1, ySlope0 * (t1 - t0), ySlope1 * (t1 - t0));
}

GCLReal EvalCubic(Cubic &cubicCoeffs, GCLReal t, GCLReal t0, GCLReal t1)
//  evaluate y(t), using coeffs computed by CalcHermiteCoeffs().
//  t0, t1 have to be same as you supplied to CalcHermiteCoeffs().
//  t should be between t0 and t1, inclusive.
{
    GCLReal u = (t - t0) / (t1 - t0);
    Cubic   uCubic(1, u, sqr(u), sqr(u) * u);

    return(dot(uCubic, cubicCoeffs));
}


/*
    Here's a dumb sample program that interpolates values of y between
    frame 0 and frame 30:
*/

#ifdef HM_DEBUG
#include <stdio.h>

main()
{
    Cubic   coeffs;
    GCLReal t0 = 0, t1 = 30;
    GCLReal y0 = 1,  y1 = 3;
    GCLReal dy0 = .2, dy1 = 0;
    Int     t;

    CalcHermiteCoeffs(t0, t1, y0, y1, dy0, dy1, coeffs);

    for(t = 0; t < 31; t++)
        printf("\ny(%d) = %f", t, EvalCubic(coeffs, t, t0, t1) );
}

#endif

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