source: downloads/Tools/LightwaveConverter/src/lwEnvelope.cpp @ 7

#include "lwEnvelope.h"

lwKey *lwEnvelope::addKey( float time, float value )
{
        lwKey *key = new lwKey(time, value);    
        keys.insert(lower_bound(keys.begin(), keys.end(), key), key);
        return key;
}

/*======================================================================
range()
  
Given the value v of a periodic function, returns the equivalent value
v2 in the principal interval [lo, hi].  If i isn't NULL, it receives
the number of wavelengths between v and v2.
        
v2 = v - i * (hi - lo)
        
For example, range( 3 pi, 0, 2 pi, i ) returns pi, with i = 1.
====================================================================== */

float lwEnvelope::range( float v, float lo, float hi, int *i )
{
        float v2, r = hi - lo;
        
        if ( r == 0.0 ) {
                if ( i ) *i = 0;
                return lo;
        }
        
        v2 = lo + v - r * ( float ) floor(( double ) v / r );
        if ( i ) *i = -( int )(( v2 - v ) / r + ( v2 > v ? 0.5 : -0.5 ));
        
        return v2;
}

/*======================================================================
hermite()

Calculate the Hermite coefficients.
====================================================================== */

void lwEnvelope::hermite( float t, float *h1, float *h2, float *h3, float *h4 )
{
        float t2, t3;
        
        t2 = t * t;
        t3 = t * t2;
        
        *h2 = 3.0f * t2 - t3 - t3;
        *h1 = 1.0f - *h2;
        *h4 = t3 - t2;
        *h3 = *h4 - t2 + t;
}

/*======================================================================
bezier()

Interpolate the value of a 1D Bezier curve.
====================================================================== */

float lwEnvelope::bezier( float x0, float x1, float x2, float x3, float t )
{
        float a, b, c, t2, t3;
        
        t2 = t * t;
        t3 = t2 * t;
        
        c = 3.0f * ( x1 - x0 );
        b = 3.0f * ( x2 - x1 ) - c;
        a = x3 - x0 - c - b;
        
        return a * t3 + b * t2 + c * t + x0;
}


/*======================================================================
bez2_time()

Find the t for which bezier() returns the input time.  The handle
endpoints of a BEZ2 curve represent the control points, and these have
(time, value) coordinates, so time is used as both a coordinate and a
parameter for this curve type.
====================================================================== */
  
float lwEnvelope::bez2_time( float x0, float x1, float x2, float x3, float time,        float *t0, float *t1 )
{
        float v, t;
        
        t = *t0 + ( *t1 - *t0 ) * 0.5f;
        v = bezier( x0, x1, x2, x3, t );
        if ( fabs( time - v ) > .0001f ) {
                if ( v > time )
                        *t1 = t;
                else
                        *t0 = t;
                return bez2_time( x0, x1, x2, x3, time, t0, t1 );
        }
        else
                return t;
}
  
  
  /*
  ======================================================================
  bez2()
  
        Interpolate the value of a BEZ2 curve.
  ====================================================================== */
  
float lwEnvelope::bez2( lwKey *key0, lwKey *key1, float time )
{
        float x, y, t, t0 = 0.0f, t1 = 1.0f;
        
        if ( key0->shape == ID_BEZ2 )
                x = key0->time + key0->param[ 2 ];
        else
                x = key0->time + ( key1->time - key0->time ) / 3.0f;
        
        t = bez2_time( key0->time, x, key1->time + key1->param[ 0 ], key1->time,
                time, &t0, &t1 );
        
        if ( key0->shape == ID_BEZ2 )
                y = key0->value + key0->param[ 3 ];
        else
                y = key0->value + key0->param[ 1 ] / 3.0f;
        
        return bezier( key0->value, y, key1->param[ 1 ] + key1->value, key1->value, t );
}
  
  
  /*
  ======================================================================
  outgoing()
  
        Return the outgoing tangent to the curve at key0.  The value returned
        for the BEZ2 case is used when extrapolating a linear pre behavior and
        when interpolating a non-BEZ2 span.
  ====================================================================== */
  
float lwEnvelope::outgoing( unsigned int key0, unsigned int key1 )
{
        float a, b, d, t, tout;
        
        switch ( keys[key0]->shape )
        {
        case ID_TCB:
                a = ( 1.0f - keys[key0]->tension )
                        * ( 1.0f + keys[key0]->continuity )
                        * ( 1.0f + keys[key0]->bias );
                b = ( 1.0f - keys[key0]->tension )
                        * ( 1.0f - keys[key0]->continuity )
                        * ( 1.0f - keys[key0]->bias );
                d = keys[key1]->value - keys[key0]->value;
                
                
                if ( key0 > 0 )
                {
                        t = ( keys[key1]->time - keys[key0]->time ) / ( keys[key1]->time - keys[ key0-1 ]->time );
                        tout = t * ( a * ( keys[key0]->value - keys[ key0-1 ]->value ) + b * d );
                }
                else
                        tout = b * d;
                break;
                
        case ID_LINE:
                d = keys[key1]->value - keys[key0]->value;
                if ( key0 > 0 )
                {
                        t = ( keys[key1]->time - keys[key0]->time ) / ( keys[key1]->time - keys[ key0-1 ]->time );
                        tout = t * ( keys[key0]->value - keys[ key0-1 ]->value + d );
                }
                else
                        tout = d;
                break;
                
        case ID_BEZI:
        case ID_HERM:
                tout = keys[key0]->param[ 1 ];
                
                if ( key0 > 0 )
                        tout *= ( keys[key1]->time - keys[key0]->time ) / ( keys[key1]->time - keys[ key0-1 ]->time );
                
                break;
                
        case ID_BEZ2:
                tout = keys[key0]->param[ 3 ] * ( keys[key1]->time - keys[key0]->time );
                if ( fabs( keys[key0]->param[ 2 ] ) > 1e-5f )
                        tout /= keys[key0]->param[ 2 ];
                else
                        tout *= 1e5f;
                break;
                
        case ID_STEP:
        default:
                tout = 0.0f;
                break;
        }
        
        return tout;
}
  
  
/*======================================================================
incoming()
  
Return the incoming tangent to the curve at key1.  The value returned
for the BEZ2 case is used when extrapolating a linear post behavior.
====================================================================== */
  
float lwEnvelope::incoming( unsigned int key0, unsigned int key1 )
{
        float a, b, d, t, tin;
        
        switch ( keys[key1]->shape )
        {
        case ID_LINE:
                d = keys[key1]->value - keys[key0]->value;
                
                if ( key1 < keys.size()-1 )
                {
                        t = ( keys[key1]->time - keys[key0]->time ) / ( keys[ key1+1 ]->time - keys[key0]->time );
                        tin = t * ( keys[ key1+1 ]->value - keys[key1]->value + d );
                }
                else
                        tin = d;
                
                break;
                
        case ID_TCB:
                a = ( 1.0f - keys[key1]->tension )
                        * ( 1.0f - keys[key1]->continuity )
                        * ( 1.0f + keys[key1]->bias );
                b = ( 1.0f - keys[key1]->tension )
                        * ( 1.0f + keys[key1]->continuity )
                        * ( 1.0f - keys[key1]->bias );
                d = keys[key1]->value - keys[key0]->value;
                if ( key1 < keys.size()-1 ) {
                        t = ( keys[key1]->time - keys[key0]->time ) / ( keys[ key1+1 ]->time - keys[key0]->time );
                        tin = t * ( b * ( keys[ key1+1 ]->value - keys[key1]->value ) + a * d );
                }
                else
                        tin = a * d;
                break;
                
        case ID_BEZI:
        case ID_HERM:
                tin = keys[key1]->param[ 0 ];
                if ( key1 < keys.size()-1 )
                        tin *= ( keys[key1]->time - keys[key0]->time ) / ( keys[ key1+1 ]->time - keys[key0]->time );
                break;
                return tin;
                
        case ID_BEZ2:
                tin = keys[key1]->param[ 1 ] * ( keys[key1]->time - keys[key0]->time );
                if ( fabs( keys[key1]->param[ 0 ] ) > 1e-5f )
                        tin /= keys[key1]->param[ 0 ];
                else
                        tin *= 1e5f;
                break;
                
        case ID_STEP:
        default:
                tin = 0.0f;
                break;
        }
        
        return tin;
}

/*======================================================================
evalEnvelope()

Given a list of keys and a time, returns the interpolated value of the
envelope at that time.
====================================================================== */
  
float lwEnvelope::evaluate( float time )
{
        lwKey *key0, *key1, *skey, *ekey;
        float t, h1, h2, h3, h4, tin, tout, offset = 0.0f;
        int noff;
        int key0index, key1index;
        
        
        /* if there's no key, the value is 0 */
        
        if ( keys.size() == 0 ) return 0.0f;
        
        /* if there's only one key, the value is constant */
        
        if ( keys.size() == 1 ) return keys[0]->value;
        
        /* find the first and last keys */
        
        key0index = 0;
        key1index = keys.size()-1;
        skey = keys[key0index];
        ekey = keys[key1index];
        
        /* use pre-behavior if time is before first key time */
        
        if ( time < skey->time )
        {
                switch ( behavior[ 0 ] )
                {
                case BEH_RESET:
                        return 0.0f;
                        
                case BEH_CONSTANT:
                        return skey->value;
                        
                case BEH_REPEAT:
                        time = range( time, skey->time, ekey->time, NULL );
                        break;
                        
                case BEH_OSCILLATE:
                        time = range( time, skey->time, ekey->time, &noff );
                        if ( noff % 2 )
                                time = ekey->time - skey->time - time;
                        break;
                        
                case BEH_OFFSET:
                        time = range( time, skey->time, ekey->time, &noff );
                        offset = noff * ( ekey->value - skey->value );
                        break;
                        
                case BEH_LINEAR:
                        tout = outgoing( key0index, key0index+1 ) / ( keys[key0index+1]->time - keys[key0index]->time );

                        return tout * ( time - skey->time ) + skey->value;
                }
        }
        
        /* use post-behavior if time is after last key time */
        
        else if ( time > ekey->time ) {
                switch ( behavior[ 1 ] )
                {
                case BEH_RESET:
                        return 0.0f;
                        
                case BEH_CONSTANT:
                        return ekey->value;
                        
                case BEH_REPEAT:
                        time = range( time, skey->time, ekey->time, NULL );
                        break;
                        
                case BEH_OSCILLATE:
                        time = range( time, skey->time, ekey->time, &noff );
                        if ( noff % 2 )
                                time = ekey->time - skey->time - time;
                        break;
                        
                case BEH_OFFSET:
                        time = range( time, skey->time, ekey->time, &noff );
                        offset = noff * ( ekey->value - skey->value );
                        break;
                        
                case BEH_LINEAR:
                        tin = incoming( key1index-1, key1index ) / ( ekey->time - keys[key1index-1]->time );
                        return tin * ( time - ekey->time ) + ekey->value;
                }
        }
        
        /* get the endpoints of the interval being evaluated */
        
        key0index = keys.size()-2;
        key1index = keys.size()-1;
        key0 = keys[key0index];
        key1 = keys[key1index];
        
        /* check for singularities first */
        
        if ( time == key0->time )
                return key0->value + offset;
        else if ( time == key1->time )
                return key1->value + offset;
        
        /* get interval length, time in [0, 1] */
        
        t = ( time - key0->time ) / ( key1->time - key0->time );
        
        /* interpolate */
        
        switch ( key1->shape )
        {
        case ID_TCB:
        case ID_BEZI:
        case ID_HERM:
                tout = outgoing( key0index, key1index );
                tin = incoming( key0index, key1index );
                hermite( t, &h1, &h2, &h3, &h4 );
                return h1 * key0->value + h2 * key1->value + h3 * tout + h4 * tin + offset;
                
        case ID_BEZ2:
                return bez2( key0, key1, time ) + offset;
                
        case ID_LINE:
                return key0->value + t * ( key1->value - key0->value ) + offset;
                
        case ID_STEP:
                return key0->value + offset;
                
        default:
                return offset;
        }
}