Max 5 API Reference

jit.cubicspline.c

/*
 * Copyright 2001-2005 - Cycling '74
 * Derek Gerstmann - derek@cycling74.com
 *
 * Cubic spline evaluation and utility methods
 *
 */

#include "jit.common.h"
#include "jit.cubicspline.h"
#include "jit.fixmath.h"

// --------------------------------------------------------------------------

static long g_jit_cubicspline_is_initialized = FALSE;

// --------------------------------------------------------------------------

t_symbol *ps_jit_cubicspline_basisname_bezier;
t_jit_cubicspline_basismatrix_float64 g_cubicspline_basismatrix_bezier = {
    { -1.0,       3.0,      -3.0,       1.0},
    {  3.0,      -6.0,       3.0,       0.0},
    { -3.0,       3.0,       0.0,       0.0},
    {  1.0,       0.0,       0.0,       0.0}
};

t_symbol *ps_jit_cubicspline_basisname_bspline;
t_jit_cubicspline_basismatrix_float64 g_cubicspline_basismatrix_bspline = {
    { -1.0/6.0,   0.5,    -0.5,      1.0/6.0},
    {  0.5,      -1.0,     0.5,      0.0},
    { -0.5,       0.0,     0.5,      0.0},
    {  1.0/6.0,  2.0/3.0,  1.0/6.0,  0.0}
};

t_symbol *ps_jit_cubicspline_basisname_catmullrom;
t_jit_cubicspline_basismatrix_float64 g_cubicspline_basismatrix_catmullrom = {
    { -0.5,       1.5,      -1.5,       0.5},
    {  1.0,      -2.5,       2.0,      -0.5},
    { -0.5,       0.0,       0.5,       0.0},
    {  0.0,       1.0,       0.0,       0.0}
};

t_symbol *ps_jit_cubicspline_basisname_hermite;
t_jit_cubicspline_basismatrix_float64 g_cubicspline_basismatrix_hermite = {
    {  2.0,     -2.0,        1.0,      1.0 },
    { -3.0,      3.0,       -2.0,     -1.0 },
    {  0.0,      0.0,        1.0,      0.0 },
    {  1.0,      0.0,        0.0,      0.0 }
};

t_symbol *ps_jit_cubicspline_basisname_power;
t_jit_cubicspline_basismatrix_float64 g_cubicspline_basismatrix_power = {
    {  1.0,       0.0,       0.0,       0.0},
    {  0.0,       1.0,       0.0,       0.0},
    {  0.0,       0.0,       1.0,       0.0},
    {  0.0,       0.0,       0.0,       1.0}
};

// --------------------------------------------------------------------------

t_jit_err jit_cubicspline_init()
{
    // generate symbols
    ps_jit_cubicspline_basisname_bezier = gensym("bezier");
    ps_jit_cubicspline_basisname_bspline = gensym("bspline");
    ps_jit_cubicspline_basisname_catmullrom = gensym("catmullrom");
    ps_jit_cubicspline_basisname_hermite = gensym("hermite");
    ps_jit_cubicspline_basisname_power = gensym("power");
    g_jit_cubicspline_is_initialized = TRUE;
    return JIT_ERR_NONE;
}

// --------------------------------------------------------------------------

t_jit_err jit_cubicspline_fillbasis_fixed(
    t_symbol *name, t_jit_cubicspline_basismatrix_fixed *matrix, 
    long *stepcount)
{
    long i, j;

    if(!g_jit_cubicspline_is_initialized)
        jit_cubicspline_init();

    if(name && matrix && stepcount)
    {
        if(name == ps_jit_cubicspline_basisname_bezier)
        {
            *stepcount = 3;
            for(i = 0; i < 4; i++)
                for(j = 0; j < 4; j++)
                    (*matrix)[i][j] = DoubleToFixed(g_cubicspline_basismatrix_bezier[i][j]);
        }
        else if(name == ps_jit_cubicspline_basisname_bspline)
        {
            *stepcount = 1;
            for(i = 0; i < 4; i++)
                for(j = 0; j < 4; j++)
                    (*matrix)[i][j] = DoubleToFixed(g_cubicspline_basismatrix_bspline[i][j]);
        }
        else if(name == ps_jit_cubicspline_basisname_catmullrom)
        {
            *stepcount = 1;
            for(i = 0; i < 4; i++)
                for(j = 0; j < 4; j++)
                    (*matrix)[i][j] = DoubleToFixed(g_cubicspline_basismatrix_catmullrom[i][j]);
        }
        else if(name == ps_jit_cubicspline_basisname_hermite)
        {
            *stepcount = 2;
            for(i = 0; i < 4; i++)
                for(j = 0; j < 4; j++)
                    (*matrix)[i][j] = DoubleToFixed(g_cubicspline_basismatrix_hermite[i][j]);
        }
        else if(name == ps_jit_cubicspline_basisname_power)
        {
            *stepcount = 4;
            for(i = 0; i < 4; i++)
                for(j = 0; j < 4; j++)
                    (*matrix)[i][j] = DoubleToFixed(g_cubicspline_basismatrix_power[i][j]);
        }
        else
        {
            // invalid basis name
            return JIT_ERR_GENERIC;
        }
        
        // no error
        return JIT_ERR_NONE;
    }
    
    // invalid pointer or index
    return JIT_ERR_GENERIC;
}

t_jit_err jit_cubicspline_fillbasis_float32(
    t_symbol *name, t_jit_cubicspline_basismatrix_float32 *matrix, 
    long *stepcount)
{
    long i, j;

    if(!g_jit_cubicspline_is_initialized)
        jit_cubicspline_init();

    if(name && matrix && stepcount)
    {
        if(name == ps_jit_cubicspline_basisname_bezier)
        {
            *stepcount = 3;
            for(i = 0; i < 4; i++)
                for(j = 0; j < 4; j++)
                    (*matrix)[i][j] = (float)g_cubicspline_basismatrix_bezier[i][j];
        }
        else if(name == ps_jit_cubicspline_basisname_bspline)
        {
            *stepcount = 1;
            for(i = 0; i < 4; i++)
                for(j = 0; j < 4; j++)
                    (*matrix)[i][j] = (float)g_cubicspline_basismatrix_bspline[i][j];
        }
        else if(name == ps_jit_cubicspline_basisname_catmullrom)
        {
            *stepcount = 1;
            for(i = 0; i < 4; i++)
                for(j = 0; j < 4; j++)
                    (*matrix)[i][j] = (float)g_cubicspline_basismatrix_catmullrom[i][j];
        }
        else if(name == ps_jit_cubicspline_basisname_hermite)
        {
            *stepcount = 2;
            for(i = 0; i < 4; i++)
                for(j = 0; j < 4; j++)
                    (*matrix)[i][j] = (float)g_cubicspline_basismatrix_hermite[i][j];
        }
        else if(name == ps_jit_cubicspline_basisname_power)
        {
            *stepcount = 4;
            for(i = 0; i < 4; i++)
                for(j = 0; j < 4; j++)
                    (*matrix)[i][j] = (float)g_cubicspline_basismatrix_power[i][j];
        }
        else
        {
            // invalid basis name
            return JIT_ERR_GENERIC;
        }
        
        // no error
        return JIT_ERR_NONE;
    }
    
    // invalid pointer or index
    return JIT_ERR_GENERIC;
}

t_jit_err jit_cubicspline_fillbasis_float64(
    t_symbol *name, t_jit_cubicspline_basismatrix_float64 *matrix, 
    long *stepcount)
{
    long i, j;

    if(!g_jit_cubicspline_is_initialized)
        jit_cubicspline_init();

    if(name && matrix && stepcount)
    {
        if(name == ps_jit_cubicspline_basisname_bezier)
        {
            *stepcount = 3;
            for(i = 0; i < 4; i++)
                for(j = 0; j < 4; j++)
                    (*matrix)[i][j] = (double)g_cubicspline_basismatrix_bezier[i][j];
        }
        else if(name == ps_jit_cubicspline_basisname_bspline)
        {
            *stepcount = 1;
            for(i = 0; i < 4; i++)
                for(j = 0; j < 4; j++)
                    (*matrix)[i][j] = (double)g_cubicspline_basismatrix_bspline[i][j];
        }
        else if(name == ps_jit_cubicspline_basisname_catmullrom)
        {
            *stepcount = 1;
            for(i = 0; i < 4; i++)
                for(j = 0; j < 4; j++)
                    (*matrix)[i][j] = (double)g_cubicspline_basismatrix_catmullrom[i][j];
        }
        else if(name == ps_jit_cubicspline_basisname_hermite)
        {
            *stepcount = 2;
            for(i = 0; i < 4; i++)
                for(j = 0; j < 4; j++)
                    (*matrix)[i][j] = (double)g_cubicspline_basismatrix_hermite[i][j];
        }
        else if(name == ps_jit_cubicspline_basisname_power)
        {
            *stepcount = 4;
            for(i = 0; i < 4; i++)
                for(j = 0; j < 4; j++)
                    (*matrix)[i][j] = (double)g_cubicspline_basismatrix_power[i][j];
        }
        else
        {
            // invalid basis name
            return JIT_ERR_GENERIC;
        }
        
        // no error
        return JIT_ERR_NONE;
    }
    
    // invalid pointer or index
    return JIT_ERR_GENERIC;
}

long jit_cubicspline_general_eval_fixed(
    long val, long stepcount, long knotcount, long *knots, 
    t_jit_cubicspline_basismatrix_fixed matrix)
{ 
    long k0, k1, k2, k3;
    long c0, c1, c2, c3;
    long a, b, c;
    long t, u;

    long span = 0;
    long spancount = 0;
    long index = 0;

    // safety
    if(!knots || stepcount < 1)
        return FloatToFixed(0.0f);

    // find the appropriate 4-point span of the spline to eval
    t = val;
    spancount = ((knotcount - 4) / stepcount) + 1;

    // sanity
    if(spancount < 1)
        return FloatToFixed(0.0f);

    u = FloatToFixed((float)spancount * FixedToFloat(t));
    span = (long)FixedToFloat(u);

    t = u - span;
    index = span * stepcount;

    // get the control points
    k0 = knots[ index + 0 ];
    k1 = knots[ index + 1 ];
    k2 = knots[ index + 2 ];
    k3 = knots[ index + 3 ];

    // evaluate using horners rule
    c0 = FixMul3(matrix[3][0], k0) + FixMul3(matrix[3][1], k1)
       + FixMul3(matrix[3][2], k2) + FixMul3(matrix[3][3], k3);

    c1 = FixMul3(matrix[2][0], k0) + FixMul3(matrix[2][1], k1)
       + FixMul3(matrix[2][2], k2) + FixMul3(matrix[2][3], k3);

    c2 = FixMul3(matrix[1][0], k0) + FixMul3(matrix[1][1], k1)
       + FixMul3(matrix[1][2], k2) + FixMul3(matrix[1][3], k3);

    c3 = FixMul3(matrix[0][0], k0) + FixMul3(matrix[0][1], k1)
       + FixMul3(matrix[0][2], k2) + FixMul3(matrix[0][3], k3);

    a = FixMul(c3, val) + c2;
    b = FixMul(a, val) + c1;
    c = FixMul(b, val) + c0;
    return c;
}

float jit_cubicspline_general_eval_float32(
    float val, long stepcount, long knotcount, float *knots, 
    t_jit_cubicspline_basismatrix_float32 matrix)
{ 
    float k0, k1, k2, k3;
    float c0, c1, c2, c3;
    float t, u;

    long span = 0;
    long spancount = 0;
    long index = 0;

    // safety
    if(!knots || stepcount < 1)
        return 0.0f;

    // find the appropriate 4-point span of the spline to eval
    t = val;
    spancount = ((knotcount - 4) / stepcount) + 1;

    // sanity
    if(spancount < 1)
        return 0.0f;

    u = (float)spancount * t;
    span = (long)u;

    t = u - span;
    index = span * stepcount;

    // get the control points
    k0 = knots[ index + 0 ];
    k1 = knots[ index + 1 ];
    k2 = knots[ index + 2 ];
    k3 = knots[ index + 3 ];

    // evaluate using horners rule
    c0 = matrix[3][0] * k0 + matrix[3][1] * k1
       + matrix[3][2] * k2 + matrix[3][3] * k3;

    c1 = matrix[2][0] * k0 + matrix[2][1] * k1
       + matrix[2][2] * k2 + matrix[2][3] * k3;

    c2 = matrix[1][0] * k0 + matrix[1][1] * k1
       + matrix[1][2] * k2 + matrix[1][3] * k3;

    c3 = matrix[0][0] * k0 + matrix[0][1] * k1
       + matrix[0][2] * k2 + matrix[0][3] * k3;

    return ( ( c3 * t + c2 ) * t + c1 ) * t + c0;
}

double jit_cubicspline_general_eval_float64(
    double val, long stepcount, long knotcount, double *knots, 
    t_jit_cubicspline_basismatrix_float64 matrix)
{ 
    double k0, k1, k2, k3;
    double c0, c1, c2, c3;
    double t, u;

    long span = 0;
    long spancount = 0;
    long index = 0;

    // safety
    if(!knots || stepcount < 1)
        return 0.0f;

    // find the appropriate 4-point span of the spline to eval
    t = val;
    spancount = ((knotcount - 4) / stepcount) + 1;

    // sanity
    if(spancount < 1)
        return 0.0;

    u = (float)spancount * t;
    span = (long)u;

    t = u - span;
    index = span * stepcount;

    // get the control points
    k0 = knots[ index + 0 ];
    k1 = knots[ index + 1 ];
    k2 = knots[ index + 2 ];
    k3 = knots[ index + 3 ];

    // evaluate using horners rule
    c0 = matrix[3][0] * k0 + matrix[3][1] * k1
       + matrix[3][2] * k2 + matrix[3][3] * k3;

    c1 = matrix[2][0] * k0 + matrix[2][1] * k1
       + matrix[2][2] * k2 + matrix[2][3] * k3;

    c2 = matrix[1][0] * k0 + matrix[1][1] * k1
       + matrix[1][2] * k2 + matrix[1][3] * k3;

    c3 = matrix[0][0] * k0 + matrix[0][1] * k1
       + matrix[0][2] * k2 + matrix[0][3] * k3;

    return ( ( c3 * t + c2 ) * t + c1 ) * t + c0;
}

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