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/*
quadbezier.c:
Copyright (C) 2016 Guillermo Senna.
This file is part of Csound.
The Csound Library is free software; you can redistribute it
and/or modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
Csound is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with Csound; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA
02110-1301 USA
*/
#include "csoundCore.h"
#include <math.h>
static MYFLT SolveQuadratic(MYFLT a, MYFLT b, MYFLT c);
static MYFLT FindTforX(MYFLT x1, MYFLT x2, MYFLT x3, int32_t x);
/*
This Gen routine fills a table with the values produced by applying the
quadratic B??zier function. It is aimed at frontend developers and will
draw the correct paths as long as it is treated like a regular function.
This means that, for example, you won't be able to create a circle and
store it inside an f-table.
References:
https://pomax.github.io/bezierinfo/ -> A very concise summary on the matter.
http://stackoverflow.com/questions/5634460/quadratic-bezier-curve-calculate-point
http://stackoverflow.com/questions/27791915/quadratic-bezier-curve-calculate-t-given-x
https://github.com/vikman90/bezier
https://en.wikipedia.org/wiki/B??zier_curve
Implementation:
It is assumed that x1 equals 0 and that x[n] can't never be equal or
greater than x[n+1]. On the other hand, cx[n] can be equal to x[n] or
x[n+1].
For the coding part, I've recycled code from some of the numbered GEN
routines and specially from the "fareygen" and other named routines.
Credit for that goes to the respective authors of those routines.
*/
static int32_t quadbeziertable (FGDATA *ff, FUNC *ftp)
{
int32_t nvals, nargs, n;
MYFLT *fp = ftp->ftable;
CSOUND *csound = ff->csound;
nvals = ff->flen;
nargs = ff->e.pcnt - 4;
if (UNLIKELY(nargs < 5)) {
return csound->ftError(ff, Str("insufficient arguments"));
}
ff->e.p[4] *= -1;
for (n = 4; n < nargs; n += 4)
{
int32_t j, x1;
j = (n < 8) ? 0 : ff->e.p[n];
x1 = j;
while (j <= ff->e.p[n+4]) {
MYFLT t;
t = FindTforX(x1, ff->e.p[n+2], ff->e.p[n+4], j);
if (j <= nvals)
fp[j++] = (FL(1.0) - t) * (FL(1.0) - t) * ff->e.p[n+1] +
FL(2.0) * (FL(1.0) - t) * t * ff->e.p[n+3] + t * t * ff->e.p[n+5];
}
}
return OK;
}
/* utility functions */
inline static MYFLT SolveQuadratic(MYFLT a, MYFLT b, MYFLT c)
{
MYFLT determinant;
determinant = b*b - 4*a*c;
if (determinant >= 0)
return (-b + SQRT(determinant)) / (FL(2.0)*a);
else
return 0;
}
static MYFLT FindTforX(MYFLT x1, MYFLT x2, MYFLT x3, int32_t
x)
{
MYFLT a = (x1 - FL(2.0)*x2 + x3), b = FL(2.0)* (-x1 + x2), c = x1 - x;
if (a)
return SolveQuadratic(a, b, c);
else
return (x-x1)/b;
}
static NGFENS quadbezier_fgens[] = {
{ "quadbezier", quadbeziertable },
{ NULL, NULL }
};
FLINKAGE_BUILTIN(quadbezier_fgens)
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