/* Copyright (c) 2004-2010, Dirk Krause All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. * Redistributions in binary form must reproduce the above opyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. * Neither the name of the Dirk Krause nor the names of contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ /** @file dkbsp.c The Bezier splines module. */ /** Inside the dkbsp module. */ #define DKBSP_C 1 #include "dkbsp.h" #if DK_HAVE_MATH_H #include #endif #if DK_HAVE_STDLIB_H #include #endif #include #line 61 "dkbsp.ctr" /** Calculate Bezier spline control points from x_0, dx/dt at x_0, dx/dt at x_1 and x_1. The result is stored in the dk_bspline_t structure. @param s Bezier spline structure. @param x0 x at start of interval. @param d0 dx/dt at x0. @param x1 x at end of interval. @param d1 dx/dt at x1. @return 1 on success, 0 on error. */ int dkbsp_calculate DK_P5(dk_bspline_t *,s,double,x0,double,d0,double,x1,double,d1) { int back = 0; /* Function result. */ int ok = 0; /* Flag: Mathematical error. */ if(s) { back = 1; s->x0 = x0; s->x1 = x1; s->dxdt0 = d0; s->dxdt1 = d1; s->xp0 = dkma_add_double_ok(x0, (d0/3.0), &ok); s->xm1 = dkma_sub_double_ok(x1, (d1/3.0), &ok); if(ok) { back = 0; } } return back; } /** Apply variable, calculate value and derivative to find minimum and maximum. @param s Bezier spline structure. @param t The t value. @return 1 on success, 0 on error. */ static int apply_t_for_min_max DK_P2(dk_bspline_t *,s,double,t) { int back = 1, ok = 0; double x, tt, ttt, a, aa, aaa; tt = dkma_mul_double_ok(t,t,&ok); ttt = dkma_mul_double_ok(tt,t,&ok); a = dkma_sub_double_ok(1.0, t, &ok); aa = dkma_mul_double_ok(a,a,&ok); aaa = dkma_mul_double_ok(aa,a,&ok); x = dkma_add_double_ok( dkma_add_double_ok( dkma_mul_double_ok(s->x0, aaa, &ok), dkma_mul_double_ok( dkma_mul_double_ok(s->xp0, aa, &ok), dkma_mul_double_ok(3.0, t, &ok), &ok ), &ok ), dkma_add_double_ok( dkma_mul_double_ok( dkma_mul_double_ok(s->xm1, a, &ok), dkma_mul_double_ok(3.0, tt, &ok), &ok ), dkma_mul_double_ok(s->x1, ttt, &ok), &ok ), &ok ); if(x > s->max) { s->max = x; } if(x < s->min) { s->min = x; } if(ok) back = 0; return back; } /** Calculate minimum and maximum x value for a Bezier spline segment. @param s Bezier spline structure. @param x0 X-value of "left" control point. @param d0 X-value of second control point. @param x1 X-value of "right" control point. @param d1 X-value of third control point. @return 1 on success, 0 on error. */ int dkbsp_minmax DK_P5(dk_bspline_t *,s,double,x0,double,d0,double,x1,double,d1) { int back = 0, ok = 0, test = 0, tneeded = 0; double a, b, c, p, q, wurzel, t, t0; if(s) { back = dkbsp_calculate(s,x0,d0,x1,d1); if(s->x0 > s->x1) { s->max = s->x0; s->min = s->x1; } else { s->max = s->x1; s->min = s->x0; } if(back) { a = dkma_mul_double_ok( 3.0, dkma_add_double_ok( dkma_sub_double_ok(s->x1, s->xm1, &ok), dkma_sub_double_ok(s->xp0, s->x0, &ok), &ok ), &ok ); b = dkma_mul_double_ok( 2.0, dkma_add_double_ok( dkma_sub_double_ok( s->xm1, dkma_mul_double_ok(2.0, s->xp0, &ok), &ok ), dkma_mul_double_ok(3.0, s->x0, &ok), &ok ), &ok ); c = dkma_sub_double_ok( s->xp0, dkma_mul_double_ok(3.0, s->x0, &ok), &ok ); t = 0.0; tneeded = 1; p = dkma_div_double_ok(b,a,&test); if(test) { t = 0.0 - dkma_div_double_ok(c,b,&ok); if((ok == 0) && (t >= 0.0) && (t <= 1.0)) { if(!apply_t_for_min_max(s, t)) { back = 0; } } } else { q = dkma_div_double_ok(c,a,&ok); t0 = 0.0 - dkma_div_double_ok(p, 2.0, &ok); wurzel = dkma_sub_double_ok( dkma_mul_double_ok(t0, t0, &ok), q, &ok ); if(wurzel >= 0.0) { wurzel = sqrt(wurzel); t = dkma_add_double_ok(t0, wurzel, &ok); if((ok == 0) && (t >= 0.0) && (t <= 1.0)) { if(!apply_t_for_min_max(s, t)) { back = 0; } } t = dkma_sub_double_ok(t0, wurzel, &ok); if((ok == 0) && (t >= 0.0) && (t <= 1.0)) { if(!apply_t_for_min_max(s, t)) { back = 0; } } } else { tneeded = 0; } } } } return back; } /** Calculate value and derivative for a given t (0<=t<=1) in a Bezier spline segment. @param s Bezier spline structure. @param x0 "Left" control point. @param xp Second control point. @param x1 "Right" control point. @param xm Third control point. @param t The t value. @return 1 on success, 0 on error. */ int dkbsp_for_t DK_P6(dk_bspline_t *,s,double,x0,double,xp,double,x1,double,xm,double,t) { int back = 0; int me = 0; double tt, ttt, omt, omtomt, omtomtomt; if(s) { back = 1; s->x0 = x0; s->x1 = x1; s->xp0 = xp; s->xm1 = xm; tt = dkma_mul_double_ok(t, t, &me); ttt = dkma_mul_double_ok(tt, t, &me); omt = dkma_sub_double_ok(1.0, t, &me); omtomt = dkma_mul_double_ok(omt, omt, &me); omtomtomt = dkma_mul_double_ok(omtomt, omt, &me); /* value */ s->xvalue = dkma_add_double_ok( dkma_add_double_ok( dkma_mul_double_ok(omtomtomt, x0, &me), dkma_mul_double_ok( dkma_mul_double_ok(3.0, t, &me), dkma_mul_double_ok(omtomt, xp, &me), &me ), &me ), dkma_add_double_ok( dkma_mul_double_ok( dkma_mul_double_ok(3.0, tt, &me), dkma_mul_double_ok(omt, xm, &me), &me ), dkma_mul_double_ok(ttt, x1, &me), &me ), &me ); /* derivative */ s->dxdt = dkma_add_double_ok( dkma_mul_double_ok( dkma_mul_double_ok(3.0, tt, &me), dkma_add_double_ok( dkma_mul_double_ok( 3.0, dkma_sub_double_ok(xp, xm, &me), &me ), dkma_sub_double_ok(x1, x0, &me), &me ), &me ), dkma_add_double_ok( dkma_mul_double_ok( dkma_mul_double_ok(6.0, t, &me), dkma_sub_double_ok( dkma_add_double_ok(xm, x0, &me), dkma_mul_double_ok(2.0, xp, &me), &me ), &me ), dkma_mul_double_ok( 3.0, dkma_sub_double_ok(xp, x0, &me), &me ), &me ), &me ); if(me) { back = 0; } } return back; }