/* Copyright (c) 2004-2005, 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 its 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. */ #define DKBSP_C 1 #include "dkbsp.h" #if DK_HAVE_MATH_H #include #endif #if DK_HAVE_STDLIB_H #include #endif #include #line 48 "dkbsp.ctr" /* {{{ dkbsp_calculate Calculate Bezier spline data for a given x0, dx/dt at x0 (d0), dx/dt at x1 (d1) and x1. */ int dkbsp_calculate DK_P5(dk_bspline_t *,s,double,x0,double,d0,double,x1,double,d1) { int back = 0, ok = 0; 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_t_for_min_max Calculate value and derivate to find minimum and maximum. */ 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; } /* }}} */ /* {{{ dkbsp_minmax Calculate minimum and maximum x value for a Bezier spline segment specified by x0, x0+ (d0), x1- (d1) and x1. */ 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; } /* }}} */ /* {{{ dkbsp_for_t Calculate value and derivate for a given t (0<=t<=1) in a Bezier spline segment specified by x0, x0+ (xp), x1- (xm) and x1. */ 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; } /* }}} */ /* {{{ SCCS ID */ #ifndef LINT static char sccs_id[] = { "@(#)dkbsp.ctr 1.96 02/19/08\t(krause) - fig2vect" }; #endif /* }}} */