cal/cal/cubic.cal

{
        Cubic Basis Functions
}

bezier(p1, p2, p3, p4, t) =     p1 * (1+t*(-3+t*(3-t))) +
                                p2 * 3*t*(1+t*(-2+t)) +
                                p3 * 3*t*t*(1-t) +
                                p4 * t*t*t ;

hermite(p0, p1, r0, r1, t) =    p0 * ((2*t-3)*t*t+1) +
                                p1 * (-2*t+3)*t*t +
                                r0 * (((t-2)*t+1)*t) +
                                r1 * ((t-1)*t*t);

bspline(pp, p0, p1, pn, t) =    pp * (1/6+t*(-1/2+t*(1/2-1/6*t))) +
                                p0 * (2/3+t*t*(-1+1/2*t)) +
                                p1 * (1/6+t*(1/2+t*(1/2-1/2*t))) +
                                pn * (1/6*t*t*t) ;
Revision:	1.1
Committed:	Sat Feb 22 02:07:21 2003 UTC (21 years, 2 months ago) by greg
Branch:	MAIN
CVS Tags:	rad5R2, rad4R2P2, rad5R0, rad5R1, rad3R7P2, rad3R7P1, rad4R2, rad4R1, rad4R0, rad3R5, rad3R6, rad3R6P1, rad3R8, rad3R9, rad4R2P1
Log Message:	Changes and check-in for 3.5 release Includes new source files and modifications not recorded for many years See ray/doc/notes/ReleaseNotes for notes between 3.1 and 3.5 release
#	Content
1	{
2	Cubic Basis Functions
3	}
4
5	bezier(p1, p2, p3, p4, t) = p1 * (1+t(-3+t(3-t))) +
6	p2 * 3t(1+t*(-2+t)) +
7	p3 * 3tt*(1-t) +
8	p4 * ttt ;
9
10	hermite(p0, p1, r0, r1, t) = p0 * ((2t-3)t*t+1) +
11	p1 * (-2t+3)t*t +
12	r0 * (((t-2)t+1)t) +
13	r1 * ((t-1)tt);
14
15	bspline(pp, p0, p1, pn, t) = pp * (1/6+t(-1/2+t(1/2-1/6*t))) +
16	p0 * (2/3+tt(-1+1/2*t)) +
17	p1 * (1/6+t(1/2+t(1/2-1/2*t))) +
18	pn * (1/6tt*t) ;