cal/cal/spline.cal

{ RCSid $Id: spline.cal,v 1.2 2018/11/21 18:10:45 greg Exp $ }
{
        Calculation of view parameters for walk-throughs.
        Uses Catmull-Rom spline.

                09Feb90 Greg Ward

        Define:
                T(i)    - time between keyframe i and i-1
        Input:
                t       - time
        Output:
                s(f)    - spline value for f at t where f(i) is value at T(i)
}


or(a,b) : if(a, a, b);

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);
Ttot : sum(T,T(0));

sum(f,n) : if(n-.5, f(n)+sum(f,n-1), 0);

tfrac = (t-sum(T,below))/T(above);

upper(s,i) = if(or(i-T(0)+.5,s+T(i)-t), i, upper(s+T(i),i+1));

below = above-1;
above = max(upper(0,1),2);
below2 = max(below-1,1);
above2 = min(above+1,T(0));

s(f) = hermite(f(below), f(above),
                (f(above)-f(below2))/2, (f(above2)-f(below))/2,
                tfrac);
Revision:	1.3
Committed:	Mon Jun 10 13:56:52 2019 UTC (5 years ago) by greg
Branch:	MAIN
CVS Tags:	rad5R4, rad5R3, HEAD
Changes since 1.2:	+1 -3 lines
Log Message:	Added max() and min() as .cal library functions
#	User	Rev	Content
1	greg	1.3	{ RCSid $Id: spline.cal,v 1.2 2018/11/21 18:10:45 greg Exp $ }
2	greg	1.1	{
3			Calculation of view parameters for walk-throughs.
4			Uses Catmull-Rom spline.
5
6			09Feb90 Greg Ward
7
8			Define:
9			T(i) - time between keyframe i and i-1
10			Input:
11			t - time
12			Output:
13			s(f) - spline value for f at t where f(i) is value at T(i)
14			}
15
16
17			or(a,b) : if(a, a, b);
18
19			hermite(p0,p1,r0,r1,t) : p0 * ((2t-3)t*t+1) +
20			p1 * (-2t+3)t*t +
21			r0 * (((t-2)t+1)t) +
22			r1 * ((t-1)tt);
23			Ttot : sum(T,T(0));
24
25			sum(f,n) : if(n-.5, f(n)+sum(f,n-1), 0);
26
27			tfrac = (t-sum(T,below))/T(above);
28
29			upper(s,i) = if(or(i-T(0)+.5,s+T(i)-t), i, upper(s+T(i),i+1));
30
31			below = above-1;
32			above = max(upper(0,1),2);
33			below2 = max(below-1,1);
34			above2 = min(above+1,T(0));
35
36			s(f) = hermite(f(below), f(above),
37			(f(above)-f(below2))/2, (f(above2)-f(below))/2,
38			tfrac);