cal/cal/spline.cal

{
        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);
min(a,b) : if(a-b, b, a);
max(a,b) : if(a-b, 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:	1.1
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
#	User	Rev	Content
1	greg	1.1	{
2			Calculation of view parameters for walk-throughs.
3			Uses Catmull-Rom spline.
4
5			09Feb90 Greg Ward
6
7			Define:
8			T(i) - time between keyframe i and i-1
9			Input:
10			t - time
11			Output:
12			s(f) - spline value for f at t where f(i) is value at T(i)
13			}
14
15
16			or(a,b) : if(a, a, b);
17			min(a,b) : if(a-b, b, a);
18			max(a,b) : if(a-b, a, b);
19
20			hermite(p0,p1,r0,r1,t) : p0 * ((2t-3)t*t+1) +
21			p1 * (-2t+3)t*t +
22			r0 * (((t-2)t+1)t) +
23			r1 * ((t-1)tt);
24			Ttot : sum(T,T(0));
25
26			sum(f,n) : if(n-.5, f(n)+sum(f,n-1), 0);
27
28			tfrac = (t-sum(T,below))/T(above);
29
30			upper(s,i) = if(or(i-T(0)+.5,s+T(i)-t), i, upper(s+T(i),i+1));
31
32			below = above-1;
33			above = max(upper(0,1),2);
34			below2 = max(below-1,1);
35			above2 = min(above+1,T(0));
36
37			s(f) = hermite(f(below), f(above),
38			(f(above)-f(below2))/2, (f(above2)-f(below))/2,
39			tfrac);