Stereo System User Manual

MOTOROLA DSP96002 USER’S MANUAL B-69
The resulting unsigned pseudorandom integer number is in d0.l.
Reference: VAX/VMS Run-Time Library Routines Reference Manual,
Volume 8C, p. RTL-433.
B.1.37 Bezier Cubic Polynomial Evaluation
Bezier polynomials are used to represent curves and surfaces in graphics. The Bezier form requires four
points: two endpoints and two points other points. The four points define (in two dimensions) a convex
polygon. The curve is bounded by the edges of the polygon.
A typical application of the Bezier cubic is generating character fonts for laser printers using the postscript
notation.
Given the four sets of points, the cubic equation for the X coordinate is:
x(t)=(P1x)
*
(1-t)
**
3 + (P2x)
*
3
*
t
*
(t-1)
**
2 + (P3x)
*
3
*
t
*
t
*
(1-t) + (P4x)t
**
3
where:
P1x = x coordinate of an endpoint
P2x = a point used for defining the convex polygon
P3x = a point used for defining the convex polygon
P4x = x coordinate of an endpoint
0.0 <= t <= 1.0
As t varies from zero to one, the x coordinate moves along the cubic from one endpoint to the other.
With a little inspiration, the equation can be factored as:
x(t)=-(t-1)
**
3
*
(P1X) + 3t(t-1)
**
2
*
(P2x) - 3t
*
t(1-t)
*
(P3x) + t
**
3
*
(P4x)
x(t)=(t-1)(-(t-1)
**
2
*
(P1x)+3t{(t-1)
*
(P2x)-t
*
(P3x)}) + t
**
3
*
(P4x)
Memory Map: X Y
r4 → t 1.0
3.0
P1x
P2x
r0 → P3x
P4x
The P coefficients are accessed in the order: P3x,P2x,P1x,P4x.