Motorola DSP96002 User Manual page 588

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:
The P coefficients are accessed in the order: P3x,P2x,P1x,P4x.
MOTOROLA
X
r4 t
P1x
P2x
r0 P3x
P4x
DSP96002 USER'S MANUAL
Y
1.0
3.0
B-69