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Motorola DSP96002 User Manual

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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.