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High Speed for Generating or Updating Graphics with Splines on a Screen

IP.com Disclosure Number: IPCOM000045686D
Original Publication Date: 1983-Apr-01
Included in the Prior Art Database: 2005-Feb-07
Document File: 3 page(s) / 54K

Publishing Venue

IBM

Related People

Wahl, FM: AUTHOR [+2]

Abstract

This invention relates to the generation of the locus of a spline curve avoiding the xplicit computation of intermediate points along the curve by a host CPU. Once an executing machine provides the display processor with a list of knots, the host CPU can be dispatched to execute another task. The display processor can then generate a curve. This overlap permits utilization efficiency. More particularly, the invention uses a spline knot vector representation of a continuous function for directly driving the display generator. This omits the point plotting and sampling steps involved in the bit representation of functions and their conversion to an analog format.

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High Speed for Generating or Updating Graphics with Splines on a Screen

This invention relates to the generation of the locus of a spline curve avoiding the xplicit computation of intermediate points along the curve by a host CPU. Once an executing machine provides the display processor with a list of knots, the host CPU can be dispatched to execute another task. The display processor can then generate a curve. This overlap permits utilization efficiency. More particularly, the invention uses a spline knot vector representation of a continuous function for directly driving the display generator. This omits the point plotting and sampling steps involved in the bit representation of functions and their conversion to an analog format.

POLYNOMIAL SPLINE FUNCTIONS. Splines are piecewise polynomial functions which meet certain continuity criteria at the locations where the pieces are joined together. They allow the user to approximate a table of discrete values with several low degree polynomials. Of course, this table of discrete values could also be a set of points previously selected from a given curve or function in order to represent this curve function with a meaningful approximation. The entire information of a spline curve of a given order is contained in this set of discrete values which is called the knot vector. In the general 2-d cases the knot vector (x(0), Y(0)), (x(1), Y(1))..........(x(n), Y(n))
has to be split up into the two knot vectors (t(0), x(0)), (t(1), x(1))..........(t(n), x(n))

(t(0), y(0)), (t(1), y(1))..........(t(n), y(n))
where t(i) (i=1,2...n) is an intermediate parameter. In other words, the coordinates x, y of a curve piece are now defined as functions of
t. In the case of polynomial splines these functions are polynoms with the independent variable t defined within an interval (O,T). It is well known that the determination of the x- and y-polynoms' coefficients lead to the simple problem of solving a set of linear equations.

HYBRID SPLINE GENERATOR. Referring now to Fig. 1, there is shown an arrangement where a discrete integer knot vector is fed into a Parameter and Control Processor (PCP). The PCP calculates for each curve piece a set of coefficients of the corresponding x- and y-polynoms and a set of initial values, and stores them into the parameter buffer (BUF). Depending on the speed requirements and on the order of polynoms, this processor can be realized by a general-purpose computer or by a special digital calculation unit. The output of BUF is fed, under PCP control, into two analog Polynom Generators (PGs). The PGs produce the analog x-, y-coordinate values of the corresponding curve piece as a function of time (of course, these quantities could be converted to integer numbers, if display devices with digital...