Optimized scan conversion of outlines for generating raster imag

Details Optimized scan conversion of outlines for generating raster imag Optimized scan conversion of outlines for generating raster imag

1993-09-27

1995-11-28

Jankus, Almis R.

395142, 395143, 395133, G06T 1100

Patent

active

054715733

ABSTRACT:
An arbitrary curve formulated as a quadratic B-spline with a plurality of second order Bezier curves is approximated. Applying a forward differencing to the parametric equation of the second degree Bezier curves, a second order difference coefficient is derived. By defining the error from approximating the curve with forward differencing as the distance between the approximated point on the curve and the midpoint between the end points of the curve, the second order differential coefficient is directly proportional to the error. Additionally, the error resulting from increasing the number of parametric intervals for the forward differencing is proportional to the original error. It follows from the relationship established for the second order differential coefficient, the number of parametric intervals, and the error threshold that the user specifies, the number of parametric intervals is determined. Knowing the number of required forward differencing steps allows the user to minimize the scan conversion overhead. The formulation of integer-based parametric intervals for the forward differencing obviates any multiplication or division instructions in approximating an arbitrary curve. Thus overall performance of the graphic display system is enhanced.

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R. H. Bartels, J. C. Beatty, & B. A. Barsky, An Introduction to Splines for use in Computer Graphics and Geometric Modeling, 1987, pp. 173-245.
J. D. Foley & A. van Dam, Fundamentals of Interactive Computer Graphics, 1982, pp. 514-536.

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