Techniques for conic splines

Abstract

A number of techniques are presented for making conic splines more effective for 2D computer graphics. We give a brief account of the theory of conic splines oriented to computer graphics. We make Pitteway's algorithm exact, and repair an "aliasing" problem that has plagued the algorithm since its introduction in 1967. The curvature-matching problem for conics is solved by way of a simple formula for curvature at an endpoint which permits curvature to be matched exactly at non-inflectior points and more closely than was previously realized possible at points of inflection. A formula for minimum-curvature-variation of conic splines is given. These techniques provide additional support for Pavlidis' position [6] that conics can often be very effective as splines.The work was motivated by, and provides much of the foundation for, an implementation of conic splines at Sun Microsystems as part of Sun's Pixrect graphics package, the lowest layer of Sun's graphics support.