ADC Home > Reference Library > Technical Notes > Legacy Documents > Graphics & Imaging >

Legacy Documentclose button

Important: This document is part of the Legacy section of the ADC Reference Library. This information should not be used for new development.

Current information on this Reference Library topic can be found here:

Understanding Conic Splines

CONTENTS

Conic splines are a useful graphic primitive. They exactly represent any conic section: line, circle, ellipse, parabola, or hyperbola. Lines and circles are of obvious importance, and parabolic splines are a primitive building block for shapes in QuickDraw GX. To maintain closure under the full set of perspective transformations allowed by QuickDraw GX, the full set of conic sections must be used.

This Technote gives a derivation of some of the mathematical formulas associated with conic splines. It defines a quadratic rational spline as a weighted mean of three control points whose weights vary quadratically in the parameter t. A canonical form is derived for the most general form of the weighted mean. Then the effect of perspective transforms on the weights and control points is explained. Finally, a method is derived for determining which conic section contains a given conic spline.

This Technote is directed primarily at developers working with the paths and perspective transforms defined in QuickDraw GX. A firm grasp of those concepts is necessary to understanding this Technote.

 Updated: [June 1 1996]




MS Word version of this Technote

This Technote is heavily dependent upon mathematical derivation, which HTML does not yet adequately support. In order to ensure the mathematical integrity of the text, we are not publishing the body of the Technote as an HTML file. You can download the Technote, in its entirety, as a PDF document, by clicking here.

Back to top

Technote 1052

Technote 1052 - QuickDraw GX ConicLibrary.c in Detail: Description, and Derivations also addresses the concept of conic splines, and approaches it from a different perspective. See Inside Macintosh: QuickDraw GX Graphics and Inside Macintosh: QuickDraw GX Objects for further documentation.

Back to top

References

Technote 1052 - QuickDraw GX ConicLibrary.c in Detail: Description, and Derivations

Inside Macintosh: QuickDraw GX Graphics

Inside Macintosh: QuickDraw GX Objects

Back to top

Downloadables

Acrobat

Acrobat version of this Note (1K).

Download

Acrobat

Full text version of this technote in PDF.

Download

Back to top

Did this document help you?
Yes: Tell us what works for you.
It’s good, but: Report typos, inaccuracies, and so forth.
It wasn’t helpful: Tell us what would have helped.