دانلود رایگان مقاله ساخت سطح جاروب گویا مبتنی بر خواص منحنی دیفرانسیل و انتگرال

Abstract

A swept surface is generated from a profile curve and a sweep curve by employing the latter to define a continuous family of transformations of the former. By using polynomial or rational curves, and specifying the homogeneous coordinates of the swept surface as bilinear forms in the profile and sweep curve homogeneous coordinates, the outcome is guaranteed to be a rational surface compatible with the prevailing data types of CAD systems. However, this approach does not accommodate many geometrically intuitive sweep operations based on differential or integral properties of the sweep curve — such as the parametric speed, tangent, normal, curvature, arc length, and offset curves — since they do not ordinarily have a rational dependence on the curve parameter. The use of Pythagorean-hodograph (PH) sweep curves surmounts this limitation, and thus makes possible a much richer spectrum of rational swept surface types. A number of representative examples are used to illustrate the diversity of these novel swept surface forms — including the oriented-translation sweep, offset-translation sweep, generalized conical sweep, and oriented-involute sweep. In many cases of practical interest, these forms also have rational offset surfaces. Considerations related to the automated CNC machining of these surfaces, using only their high-level procedural definitions, are also briefly discussed.

9. Closure

The use of Pythagorean-hodograph sweep curves opens up a rich spectrum of rational swept surface constructions, arising from families of transformations of a profile curve that depend explicitly on differential and integral properties of the sweep curve. A number of representative examples have been presented herein, to illustrate the diversity of surface geometries that can be intuitively generated in a manner exactly compatible with the prevailing representation schemes of modern CAD systems. Preliminary considerations regarding the automated CNC machining of such surfaces, based only on their highlevel procedural definitions, have also been presented (the technical aspects of this topic will be more fully addressed in a forthcoming study). The versatility of these generalized rational swept surfaces makes their complete categorization a non-trivial task, that is worthy of further investigation.