Generalized Solids of Revolution

Peter Čech
peter@cech.cjb.net

Faculty of Mathematics, Physics and Informatics
Comenius University
Bratislava / Slovakia

Abstract

Modeling technique based on sweeping is introduced. Generalizations of solids of revolution by axis bending, usage of multiple axes and usage of various metrics are presented. Generalized solids of revolution are 2.5D objects and depending on input parameters, they may contain gaps. Constrained variants offer additional modeling possibilities and easier input. Finally some examples are given.

Keywords: geometric modeling, sweeping, solids of revolution

Table of Contents

1. Introduction
2. Generalization

2.1 Axis Bending
2.2 Multiple Axes
2.3 Various Metrics
2.4 Segments

3.1 Reducing Number of Foci
3.2 Degenrated Generalized Conic

4.1 Generalized Solids of Revolution as 2.5D Object
4.2 Gaps

4.2.1 Discontinuity of leading curve
4.2.2 Tangent of leading curve does not exist
4.2.3 No foci in slice
4.2.4 Infinite number of intersection points in slice
4.2.5 No intersection of rotated curve and slice
4.2.6 Value of distance function is too small
4.2.7 Change in number of foci
4.2.8 Discontinuous change in weights of foci

5.1 Simplified Variant of Generalized Solids of Revolution
5.2 Lofted Variant of Generalized Solids of Revolution
5.3 Slice choosing Curve

6.1 Modeling a Shell
6.2 Square to Circle Transition Using Two Metrics