Research And Application Of Irregular Variable-radius Offset Curves And Surfaces

With the wide application of Computer Aided Geometric Design (CAGD) in the field ofindustrial design, offset curves and surfaces is one of important geometric modelings of theCAGD, so the further probe and settlement are req uired on the problem of theself-intersection. In the practical application of the offset curves, offset curve/surface mayself-intersect locally when the absolute value of the offset distance in the normal directionexceeds the minimum radius of curve/surface. Also the offset curve/surface mayself-intersection globally when the absolute value of the offset distance less than the distancebetween the point on the base curve/surface and the corresponding point on the offsetcurve/surface. More complex forms of the self-intersection are presented because of thediversity of the offset distance function. In this work, the problem of the self-intersection ofthe variable radius offset curve/surface including the Equivolumetric curve/surface isexplored and settled.At first, the problem of self-intersection of variable radius offset curve/surface is settledby the method of disk scanning in this work, the thought of which is the center of a disk withthe radius is offset distance function scans when it moves alo ng the base curve/surface, thenthe points on the normal of base curve/surface are confirmed to get rid of the area withoutintersection case. The phenomenons of self-inersection of the irregular curve/surface aredetected and tirmmed by using the solution space of the corresponding polynomial equationof the proposed the thought to detect and trim the self-intersection area of the irregularcurve/surface.Then the special property of the volumetric ratio of the Equivolumetric offset curve isused to settle the self-intersection problem of Equivolumetric offset curve in the paper.When the Equivolumetric offset self-intersect, the area of the region between base curve andEuqivolumetric curve changes, so the problem of self-intersectin of the irregularEquivolumetric offset curve can be settled by the a series of the polynomial equation obtainedby the relation between the volumetric ratio and the area.At last, since the geometric property of the Equivolumetric offset surface is relativelycomplex, the regularity is emphasized. The new method are proposed to settle theself-intersection problem, i.e., the relation betweent the volumetric ratio of theEquivolumetric offset surface and the volume of the spatial region circled by the base surfaceand the Equivolumetric offset surface is used to settle the problem of self-intersection.In this work, a new method is proposed to settle the self-intersection problem of Equiv-olumetric offset curve/surface, so that the knowlege of the Equivlumetric curve/surface iswidely used in the graphic design.