有理曲面之交線研究

Development of an Intersection Curve Solver for Rational B-spline Surfaces

阮台平(T.P. JUAN)

指導教授 ： 楊大中

元智大學/工程學院/機械工程學系/碩士(1993年)

摘要

本論文的目的，是發展一套Rational B-spline Surfaces的交線(
Intersection Curves)產生器。因要求得完全正確(Exact)的相交曲線，
除圓錐曲面等特殊曲面之交線外，對其它任意曲面 (Free Form
Surface) 而言是不可能的。所以曲面交線在做近似解(Approximate
Solutions)之數值求解過程中，其方法的效率，精確度及穩定性成為本所
論文所要追求及探討的重要課題。本論文主要採用前進法(Maching
Method)。首先評估現有各種前進法之優缺點，以建立適合應用於
Rational B-Spline曲面之理論模式。再配合邊界箱與細分法尋求起始點(
Starting Point)及精緻化程序(Refinement Procedure)以提升交線之精
確度。最後所得之交線為Rational B-Spline曲線，以供後續之CAD/CAM圖
形處理之使用。

關鍵字

相交曲線 ； 有理曲面 ； 電腦輔助設計

並列摘要

The aim of this paper is to develop an intersection curve
solver for Rational B-spline surfaces. Presently,finding exact
solutions of intersection curves wererestricted to limited
cases,for example,planes and quadratic surfaces.
Exactintersection curves are impossible for free form sur-
faces,especially,Rational B-spline surfaces. Therefor,when the
approach of approximate solutions is adopted,the effi- ciency,
accuracy control, and stability are critical for the
implementation of the selected numerical process. Marching
method is used in the paper. Various marching algorithms will
be valuated and adequate marching method of locating
intersection curves will be established for Rational B-spline
surfaces. A min-max box and subdivision method will be used to
finding the starting point. The accuracy of inter- section
curves will be improved by a refinement procedure. The resulted
intersection curves are in the forms of Rational B-spline cures
for later processing.

並列關鍵字

Intersection Curve ； Rational B-spline Surfaces ； CAD