计算机工程与应用
計算機工程與應用
계산궤공정여응용
COMPUTER ENGINEERING AND APPLICATIONS
2013年
8期
195-197
,共3页
基函数%有理样条%曲线逼近
基函數%有理樣條%麯線逼近
기함수%유리양조%곡선핍근
basis functions%rational spline%curve approximation
在空间四个有序数据点所确定的一个二次曲面上,可以构造一类特殊的曲线.给出了四个形状控制因子的有理基函数,以及通过研究其参数间的函数关系定义函数集,构造一类样条曲线,使得通过改变控制因子能任意精确地逼近控制多边形.这类样条曲线端点处满足一定切线方向和有界曲率,容易将它们拼接成一条逼近样条曲线.利用这些样条构造出逼近样条曲面,具有更多的自由度.
在空間四箇有序數據點所確定的一箇二次麯麵上,可以構造一類特殊的麯線.給齣瞭四箇形狀控製因子的有理基函數,以及通過研究其參數間的函數關繫定義函數集,構造一類樣條麯線,使得通過改變控製因子能任意精確地逼近控製多邊形.這類樣條麯線耑點處滿足一定切線方嚮和有界麯率,容易將它們拼接成一條逼近樣條麯線.利用這些樣條構造齣逼近樣條麯麵,具有更多的自由度.
재공간사개유서수거점소학정적일개이차곡면상,가이구조일류특수적곡선.급출료사개형상공제인자적유리기함수,이급통과연구기삼수간적함수관계정의함수집,구조일류양조곡선,사득통과개변공제인자능임의정학지핍근공제다변형.저류양조곡선단점처만족일정절선방향화유계곡솔,용역장타문병접성일조핍근양조곡선.이용저사양조구조출핍근양조곡면,구유경다적자유도.
A kind of special curves can be constructed in the surface, which is formed with four sequence and non-coplanar points in space. On this basis, the four rational basis functions with control handle are presented, studying on the functional rela-tions between these two parameters and defining a new function set, it can define a kind of spline curve. The spline curve can approximate the control polygon with arbitrary precision through changing the control handle. Additionally, the curve segments of this kind which meet prescribed tangent direction and bounded curvature at any endpoint, are then easy to connect into a approxi-mating spline curve. Finally, this spline is used to construct the surfaces for spatial mesh, which also has many freedoms.
