计算机工程与应用
計算機工程與應用
계산궤공정여응용
COMPUTER ENGINEERING AND APPLICATIONS
2010年
7期
39-43
,共5页
三角多项式%三角基%B-L曲线曲面
三角多項式%三角基%B-L麯線麯麵
삼각다항식%삼각기%B-L곡선곡면
trigonometric polynomial%trigonometric basis%B-L curves and surfaces
在三角函数空间φ_7=span{1,sint,cost,cost2t,sin3t,cos3t,sin4t,coas4t}和φ_8=span{1,sint,cost,sin2t,cos2t,sin3t,cos3t,sin4t,cos4t}中构造了B-L(Bézier-Like)曲线;并给出其显式表达式.进一步讨论了该曲线的若干性质和应用,给出了不需要有理形式的心脏线、椭圆(圆)弧等的B-L曲线精确表示,椭球(球)面的B-L曲面精确表示,以及圆柱螺线的B-L曲线逼近表示.通过实例说明在造型设计方面使用简便且有效.
在三角函數空間φ_7=span{1,sint,cost,cost2t,sin3t,cos3t,sin4t,coas4t}和φ_8=span{1,sint,cost,sin2t,cos2t,sin3t,cos3t,sin4t,cos4t}中構造瞭B-L(Bézier-Like)麯線;併給齣其顯式錶達式.進一步討論瞭該麯線的若榦性質和應用,給齣瞭不需要有理形式的心髒線、橢圓(圓)弧等的B-L麯線精確錶示,橢毬(毬)麵的B-L麯麵精確錶示,以及圓柱螺線的B-L麯線逼近錶示.通過實例說明在造型設計方麵使用簡便且有效.
재삼각함수공간φ_7=span{1,sint,cost,cost2t,sin3t,cos3t,sin4t,coas4t}화φ_8=span{1,sint,cost,sin2t,cos2t,sin3t,cos3t,sin4t,cos4t}중구조료B-L(Bézier-Like)곡선;병급출기현식표체식.진일보토론료해곡선적약간성질화응용,급출료불수요유리형식적심장선、타원(원)호등적B-L곡선정학표시,타구(구)면적B-L곡면정학표시,이급원주라선적B-L곡선핍근표시.통과실례설명재조형설계방면사용간편차유효.
The B-L(Bézier-Like) curves over the trigonometric function space φ_7 =span{ 1, sint, cost, cos2t, sin3t, cos3t, sin4t, cos4t}and φ_8=span {1,sint,cost,sin2t,cos2t,sin3t,cos3t,sin4t,cos4t} are constructed,the explicit expressions of the B-L curves are pre-sented.Then some properties and applications of this kind of curves are discussed.Cardioid,elliptic curves,circular arc,ellipsoid, sphere without rational form are precisely expressing,and circular helix is approximated by the B-L curves.Examples are given to illustrate the convenience and validity in model design.
