计算机辅助设计与图形学学报
計算機輔助設計與圖形學學報
계산궤보조설계여도형학학보
JOURNAL OF COMPUTER-AIDED DESIGN & COMPUTER GRAPHICS
2009年
7期
924-929
,共6页
有理参数曲线%恰当参数化%近似非恰当指数%近似最大公因子%半代数系统
有理參數麯線%恰噹參數化%近似非恰噹指數%近似最大公因子%半代數繫統
유리삼수곡선%흡당삼수화%근사비흡당지수%근사최대공인자%반대수계통
rational curves%approximate proper parameterization%approximate improper index%approximate GCD%semi-algebraic system
有理参数曲线的恰当性是曲线的基本性质,虽然其在有理系数情况下已经有完备的结果,但在工程和CAGD应用中常常得到带误差浮点系数的有理表示形式.为此,讨论了这类有误差的有理参数曲线,定义了近似非恰当参数形式和近似非恰当指数,并通过半代数系统计算近似非恰当指数;在给出近似非恰当指数的同时,得到近似最大公因子.最后基于最小二乘法给出近似参数有理变换表示,计算出曲线恰当的近似有理参数表示.
有理參數麯線的恰噹性是麯線的基本性質,雖然其在有理繫數情況下已經有完備的結果,但在工程和CAGD應用中常常得到帶誤差浮點繫數的有理錶示形式.為此,討論瞭這類有誤差的有理參數麯線,定義瞭近似非恰噹參數形式和近似非恰噹指數,併通過半代數繫統計算近似非恰噹指數;在給齣近似非恰噹指數的同時,得到近似最大公因子.最後基于最小二乘法給齣近似參數有理變換錶示,計算齣麯線恰噹的近似有理參數錶示.
유리삼수곡선적흡당성시곡선적기본성질,수연기재유리계수정황하이경유완비적결과,단재공정화CAGD응용중상상득도대오차부점계수적유리표시형식.위차,토론료저류유오차적유리삼수곡선,정의료근사비흡당삼수형식화근사비흡당지수,병통과반대수계통계산근사비흡당지수;재급출근사비흡당지수적동시,득도근사최대공인자.최후기우최소이승법급출근사삼수유리변환표시,계산출곡선흡당적근사유리삼수표시.
Properness of a parameterization is a basic property of rational parametric curves and it has been well studied when the coefficients of the parameterization are rational. However, such coefficients in engineering and CAGD are often represented with float numbers with errors. This work gives an algorithm to simplify the rational curves in this situation. After the approximate proper index is defined, it is computed by solving the semi-algebra system. The greatest common divisor is obtained according to the computing process of approximate proper index. Finally, the approximate proper reparameterization is obtained by the least squares method.
