CAJ | 학술논문

提出了一种以隐式B-样条曲线为表达形式，基于直接Greville纵标的曲线重建方法。根据点云建立有向距离场，并作为B-样条函数的Greville纵标，然后根据高影响区内的平均代数误差优化Greville纵标；得到一个隐式B-样条函数，该函数的零点集即为重建曲线。该方法具有模型简单，重建速度快，无多余分支，无需手工调节任何参数的优点。实验结果证实了该直接法的效率明显高于点拟合法和普通场拟合法，以几何误差为准则的精度亦优于普通场拟合方法。
제출료일충이은식B-양조곡선위표체형식，기우직접Greville종표적곡선중건방법。근거점운건립유향거리장，병작위B-양조함수적Greville종표，연후근거고영향구내적평균대수오차우화Greville종표；득도일개은식B-양조함수，해함수적영점집즉위중건곡선。해방법구유모형간단，중건속도쾌，무다여분지，무수수공조절임하삼수적우점。실험결과증실료해직접법적효솔명현고우점의합법화보통장의합법，이궤하오차위준칙적정도역우우보통장의합방법。
This paper proposes a new implicit B-spline curve reconstruction algorithm based on direct Greville ordinates. For a given point cloud, it creates signed distance field first and lets them to be the Greville ordinates of B-spline function, and then optimizes Greville ordinates according to average algebraic error of raw points in high influence region. Finally, an implicit curve is obtained which is the zero level set of B-spline function. The proposed algorithm has benefits of simple model, fast speed, additional branch free, and being without manual tuning any parameters. Experimental results demonstrate that the reconstructing efficiency is higher than point fitting method as well as ordinary field fitting method, and the recon-struction accuracy expressed in geometric errors is better than ordinary field fitting method.