CAJ | 학술논문

针对 T 样条无法精确表示双曲超越曲面的问题，构造了一种样条曲面——双奇次代数双曲 T 样条曲面(NUAH T样条)，探讨了其细分算法和调配函数的线性无关性。通过将非均匀代数双曲B样条曲面(NUAH B样条曲面)定义在T网上，给出了双奇次NUAH T样条的定义；基于NUAH B样条的节点插入公式，提出NUAH T样条的一种局部细分算法；并证明了NUAH T样条的调配函数线性无关的充要条件，即由NUAH T样条转化为NUAH B样条曲面的过渡矩阵是满秩矩阵。最后，通过实例验证了曲面构建和细分算法的有效性。
침대 T 양조무법정학표시쌍곡초월곡면적문제，구조료일충양조곡면——쌍기차대수쌍곡 T 양조곡면(NUAH T양조)，탐토료기세분산법화조배함수적선성무관성。통과장비균균대수쌍곡B양조곡면(NUAH B양조곡면)정의재T망상，급출료쌍기차NUAH T양조적정의；기우NUAH B양조적절점삽입공식，제출NUAH T양조적일충국부세분산법；병증명료NUAH T양조적조배함수선성무관적충요조건，즉유NUAH T양조전화위NUAH B양조곡면적과도구진시만질구진。최후，통과실례험증료곡면구건화세분산법적유효성。
Since T-splines cannot represent hyperbolic spline surfaces exactly, this paper presents a kind of spline surfaces, called non-uniform algebraic hyperbolic T-spline surfaces (NUAH T-splines for short) of odd bi-degree. The NUAH T-splines are defined by applying the T-spline framework to the non-uniform al-gebraic hyperbolic B-spline surfaces (NUAH B-spline surfaces). Based on the knot insertion of NUAH B-splines, a local refinement algorithm for NUAH T-splines of odd bi-degree is shown. This paper proves that, for any NUAH T-spline of odd bi-degree, the linear independence of its blending functions can be de-termined by computing the rank of the NUAH T-spline-to-NUAH B-spline transformation matrix. Finally, the examples verify the effectiveness of the local refinement algorithm of NUAH T-splines.