TY - GEN

T1 - Shape representations with blossoms and buds

AU - Stefanus, Lim Yohanes

PY - 2006

Y1 - 2006

N2 - Polynomials, either on their own or as components of splines, play a fundamental role for shape representations in computer-aided geometric design (CAGD) and computer graphics. This paper shows that any polynomial p(t) of degree d ≤ n can be represented in the form of a blossom of another polynomial b(t) of degree d evaluated off the diagonal at the linear functions Xj(t), j = 1,..., n, chosen under some conditions expressed in terms of the elementary symmetric functions. The polynomial b(t) is called a bud of the polynomial p(f). An algorithm for finding a bud b(t) of a given polynomial p(t) is presented. Successively, a bud of b(t) can be computed and so on, to form a sequence of representations. The information represented by the original polynomial is preserved in its buds. This scheme can be used for encoding/decoding geometric design information.

AB - Polynomials, either on their own or as components of splines, play a fundamental role for shape representations in computer-aided geometric design (CAGD) and computer graphics. This paper shows that any polynomial p(t) of degree d ≤ n can be represented in the form of a blossom of another polynomial b(t) of degree d evaluated off the diagonal at the linear functions Xj(t), j = 1,..., n, chosen under some conditions expressed in terms of the elementary symmetric functions. The polynomial b(t) is called a bud of the polynomial p(f). An algorithm for finding a bud b(t) of a given polynomial p(t) is presented. Successively, a bud of b(t) can be computed and so on, to form a sequence of representations. The information represented by the original polynomial is preserved in its buds. This scheme can be used for encoding/decoding geometric design information.

UR - http://www.scopus.com/inward/record.url?scp=33749317484&partnerID=8YFLogxK

U2 - 10.1007/11802914_28

DO - 10.1007/11802914_28

M3 - Conference contribution

AN - SCOPUS:33749317484

SN - 9783540367116

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 397

EP - 408

BT - Geometric Modeling and Processing, GMP 2006 - 4th International Conference, Proceedings

PB - Springer Verlag

T2 - 4th International Conference on Geometric Modeling and Processing, GMP 2006

Y2 - 26 July 2006 through 28 July 2006

ER -