The analysis of <italic>C</italic><sup>1</sup> regularity of ternary Loop subdivision surface

Abstract

In this paper, by using a computer algebra system, we prove that ternary Loop subdivision scheme can guarantee C 1 regularity at the extraordinary point of the subdivision surface based on the construction and analysis of its subdivision matrix and the characteristic maps. Besides, an interval is given for the sub-dominant eigenvalue of the subdivision matrix, which can guarantee that ternary Loop rules always generate C 1 subdivision surface. Finally, we propose a new edge rule. This can guarantee the C 1 regularity of the subdivision surface. And also comparing with Loop rules, this scheme has simpler form and faster convergence speed around the extraordinary point.