In this paper we construct a family of ternary interpolatory Hermite subdivision schemes of order 1 with small support and \({\mathscr{H}}\mathcal {C}^{2}\)-smoothness. Indeed, leaving the binary domain, it is possible to derive interpolatory Hermite subdivision schemes with higher regularity than the existing binary examples. The family of schemes we construct is a two-parameter family whose \({\mathscr{H}}\mathcal {C}^{2}\)-smoothness is guaranteed whenever the parameters are chosen from a certain polygonal region. The construction of this new family is inspired by the geometric insight into the ternary interpolatory scalar three-point subdivision scheme by Hassan and Dodgson. The smoothness of our new family of Hermite schemes is proven by means of joint spectral radius techniques.

在本文中，我们构造了一个三阶插值Hermite细分方案，该方案具有小的支持和\（{\ mathscr {H}} \ mathcal {C} ^ {2} \）平滑度。确实，离开二进制域，有可能获得比现有二进制示例具有更高规则性的插值Hermite细分方案。我们构造的方案族是一个两参数族，只要从某个多边形区域选择参数，就可以保证其\（{\ mathscr {H}} \ mathcal {C} ^ {2} \）的平滑性。这个新家族的构造受到Hassan和Dodgson对三元插值标量三点细分方案的几何洞察力的启发。我们的新Hermite方案系列的平滑性已通过联合光谱半径技术得到了证明。