We propose a new method to approximate curves that interpolate a given set of time-labeled data on Riemannian symmetric spaces. First, we present our new formulation on the Euclidean space as a result of minimizing the mean square acceleration. This motivates its generalization on some Riemannian symmetric manifolds. Indeed, we generalize the proposed solution to the the special orthogonal group, the manifold of symmetric positive definite matrices, and Riemannian n-manifolds with constant negative curvature. By means of this generalization, we are able to prove that the approximates enjoy a number of nice properties: The solution exists and is optimal in many common situations. Several examples are provided together with some applications and graphical representations.

中文翻译：

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黎曼对称空间上插值贝塞尔曲线的构造近似

我们提出了一种近似曲线的新方法，该方法在黎曼对称空间上插入一组给定的时间标记数据。首先，我们在欧几里得空间上展示我们的新公式，作为最小化均方加速度的结果。这激发了它在一些黎曼对称流形上的推广。实际上，我们将所提出的解决方案推广到特殊正交群、对称正定矩阵的流形和具有恒定负曲率的黎曼 n 流形。通过这种概括，我们能够证明近似具有许多很好的特性： 该解决方案存在并且在许多常见情况下是最优的。提供了几个示例以及一些应用程序和图形表示。