L1-Splines-Based Geometric-Physics Modeling of Deformable Objects with Force-Torque Feedback

目前，在触觉反馈系统中，几乎所有的物体都是由大量的平面三角片组成的表面来表示的。这种表面具有符合当前计算机硬件限制的优点。然而，它们在计算上非常昂贵，因为平面三角形面片必须小而多，才能使模型准确。在这个项目中，将采用一种新的方法。我们的计划是用L1样条线取代平面三角形面片，L1样条线是一种新的几何模型，其压缩和精度远远高于平面三角形面片和其他替代方法。使用L1样条线将允许使用更少的元素进行精确建模，从而减少计算负荷。该项目将在四面体不规则网格上开发三变量参数L1样条线，作为同一四面体网络上的几何模型和力学模型，然后通过两级优化过程将几何模型和力学模型集成在一起。集成的几何/机械模型将在可操作的六自由度触觉系统的软件中实现。该项目的成功将带来既快速又准确的高性能触觉力反馈设备。更广泛地说，该项目将为科学界和国民经济提供一种新的计算效率的L1样条线，用于对各种不规则形状的对象和过程的几何和力学进行建模，包括但不限于人类、衣服、生物对象、机械对象、自然和城市地形、地球物理特征、地理数据、图像，如计算机游戏、经济过程和社会过程中的图像。这项研究将被纳入研究生和本科教育，以丰富常规课程，并吸引不同的本科生群体，因为触觉研究适用于如此广泛的学科和社会应用。

Currently, virtually all objects in haptic force-feedback systems are represented by surfaces consisting of large numbers of flat triangular patches. Such surfaces have the advantage of fitting within current computer hardware constraints. However, they are computationally very expensive because the flat triangular patches must be small and numerous for the model to be accurate. In this project, a new approach is to be adopted. The plan is to replace the flat triangular patches by L1 splines, a new class of geometric models that achieve compression and accuracy much greater than that of flat triangular patches and other alternatives. Use of L1 splines will permit accurate modeling with far fewer elements, thus reducing the computational load. This project will develop trivariate parametric L1 splines on tetrahedral irregular networks as geometric models and mechanical models on the same tetrahedral networks, and then integrate the geometric and mechanical models via a two-level optimization procedure. The integrated geometric/mechanical model will be implemented in software for an operational 6-degree-of-freedom haptic system. Success in this project will lead to high-performance haptic force-feedback devices with both speed and accuracy. More generally, this project will provide the scientific community and the national economy with a new class of computationally efficient L1 splines for modeling the geometry and mechanics of many kinds of irregularly shaped objects and processes, including but not limited to human beings, clothes, biological objects, mechanical objects, natural and urban terrain, geophysical features, geographical data, images such as those in computer games, economic processes and social processes. This research will be incorporated into graduate and undergraduate education to enrich regular courses and to attract a diverse group of undergraduate students, as the haptic research is applicable to such a wide set of disciplinary and societal applications.