ITR: Representations and Algorithms for Deformable Objects

可变形物体在从分子到天体物理的所有尺度的物理世界中无处不在。生命的许多基本功能，从微观层面的蛋白质折叠和配体结合，到细胞层面的减数分裂和有丝分裂，再到宏观层面的心脏跳动，最好的描述是时间上的形状变形。柔性材料在工程中的应用越来越多，涉及测试和制造等领域，特别是在生物医学应用中，包括假肢设备和微创成像和外科手术。娱乐业的特效和基于触觉的人机界面也需要更好的柔性对象模型。虽然自然界中的变形可以基于各种潜在的物理过程，但我们认为有许多统一的原则可以共同理解所有的变形。然而，对于如何感知、表示、模拟、近似、驱动、控制和渲染可变形物体，我们缺乏一个通用的计算理论。研究目标和方法本方案的目标是对可变形物体的计算建模的表示和算法进行基础性研究。这样的建模具有挑战性，因为变形涉及形状和运动的表示，并将连续和离散的现象以及局部和全局约束结合在一起。必须解决的一些具体挑战是：1.可变形物体的行为由几何和物理两方面定义，并以复杂的高维能量场景为特征，需要对其进行紧凑编码并有效地询问以用于驱动、控制和规划；2.对变形的物理精确模拟的计算代价高达十分之一；我们必须找到方法来近似完整的物理，同时仍保证我们在所关心的系统部分计算的解的正确性或至少适当性；3.离散事件，如碰撞和自碰撞，改变了系统的连续演化规律；必须有效地预测或检测并处理这些事件；4.接触和自我接触必须在接触流形中的快速变化上建模，包括其维度(例如，布料覆盖在刚性物体上)；5.变形通常与形状拓扑的变化相关联(例如，外科医生的手术刀切割患者的皮肤组织)；为了实现这一目标，我们组建了一支PI和顾问/顾问团队，他们结合了科学计算和物理模拟、几何建模和计算、运动规划和控制、本地和分布式传感和驱动、模型参数估计以及从分子到纺织品以及从医学到娱乐的应用程序的计算建模方面的丰富经验

Deformable objects are ubiquitous in the physical world at all scales, from the molecular to the astrophysical. Many of life's basic functions, from protein folding and ligand binding at the micro level, to meiosis and mitosis at the cellular level, to the beating of a heart at the macro level, are best described as shape deformations in time. Flexible materials are finding increasing applications in engineering, across areas such as testing and manufacturing, and especially in biomedical applications, including prosthetic devices and minimally invasive imaging and surgical procedures. Special effects in the entertainment industry and haptics-based human-computer interfaces also require better models for flexible objects. Though deformation in nature can be based on a variety of underlying physical processes, we believe that there are a number of unifying principles common to understanding all deformations. Today, however, we lack a general computational theory of how to sense, represent, simulate, approximate, actuate, control, and render deformable objects.Research Goals and MethodsThe goal of this proposal is to undertake a foundational study of representations and algorithms for the computational modeling of deformable objects. Such modeling is challenging because deformations involve representations of shape and motion, and bring together continuous and discrete phenomena, as well as local and global constraints. Some of the specific challenges that have to be addressed are:1. the behavior of deformable objects is defined by both geometry and physics and characterized by complex high-dimensional energy landscapes that need to be compactly encoded and efficiently interrogated for actuation, control, and planning;2. physically accurate simulation of deformations is of-ten computationally expensive; we must find ways to approximate the full physics, while still guaranteeing the correctness, or at least appropriateness, of the solution that we compute in the parts of the system we care about;3. discrete events, such as collisions and self-collisions, alter the continuous evolution law of the system; these events must be efficiently predicted or detected, and processed;4. contact and self-contact must be modeled across rapid changes in the contact manifold, including its dimensionality (e.g., cloth draping over a rigid object);5. deformations are often associated with changes in the shape topology (e.g., the surgeon's scalpel cutting the patient's skin tissue); such topology modifications must be smoothly accommodated in our models.Towards this goal we have put together a team of PIs and consultants/advisors that combines expertise in scientific computing and physical simulation, geometric modeling and computation, motion planning and control, local and distributed sensing and actuation, model parameter estimation, as well as extensive experience in the computational modeling of specific deformable objects, from molecules to textiles, and in applications from medicine to entertainment