ITR: Representations and Algorithms for Deformable Objects

从分子到天体物理学，可变形的物体在物理世界的各个尺度上都无处不在。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，都可以用形状的及时变形来描述。柔性材料在工程、测试和制造等领域的应用越来越多，特别是在生物医学应用中，包括假肢设备、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物体模型。虽然自然界中的变形可以基于各种潜在的物理过程，但我们相信有一些统一的原则可以理解所有的变形。然而，今天，我们缺乏关于如何感知、表示、模拟、近似、驱动、控制和渲染可变形物体的一般计算理论。研究目标和方法本提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研究。这样的建模是具有挑战性的，因为变形涉及形状和运动的表示，并汇集连续和离散的现象，以及局部和全局约束。必须解决的一些具体挑战是：1。可变形物体的行为是由几何和物理定义的，其特征是复杂的高维能量景观，需要对其进行紧凑的编码和有效的查询，以实现驱动、控制和规划；物理上精确的变形模拟通常需要大量的计算；2 .我们必须找到近似整个物理的方法，同时仍然保证在我们关心的系统部分中计算的解的正确性，或者至少是适当性；碰撞、自碰撞等离散事件改变了系统的连续演化规律；3 .必须有效地预测或检测这些事件，并对其进行处理；4 .接触和自接触必须在接触歧管的快速变化中建模，包括其尺寸（例如，布料在刚性物体上悬垂）；变形通常与形状拓扑的变化有关（例如，外科医生的手术刀切割患者的皮肤组织）；这种拓扑修改必须顺利地适应于我们的模型中。为了实现这一目标，我们组建了一支由pi和顾问/顾问组成的团队，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、局部和分布式传感和驱动、模型参数估计等方面的专业知识，以及从分子到纺织品，从医学到娱乐等应用的特定可变形物体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