Creation of Detailed Virtual Shapes: Foundations and Tools

我们生活在一个三维世界中，物体的形状或几何是它们的主要特征之一。因此，处理真实对象的计算机应用程序，例如计算机图形、工程或医学可视化，需要工具来创建和处理3D形状。随着3D数据的使用变得越来越普遍，各种行业的用户对能够创建新的个性化的复杂3D内容变得越来越感兴趣；然而，用于创建此类内容的几何处理方法正在落后。 我研究的总体目标是通过开发基础的基本几何分析和处理技术，为用户提供尽可能容易和有效地执行这些任务所需的工具。由于用户对内容创作兴趣的增加，在这一发现基金的框架内，我将专注于开发工具来构建详细可信的虚拟形状，并解决在这一背景下出现的基本形状处理问题。 由于我们周围形状的多样性，一般的形状创建方法的适用性受到限制，因为它们可以对预期的输出形状做出很少的假设。因此，我的工作将探索一种更有针对性的方法，为特定类别的形状开发一些内容创作机制，利用适当的领域知识和其他先验知识来促进这一过程。我还将调查导致新的基本几何分析和处理问题的公式和解决方案的不同领域之间的共性，解决这些问题将有助于总体内容的创建。

We live in a three-dimensional world where the shape, or geometry, of objects is one of their major characteristics. Consequently, computer applications that deal with real-life objects, such as computer graphics, engineering, or medical visualization, require tools to create and process 3D shapes. As the use of 3D data becomes increasingly ubiquitous, users in a variety of industries are becoming more interested in being able to create new personalized complex 3D content; however the geometry processing methods for creation of such content are lagging behind. The general objective of my research is to provide users the tools necessary to perform these tasks as easily and efficiently as possible by developing the underlying fundamental geometry analysis and processing technologies. Motivated by the increased user interest in content creation, in the framework of this discovery grant, I will focus on developing tools for constructing detailed believable virtual shapes and address the fundamental shape processing problems that arise in this context. Due to the diversity of the shapes around us generic shape creation methods are limited in their applicability as they can make very few assumptions about the expected output shapes. My work will therefore explore a more targeted approach, developing a number of content creation mechanisms for specific classed of shapes, utilizing appropriate domain knowledge and other priors to facilitate the process. I will also investigate the commonalities between the different domains leading to formulation and solution of new fundamental geometry analysis and processing problems, solving which will benefit content creation in general.