Multiresolution for Interactive Modeling

在过去的三十年里，计算机图形学领域经历了一场革命，得益于重大的研究和技术成就。创建详细的数字内容是游戏、电影和CAD等行业的一项主要任务，需要结构良好、高质量的几何模型。然而，即使有了复杂的软件包，几何建模仍然是一项具有挑战性、繁琐和耗时的任务。这个问题是由于几何模型的数学基础，我们与它们交互的方式，以及这些几何模型在宏观和微观特征方面的增强。这个研究项目试图通过开发高效的方法来解决几何建模的挑战，通过交互建模来创建直观和灵活的多尺度几何对象(曲线、曲面和体积)。为了支持更自然的界面，更好地适应无处不在的触觉设备，本程序考虑使用基于草图和基于造型的界面。目标数学表示是多分辨率模型，其中高分辨率模型可以经济地(在时间和存储方面)分解为低分辨率模型和细节信息(小波系数)。通过在基础表面或体积上增加草图特征(例如折痕)来添加多比例细节，而不会对这些基础模型的几何形状或连接性造成很大的干扰。提出的研究的一个重要的新方面是开发一种多分辨率框架，该框架在不同的分辨率下适当地保留增强的特征，同时保持较低的预处理时间和存储需求。这些增强的特征可以交互地应用，也可以从数据集继承。为了创建有效的方法，还需要探索一种自然支持对象的多分辨率和分层表示的数据结构。

In the past three decades, the field of Computer Graphics has experienced a revolution, benefiting from significant research and technical achievements. Creating detailed digital content is a major task in industries such as Game, Film and CAD, and requires well-constructed, high quality geometric models. However, even with sophisticated software packages, geometric modeling is still a challenging, tedious and time consuming task. This issue is due to the mathematical foundation of geometric models, our way of interacting with them, and the augmenting of these geometric models with respect to their macro- and microscopic character. This research program tries to address the challenge of geometric modeling by developing efficient methods for creating intuitive and flexible multiscale geometric objects (curves, surfaces and volumes) through interactive modeling. To support a more natural interface with a better fit to the ubiquity of tactile devices, sketch-based and sculpt-based interfaces are considered for this program. The target mathematical representation is a multiresolution model, wherein a high-resolution model can be decomposed economically (in terms of time and storage) into a low resolution model and detail information (wavelets coefficients). Multiscale details are added by augmenting sketched features (e.g. creases) on base surfaces or volumes without a large disturbance of the geometry or connectivity of these base models. An important novel aspect of the proposed research is to develop a multiresolution framework that preserves augmented features properly at different resolutions, while keeping the pre-processing time and memory requirements low. These augmented features can be applied interactively or inherited from datasets. To create efficient methods, it is also necessary to explore a data structure that naturally supports multiresolution and hierarchical representations of objects.