CAREER: Parameterization and Tessellation for Computer Graphics

职业：计算机图形学的参数化和曲面细分

• 批准号: 1148976
• 负责人: Scott Schaefer
• 金额: $ 47.3万
• 依托单位: Texas A&M Engineering Experiment Station
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-06-01 至 2018-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1148976&HistoricalAwards=false
• 关键词: CAREER; Parameterization; Tessellation; Computer; Graphics

The digital age with its widespread availability of cheap computing power has transformed the way we search for information, distribute content and even navigate cities. Computation has also transformed the way we design shapes. Whereas in the past engineers and artists often sculpted objects from clay, today most shapes are designed virtually with computers. Computer-aided design of curves, surfaces and volumetric functions has applications in diverse fields such as industrial design, the entertainment industry and even architectural design. However, in all of these applications the designer is limited by the capabilities of the representations employed. The quality and geometric properties of parametric surface representations such as NURBS and subdivision surfaces are strongly dependent on their parameterization. Yet this is a degree of freedom that few designers use or understand. Furthermore, the connection between parameterization and the geometric properties of these shapes is not well understood. We currently have only rudimentary tools for controlling the parameterization of higher dimensional shapes such as surfaces or volumes. The inability to control this parameterization leads to poor quality shapes and more effort on the part of designers to alleviate these artifacts. In this project, the PI will explore new representations of surfaces and volumes that allow for more geometric freedom in creating the underlying shapes. He will investigate the fundamental connection between parameterization and surface shape/quality for parametric curves, surfaces and volumes. He will expand upon the concept of non-uniform parameterization of surfaces to show that knot spacing (edge lengths) is not sufficient to completely control the parameterization of surfaces or volumes. And he will design new representations that allow the user to control or automatically adapt the parameterization of these shapes during the design process, and incorporate methods of non-uniform parameterization that are currently not possible. As part of this process, he will develop new higher order barycentric coordinates specifically adapted to this problem. Finally, he will investigate the effect and manipulation of parameterization for the purposes of tessellation and rendering of these parametric surfaces, and develop high quality GPU tessellation algorithms.Broader Impacts: Project outcomes will significantly advance the state of the art not only in computer graphics and geometric modeling, but also in other areas of applied mathematics and computer science where the representation and precise control of smooth freeform shapes play a key role. Approximation theory, architectural design, the entertainment industry and industrial manufacturing will all benefit from the results of this research.

数字时代以其广泛可用的廉价计算能力改变了我们搜索信息，分发内容甚至导航城市的方式。 计算也改变了我们设计形状的方式。 在过去，工程师和艺术家经常用粘土雕刻物体，而今天，大多数形状都是用计算机虚拟设计的。 曲线、曲面和体积函数的计算机辅助设计在工业设计、娱乐业甚至建筑设计等各个领域都有应用。 然而，在所有这些应用程序中，设计者受到所采用的表示的能力的限制。 参数曲面表示的质量和几何性质，如NURBS和细分曲面，强烈依赖于它们的参数化。 然而，这是一个很少有设计师使用或理解的自由度。 此外，参数化和这些形状的几何属性之间的联系还没有得到很好的理解。 我们目前只有基本的工具来控制更高维度的形状，如表面或体积的参数化。 无法控制这种参数化会导致形状质量差，设计人员需要付出更多努力来减轻这些伪影。 在该项目中，PI将探索表面和体积的新表示法，以便在创建底层形状时提供更多几何自由度。 他将研究参数化和表面形状/参数曲线，曲面和体积质量之间的基本联系。 他将扩展曲面的非均匀参数化概念，以表明节点间距（边长）不足以完全控制曲面或体积的参数化。 他将设计新的表示，允许用户在设计过程中控制或自动适应这些形状的参数化，并结合目前不可能的非均匀参数化方法。 作为这一过程的一部分，他将开发新的高阶重心坐标专门适应这个问题。 最后，他将研究参数化的效果和操作，以实现这些参数曲面的细分和渲染，并开发高质量的GPU细分算法。更广泛的影响： 项目成果不仅将显著推进计算机图形学和几何建模领域的最新技术水平，还将在应用数学和计算机科学的其他领域中发挥关键作用，这些领域中光滑自由形状的表示和精确控制发挥着关键作用。 近似理论、建筑设计、娱乐业和工业制造业都将受益于本研究的成果。