Geometry-guided synthesis of patterns and textures

装饰--用图案或纹理装饰表面--自史前以来一直是人类艺术表现的一种形式。这种做法今天仍然至关重要：装饰图案可以在产品包装，平面设计，服装，室内设计和建筑中找到，更不用说计算机生成的环境了。装饰在任何情况下都是有用的，其中绘图或表面可能会受益于额外的视觉冲击，或者作为一种以人为尺度用细节打破空白建筑形式的手段。最简单的图案是平面的，重复的几何图案，你可能会发现这些图案印在衣服或室内装饰的织物上。这些图案赋予它们所应用的对象和表面以生命，但它们通常不适应或符合这些表面。当用一组印花布缝制一件衣服时，我们承认纸样会在接缝处不连续地跳动。在建筑环境中应用的展开模式在包裹具有弯曲蒙皮的建筑时会出现折叠或撕裂。这项研究的目标是发明新的数学和计算技术，以提高我们设计，应用和评估能力。我将考虑有助于实现这一目标的三个主要研究目标。我将研究计算机演示的表现力，使艺术家和设计师能够更好地控制图案中特征的样式和形状，以及更广泛的表面，可以应用图案而不会产生接缝或撕裂。我将研究在新空间中的应用，包括无缝适应服装等表面的图案，由多个断开的部件组装而成，以及在两个空间维度和一个时间维度中的动画图案。最后，我将探讨对表现力的评价，利用知觉心理学的思想为测量和比较模式的质量提供严格的科学依据。这项研究计划将使我能够培养众多的研究生和本科生在几何和计算机图形学的交叉的最新技术。学生将发展他们的数学，编程和沟通技能，并与科学研究的广泛的跨学科观点出现，在学术界或工业研究和开发的职业生涯做好准备。我和我的学生将创建工具，艺术家和设计师可以使用这些工具来绘制比以前更灵活，更可控和更有表现力的图案。艺术家也将能够在更广泛的装饰环境中应用他们的图案。这些工具，无论是作为独立的商业或开源软件，还是作为Adobe Illustrator等流行软件包的附加组件，都将在艺术、设计和建筑领域找到令人兴奋的商业和工业应用。

Ornamentation-the decoration of surfaces with patterns or textures-has been a form of human artistic expression since prehistory. This practice remains vital today: ornamental patterns can be found in product packaging, graphic design, clothing, interior design, and architecture, not to mention computer-generated environments. Ornamentation is useful in any context where a drawing or surface might benefit from extra visual impact, or as a means of breaking up a blank architectural form with detail at a human scale. The simplest varieties of ornamentation are flat, repeating geometric patterns that you might find printed on fabrics for clothing or upholstery. These patterns give life to the objects and surfaces to which they are applied, but they do not typically adapt or conform to those surfaces. When sewing a garment from a set of printed fabric pieces, we accept that the pattern will jump discontinuously at the seams. A flat pattern applied in an architectural setting will appear to fold or tear when wrapped around a building with a curved skin. The goal of this research is to invent new mathematical and computational techniques that will enhance our abilities to design, apply, and evaluate ornamentation. I will consider three main research objectives that contribute to this goal. I will study the expressivity of computer ornamentation, giving artists and designers more control over the styles and shapes of features in a pattern, and a broader range of surfaces to which patterns can be applied without producing seams or tears. I will investigate the application of ornamentation in new spaces, including patterns that adapt seamlessly to surfaces like garments, assembled from multiple disconnected pieces, and animated patterns in two dimensions of space and one of time. Finally, I will explore the evaluation of ornamentation, using ideas from perceptual psychology to provide a rigorous scientific basis for measuring and comparing the quality of patterns. This research program will allow me to train numerous graduate and undergraduate students in the latest techniques in the intersection of geometry and computer graphics. Students will develop their mathematical, programming, and communication skills, and emerge with a broad interdisciplinary view of scientific research, prepared for careers in academia or in industrial research and development. My students and I will create tools that artists and designers can use to draw patterns with greater flexibility, control, and expressive range than they could before. Artists will also be able to apply their patterns in a wider range of decorative contexts. These tools, whether as standalone commercial or open-source software, or add-ons for popular packages like Adobe Illustrator, will find exciting commercial and industrial applications in the worlds of art, design, and architecture.