Geometry-guided synthesis of patterns and textures

装饰用图案或纹理装饰表面自史前以来就是人类艺术表现的一种形式。这种做法在今天仍然至关重要：装饰性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，在任何情况下，图纸或表面可能会从额外的视觉冲击中受益，或者作为一种手段，在人类尺度上打破带有细节的空白建筑形式。 最简单的装饰是平坦的、重复的几何图案，你可能会发现这种图案印在服装或室内装饰的面料上。这些图案赋予应用它们的对象和曲面以生命，但它们通常不适应或符合这些曲面。当用一套印花面料缝制一件衣服时，我们认为图案会在接缝处不连续地跳跃。在建筑环境中应用的展开模式在包裹具有曲面外观的建筑时会显示为折叠或撕裂。 这项研究的目标是发明新的数学和计算技术，提高我们设计、应用和评估装饰品的能力。我将考虑有助于实现这一目标的三个主要研究目标。我将研究计算机装饰的表现力，让艺术家和设计师更好地控制图案中特征的样式和形状，以及更广泛的表面，图案可以应用于这些表面，而不会产生接缝或撕裂。我将研究装饰在新空间中的应用，包括无缝适应服装等表面的图案，由多个不相连的部件组装而成，以及二维空间和一维时间的动画图案。最后，对纹饰的评价进行探讨，运用知觉心理学的思想，为纹样质量的衡量和比较提供严谨的科学依据。 这项研究计划将使我能够在几何学和计算机图形学的交集中培训无数研究生和本科生掌握最新的技术。学生将发展他们的数学、编程和沟通技能，并拥有广泛的跨学科科学研究视野，为在学术界或工业研究和发展领域的职业生涯做好准备。 我和我的学生将创建一些工具，艺术家和设计师可以使用这些工具来绘制图案，具有比以前更大的灵活性、可控性和表现力。艺术家还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。

Ornamentationthe decoration of surfaces with patterns or textureshas 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.