| This project focuses
on developing theoretical foundations of ray differential geometry, studying
visual phenomenon such as reflection refraction distortions and caustics
using ray geometry, and applying them to shape acquisition, geometric
modeling, and computer graphics. Our proposed theoretical framework is
explicitly developed to characterize the geometric ray structures and to
compute the ray differential attributes. For applications, we apply the
differential geometry analysis to modeling the reflection/refraction rays.
Specifically, we will develop practical algorithms and acquisition systems
to robustly reconstruct ray geometry and use them to directly estimate
second-order surface characteristics such as the curvatures. We have
employed a new normal-ray representation to convert a smooth 3D surface into
a 2D ray manifold and compute surface differential geometry using the
first-order ray differential analysis. This will lead to a real-time
discrete shape operator. We further plan to develop new interpolation
schemes for creating smooth surfaces consistent with the underlying caustic
surfaces and normal-ray geometry. The development of these tools will
benefit shape designs in aircraft, automobile, and many other industries,
where higher-order shape consistencies are required. |
| Related Papers |
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Image-space Caustics and Curvatures Xuan Yu, Feng Li, and Jingyi Yu To Appear Pacific Graphics (PG) 2007 (video) |
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Focal Surfaces of Discrete Geometry Jingyi Yu, Xiaotian Yin, Xianfeng Gu, Leonard McMillan, Steve Gortler To Appear 5th Eurographics Symposium on Geometry Processing (SGP), 2007 |
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Geometric Modeling Using Focal Surfaces Jingyi Yu, Xiaotian Yin, Xianfeng Gu, Leonard McMillan, Steve Gortler To Appear on ACM SIGGRAPH 2007, Technical Sketch |
