Original Surface

Deformed Surface

1st Principal Strain

2nd Principal Strain

This started as a class project for CSE552A (Advanced Computer Graphics) that I took in Fall 2007. I have got to talk about this project quite several times (including Siggraph 2008 Informal Forum). This work has also won the 2nd place at the Student Research Competition at SIGGRAPH 2008. Even though I'm no longer actively working on this, it is still an on-going project.

Abstract - Poster Abstract (PDF) - Poster (PDF) - Talk (PDF)

Generating surfaces from scattered data points has been of great interest in the geometric processing community due to recent advances in scanning technologies. A mathematical definition of such surfaces was proposed in the seminal work of Amenta 2004 as the extremal surface of an un-oriented vector field and an energy function. Although precisely defined, the surface was constructed indirectly by a projection process that results in a dense point set instead of explicit mesh geometry. While later works have improved the vector field and energy function, the surface construction process remains indirect. We propose a grid-based algorithm that directly extracts the extremal surface geometry, given a smooth vector field and energy function. The key observation that enables this direct construction is that the extremal surface can be considered as the singularity of an oriented vector field, which can be computed directly using a contour-like approach.

This started as a class project for CSE546T (Computational Geometry) that I took in Spring 2007. The idea is to divide up the surface into equal patches (charts) using Voronoi relaxation adapted to simplicial surface. Since then, even though the idea remains the same, I have made many changes to the implementation (one such change is that a chart consists of faces instead of vertices), so it is no longer as described on the project webpage. This project has become a part of our big code database and is included in some of our later projects.

I worked at M&M Lab during the summer of 2005 as a DMP student participant. Our project was on creating a sketching interface to generate Reaction-Diffusion texture. In May 2006, I came back to Washington University in St. Louis for another summer internship. In early June, we submitted a paper on our summer 2005 project titled "Sketching Reaction-Diffusion Texture" to the 3rd Eurographics Workshop on Sketch-Based Interfaces and Modeling (SBIM '06). The paper was accepted and in Sept. 06, I went to Vienna, Austria, to present it.

Abstract - Paper (PDF) - Talk (PDF)

In this work, we present an interactive interface for sketching synthesized textures. Reaction-Diffusion (RD) is used as the basis for texture synthesis. RD allows an unlimited amount of non-repeating texture and offers great flexibility for mapping textures to arbitrary surfaces. However, it can be difficult to find starting values of parameters that will produce interesting patterns. We use machine learning to resolve the difficulty of determining appropriate initial values of the RD system. The system described here allows a user to sketch a pattern of spots or stripes with arbitrary orientations, and then automatically generates a pattern with the same attributes as the sketch. It also allows the user to interactively create more complex textures by adding another layer of pattern, as well as manipulate the color of the resulting texture. We also show that this procedure can be applied to realistic 3D surfaces.

You can also visit my DMP website for more details related to the project.