INTERACTIVE IMPLICIT MODELING
While I was a Master student in Georgia Tech, my interest in modeling started with fractal geometry. Mathematician Michael F. Barnsley, a pioneer in Fractal geometry, as an exceptionally energetic and creative researcher influenced me a lot and I initially started to work in fractal geometry and published a few papers. During my PhD I discovered implicit research, I slowly moved to implicit modeling from fractal geometry.
Looking back 1990's, I realize now that I was always interested in creating high genus shapes. During 1990's, we only had implicit surfaces and solid modeling to provide such high genus models. I believed that implicit surface design must be like parametric surface design with control meshes and guaranteed interactivity.
During my PhD, I have developed an piecewise implicit framework for this purpose. Although, the framework was mathematically interesting, for all practical/engineering purposes, it was too complicated. I have improved and simplified the mathematics and I have eventually achieved guaranteed interactivity. The only problem was to reduce construction time for interactive rates, I had to impose some topological restrictions (I could have very high genus though).
In 1999, I showed what is needed to guarantee interactivity for modeling any general shape with implicit techniques. In that time, we needed faster computers to handle reconstruction time. Moreover, with rising popularity of subdivision surfaces, It was hard to motivate any student to work on implicit surfaces. I eventually moved to topological mesh modeling, which can work in sync with subdivision schemes.
See Papers and Manuscript for detailed information.