Physically-based modeling techniques for interactive digital painting

In this dissertation I present a novel, physically-based approach to digital painting. With the interactive simulation techniques I present, digital painters can work with digital brushes and paints whose behavior is similar to real ones. Using this physically-based approach, a digital painting system can provide artists with a versatile and expressive creative tool, while at the same time providing a more natural style of interaction enabled by the emulation of real-world implements. I introduce several specific modeling techniques for digital painting. First, I present a physically-based, 3D, deformable, virtual brush model based on non-linear quasi-static constrained energy minimization. The brush dynamics are computed using a skeletal physical model, which then determines the motion of a more complex geometric model. I also present three different models for capturing the dynamic behavior of viscous paint media, each offering a different trade-off between speed and fidelity—from 2D heuristics, to 3D partial differential equations. Accurate modeling of the optical behavior of paint mixtures and glazes is also important, and for this I present a real-time, physically-based rendering technique, based on the Kubelka-Munk equations and an eight-sample color space. Finally, I present techniques for modeling the haptic response of brushes in an artist's hand, and demonstrate that all these techniques can be combined to provide the digital painter with an interactive, virtual painting system with a working style similar to real-world painting.