Wave-Based Computer Graphic Light Modeling with Applications to Computer Aided Design

Abstract

This work demonstrates the utility of wave-based optics in computer graphics. Whereas computer graphics is ordinarily done with mostly ray-based optics and relatively little wave-based optics, this research illustrates the possibility of creating pictures using only wave-based optics and no ray-based optics. Also, ray-based optics and wave-based optics are combined to produce images that demonstrate how an understanding of both approaches, using only ray-based optics and using only wave-based optics, gives the perspective needed to make a judgment about what is truly a good middle ground. This improved understanding of physically based rendering is leveraged for computer aided design. Pure wave-based optics is applied to nanotechnology with a focus on plasmonic biosensing. Then a healthy balance of ray-based optics and wave-based optics drives computer aided design of car paint. To start, light is simulated with the well-established finite difference time domain method for solving Maxwell's equations. Maxwell's equations are a tightly coupled system of differential equations that describe electromagnetic radiation, and this expression lies at the heart of wave-based optics because light waves are electromagnetic waves. This straightforward numerical solution scheme is shown to constitute a rendering algorithm, proving that it is possible to synthesize an image without using ray-based optics at all. The approach is also shown to be useful for making a shader which can be employed in a ray-based rendering algorithm. Toward computer aided design, the focus is on photonic crystals which can be modeled by a recently proposed high order perturbation scheme that is more efficient than the broadly applicable finite difference time domain method. The algorithm is parallelized to take advantage of a CPU with multiple cores and to allow the algorithm to run at interactive rates. The computation speed is leveraged to deliver real time feedback in a computer aided design system for nanotechnology. Spectral reflectance plots are continuously updated during click-and-drag operations that modify the geometry profile of a nanostructure. The high order perturbation scheme is then combined with a path tracer to facilitate computer aided design for car paint. This contribution places more serious demands on the high order perturbation scheme, namely three dimensions and multiple layers, making real time performance more difficult. Real time feedback is achieved partly by precomputation and partly because in simple cases, commonly occurring in car paint, the high order perturbation scheme reduces to the Fresnel equations for multilayer thin film interference. A new paint product with a novel color appearance is proposed. Supplementary material: butterfly.mov is a video portraying a morpho butterfly sitting on one of the leaves of a plant and flapping its wings to show off the iridescence modeled in this work. This animation was created with a shader based on the finite difference time domain method for Maxwell's equations.