Computer-Generated Marbling Textures

Marbling is a traditional art of aqueous surface design to create intricate fluid-like patterns. The simulation of marbling is one of the popular techniques for modeling traditional artistic media in computer graphics. The simulation of marbling art plays important role in broadcasting, inheritance and protection of the ancient civilization and traditional art. Consequently, it has not only the important theoretical significance but also the realistic application value. The thesis mainly focuses on some key issues on the marbling simulation, including physically-based marbling simulation, mathematical marbling, image and video marbleization, and evolutionary design of marbling patterns. The results of the thesis consist of the followings.1. We present a fast and accurate marbling simulation system, which is based on the physical model of the traditional marbling process. The method borrows some idea from the two-dimensional computer fluid dynamic simulation. We first numerically solve the Navier-Stokes fluid equations to get the velocity field. Then, we advect the density field to obtain the marbling patterns. To simulate the very sharp lines among different paints, a third-order accurate but fast Unsplit semi-Lagragian Constrained Interpolation Profile method and a simple yet effective transformation function are applied. The system is implemented on the GPU and allows artists to create marbling textures with real-time visual feedback.2. We present a real-time image marbleization method that converts an image or video into a marble-like appearance automatically. Firstly, our method converts the input image from RGB color space to CIE-Lab color space. Then, it iteratively constructs a smooth and coherent edge tangent flow field by using a bilateral filter. Next, the obtained flow field is used as the external force in Navier-Stokes equation and the color advection of the input image results in a marbleized image. Since the image flows along its salient features, the resulted patterns not only possess the fluid-like characteristics, but also preserve the shape of the objects well in the images. We advect images’texture coordinates to avoid color mixture. 3. We proposed a mathematical approach with closed-form expressions to simulate marbling. The method abstracts the frequently used tools of marbling (i.e. eye dropper, brush, stylus, comb, and curl) as corresponding mathematical formulas. These tool functions are incompressible and invertible. A forward application is appropriate for creating vector-based marbling patterns, and an inverse application is appropriate for pixel-based ones. In addition, the method has wide applications include surface details rendering on3D objects, image editing, and interactive video processing.4. By integrating design methodology theories with evolutionary computation, we developed a design system to evolve preferred designs on complex marbling patterns. The system is formulated in a way to assist the productive-deductive-inductive design reasoning process of the users. Therefore, complex mathematical functions do not cognitively overload the designers, who are released for the more critical tasks of aesthetic assessment and new design rules induction. In addition, the resulting patterns fulfill the textile industry requirements of seamless tiling, different colourways, and vector output.