Functional representation and manipulation of shapes with applications in surface and solid modeling

Real-valued functions have wide applications in various areas within computer graphics. In this work, we examine three representation of shapes using functions. In particular, we study the classical B-spline representation of piece-wise polynomials in the univariate domain. We provide a generalization of B-spline to the bivariate domain using intuition gained from the univariate construction. We also study the popular scheme of representing 3D density distribution using a uniform, rectilinear grid, where we provide a novel contouring scheme that culls occluded inner geometries. Lastly, we examine a ray-based representation for 3D indicator functions called ray-rep, for which we present a novel meshing scheme with multi-material extensions

Real-Time deep image rendering and order independent transparency

In computer graphics some operations can be performed in either object space or image space. Image space computation can be advantageous, especially with the high parallelism of GPUs, improving speed, accuracy and ease of implementation. For many image space techniques the information contained in regular 2D images is limiting. Recent graphics hardware features, namely atomic operations and dynamic memory location writes, now make it possible to capture and store all per-pixel fragment data from the rasterizer in a single pass in what we call a deep image. A deep image provides a state where all fragments are available and gives a more complete image based geometry representation, providing new possibilities in image based rendering techniques. This thesis investigates deep images and their growing use in real-time image space applications. A focus is new techniques for improving fundamental operation performance, including construction, storage, fast fragment sorting and sampling. A core and driving application is order-independent transparency (OIT). A number of deep image sorting improvements are presented, through which an order of magnitude performance increase is achieved, significantly advancing the ability to perform transparency rendering in real time. In the broader context of image based rendering we look at deep images as a discretized 3D geometry representation and discuss sampling techniques for raycasting and antialiasing with an implicit fragment connectivity approach. Using these ideas a more computationally complex application is investigated — image based depth of field (DoF). Deep images are used to provide partial occlusion, and in particular a form of deep image mipmapping allows a fast approximate defocus blur of up to full screen size