B-splines for physically-based rendering

technical reportAlthough B-spline curves and surfaces have enjoyed a long established place in the graphics community as constructive modeling tools, the use of B-spline approximation techniques has received relatively little attention in rendering. In this work we explore the use of 4D and 5D tensor product B-spline functions to represent surface radiance, and establish that, when appropriately applied, they can be used effectively for static scenes with diffuse to moderately specular elements. Once computed, the surface radiance representation is view independent, can be evaluated quickly, and is equally suited for incorporation into ray tracing or scan-line rendering algorithms. Furthermore, we use B-spline approximation techniques to solve the problem of global illumination for general parametric surfaces with a wide range of reflectance and transmission properties. We conclude that addressing functional approximation aspects offers a fertile research ground relative to the already impressive gains that splines have made in other fields

Improving Filtering for Computer Graphics

When drawing images onto a computer screen, the information in the scene is typically more detailed than can be displayed. Most objects, however, will not be close to the camera, so details have to be filtered out, or anti-aliased, when the objects are drawn on the screen. I describe new methods for filtering images and shapes with high fidelity while using computational resources as efficiently as possible. Vector graphics are everywhere, from drawing 3D polygons to 2D text and maps for navigation software. Because of its numerous applications, having a fast, high-quality rasterizer is important. I developed a method for analytically rasterizing shapes using wavelets. This approach allows me to produce accurate 2D rasterizations of images and 3D voxelizations of objects, which is the first step in 3D printing. I later improved my method to handle more filters. The resulting algorithm creates higher-quality images than commercial software such as Adobe Acrobat and is several times faster than the most highly optimized commercial products. The quality of texture filtering also has a dramatic impact on the quality of a rendered image. Textures are images that are applied to 3D surfaces, which typically cannot be mapped to the 2D space of an image without introducing distortions. For situations in which it is impossible to change the rendering pipeline, I developed a method for precomputing image filters over 3D surfaces. If I can also change the pipeline, I show that it is possible to improve the quality of texture sampling significantly in real-time rendering while using the same memory bandwidth as used in traditional methods

Analytic Antialiasing with Prism Splines

The theory of the multivariate polyhedral splines is applied to analytic antialiasing: a triangular simplex spline is used to represent surface intensity, while a box spline is used as a filter. Their continuous convolution is a prism spline that can be evaluated exactly via recurrence. Evaluation performance can be maximized by exploiting the properties of the prism spline and its relationship to the sampling grid. After sampling, digital signal processing can be used to evaluate exactly and efficiently the sampled result of any analytic spline filter in the span of the box spline basis used as the original analytic filter