Surface design and reconstruction techniques in computer graphics

The pivotal role of geometric modeling is to build computer-compatible shape descriptions for real world objects and to virtually construct and deform geometric models interactively with a computer (CAGD). This dissertation presents work on surface reconstruction and surface design techniques for computer graphics.; In a computer system, geometric objects like curves, surfaces and solids are internally expressed as mathematical formulations, in which the shape of an object is quantified by a set of shape control variables. Traditional shape modeling algorithms heavily rely on the designers' expertise to manually adjust a large set of shape control variables in order to achieve the desired shape. This is often non-intuitive and laborious. The energy optimization method and the physics-based dynamic models have the ability to bridge the gap between the shape design specification and the geometric representation. In this dissertation, we propose a systematic approach to the use of energy functionals and physics-based dynamic models as basic geometric modeling tools. In our geometric modeling system, the designers interactively manipulate surfaces via energy functionals, simulated forces, qualitative and quantitative constraints, and leave the system to determine the large number of shape control variables including control points, weights, NURBS knots and non-uniform subdivision rules.; The second part of this dissertation proposes our novel surface reconstruction technique built on Shepard implicits. In our system, the surface is assumed to be a 2-manifold of piecewise continuity, with isolated small regions of high curvature, complex topology, loss of data and abrupt bursts of noise. We employ a fitting-and-blending approach toward the problem of surface reconstruction from noisy and defective data sets. A global implicit function is generated by blending locally-fitted implicit quadrics using the modified Shepard's method. The result surface is the zero level set of the global implicit function. In addition, our new approach has the desirable capability of detecting and preserving sharp features during the reconstruction process even with noisy and defective data sets.