This paper is focused on the complex shape modeling and rendering problems in CAGD and CAM field. Based on the viewpoints of from discrete to discrete and intuited geometric operation, we roundly summarize our theoretical research works and experimental system development in this paper. The main contents include geometric continuity preserving problem in parametric curve/surface shape blending; subdivision surface generating rules, subdivision surface modeling techniques with corresponding continuity analysis and implementary methods; the uncertainty solution method of surface reflectance.

We first review the research history, classification, characteristic and significance of complex shape modeling and rendering. Mainly on subdivision methods, we then present a survey of the theoretical results and applications on
discrete modeling in resent ten years, and we further analyze the new trends on this realm. This is a base motivation of our research topics.

Coming of the computer animation, the shape blending technique is an important class method in dynamic shape representations. However, the geometric continuity problem on this topic is always ignored and misunderstood by
researchers. For combined Bézier curves case, after we strictly analyze the shape blending process, we introduce the balance geometric continuity condition to ensure the shape feature and give a set of logical solutions. Further more, in patch based parametric surface case, we further point out the difficulty of continuity-preserving shape blending process. Base on this observation, we turn to later subdivision researches.

Focused on the discrete construction of arbitrary topologic shape, we give a novel set of semi-stationary subdivision algorithm. These methods remedy the shortages of traditional stationary cases, and also cover the discrete curve
rendering, quad-based and triangle-based subdivision methods. It is a dynamic extension of stationary subdivisions, expand the representation ability of later cases, and solve the amalgamation problem of subdivision and revolving surface.

Whereas the continuity analysis theory given by Reif et. al. can not be directly used in our case, we employ the sympatric property of subdivision matrix to process analyzing, and finally find out the convergence condition and sufficient tangent continuity condition.

As a powerful reinforce of these approximation subdivision methods, combined with the advantage of unified subdivision framework, semi-stationary control and push-back operator, based on subdivision operator, the push-back semi-stationary subdivision schemes are given in this paper. It is a unification of approximation and interpolation subdivision. Moreover, by employing the longitude-latitude tags in meshes, we introduce the directional constraints into subdivision, and break through the limitation of isotropic subdivision methods.

Also, this method can act as an alternative method of rational subdivision methods.
Base on the mesh dual operation, we propose a novel hexagonal based subdivision algorithm, named honeycomb subdivision. This algorithm is an important extension of topologic rules in subdivision theory research. Different
from quad-based or triangle-based methods, we introduce the concept of central control vertex to improve the shape control ability. It is a subdivision method much fitful for natural shape modeling.

After analyzed the advantages and shortages of several kinds of subdivision surface methods, we generate an abstract subdivision structure from our schemes.

And through improving the mesh half-edge data structure, we have built an experimental subdivision modeling system to test all our algorithms, which is much valuable for real modeling subdivision system.

In the last part of the paper, as a joint topic of shape modeling, rendering and vision cognition fields, we research a key problem in image based relighting and rendering: reflectance estimation. We innovatively contribute BRDF region
segmentation and parametric subspace intersection to solve uncertainty problem in reflectance parameter estimations. This solution is used in shape photo realistic rendering and NPR, and is a potential developing direction of shape modeling and rendering field.

The results of this paper can provide a brand-new total solution for industrial prototype design and computer animation. The semi-stationary subdivision, honeycomb subdivision algorithm and reflectance estimation have high theoretical and practicable values both in the applications of fast prototype design and manufacture , key frame animation; and in the pioneer research of computer graphics and visualization, e.g., shape representations in virtual reality, digital mesh processing, NPR and realistic rendering, etc.

Keywords: CAGD, CAM, Bézier curve, Bézier surface, geometric
continuity, computer animation, shape blending, surface modeling, subdivision
surface, curve rendering, semi-stationary subdivision, subdivision matrix,
convergence, modeling system, photo-realistic graphics, non-photo realistic
rendering, reflectance model, parameter estimation, uncertainty, BRDF.

No tag for this post.