Parametric curve approximations for surface intersections

A new algorithm is presented for creating a piecewise rational parametric approximation for general bivariate algebraic curves. This problem has been directly linked to the key obstacle which currently restricts the geometric coverage of solid geometric modelers, that of representing the intersection curve between two free-form surfaces. Even though numerical schemes have evolved to generate representations for these curves, there have remained critical deficiencies in the mathematical understanding and completeness of the solutions which severly limit modeling with high degree surfaces. The algorithm proposed in this thesis couples contemporary subdivision methods with techniques and insights derived from classical algebraic and projective geometry to generate the necessary piecewise approximate representation. In addition to solid geometric modeling, the piecewise C\sp0 continuous approximation is also applicable to problems in surface or scattered data contouring and in representing offset curves needed for numerical control tool path generation

Reassembling 3D thin shells using integrated template guidance and fracture region matching

Geometric restoration that composes 3D fragmented pieces into the original complete object is an important computer graphics and geometric processing problem. Automatic and effective restora- Tion has applications in many fields such as archeological recon- struction, digital heritage archiving, forensic evidence processing, to name a few. For example, archaeologists reconstruct ceramic fragments (sherds) into complete pots in order to analyze the infor- mation of the ancient society. Forensic scientists reassemble skull fragments into complete skull for face reconstruction and body i- dentification. In both of these problems we need to solve a compo- sition of digitized thin-shell fragments with different shapes, sizes, and resolutions. This problem remains very challenging

3D fragment reassembly using integrated template guidance and fracture-region matching

This paper studies matching of fragmented objects to recompose their original geometry. Solving this geometric reassembly problem has direct applications in archaeology and forensic investigation in the computer-aided restoration of damaged artifacts and evidence. We develop a new algorithm to effectively integrate both guidance from a template and from matching of adjacent pieces\u27 fracture-regions. First, we compute partial matchings between fragments and a template, and pairwise matchings among fragments. Many potential matches are obtained and then selected/refined in a multi-piece matching stage to maximize global groupwise matching consistency. This pipeline is effective in composing fragmented thin-shell objects containing small pieces, whose pairwise matching is usually unreliable and ambiguous and hence their reassembly remains challenging to the existing algorithms

Intramolecular Binding of Nitrogen Bases to a Cofacial Binuclear Copper(II) Complex

Coordination of pyrazines and pyridines to the cofacial binuclear complex Cu2(NBA)2 (NBAH2 = 3,3′-[2,7-naphthalenediyl-bis(methylene)]bis(2,4-pentanedione)) has been studied by structural and spectroscopic methods. Pyrazines bind more strongly than the corresponding pyridines, suggesting intramolecular, or endo, coordination, which X-ray analysis of the adduct with 2, 5-dimethylpyrazine (2, 5-Me2pyz) confirms: Cu2(NBA)2(μ-2,5-Me2pyz)-4CH2Cl2, monoclinic, space group C2/m (No. 12); a = 22.941 (6), b = 22.432 (4), c = 11.677 (2) Å; β = 97.32 (2)°; V = 5960 (4) Å3; Z = 4; R = 0.096, Rw = 0.093 for 372 parameters and 3358 reflections with I \u3e 1σ(I). The structure contains two independent Cu2(NBA)2(μ-2,5-Me2pyz) molecules (CU⋯CU = 7.596 (2), 7.559 (2) Å), each with a disordered 2,5-Me2pyz moiety and overall 2/m (C2h) symmetry. Equilibrium constants for binding of substituted pyrazines to Cu2(NBA)2 range from ca. 0.2 M−1 (2,3-diethylpyrazine) to 93 M−1 (2-aminopyrazine); binding constants for comparably substituted pyridines are significantly smaller in all cases. Hydrogen bonding between the NH2 group of 2-aminopyrazine and the O atoms of the Cu2(NBA)2 host is probably responsible for its unusually large binding constant. © 1990, American Chemical Society. All rights reserved