We developed a software tool for art scholars studying geometrical perspective in realist art. Our software, written in Mathematica, accepts a digital image of an artwork that may not obey the rigorous rules of geometrical prospective. The user/scholar marks…
This paper presents a new unified subdivision scheme that is defined over a k-simplicial complex in n-D space with k<=3. We first present a series of definitions to facilitate topological inquiries during the subdivision process. The scheme is derived from the double (k+1)-directional box splines…
In this dissertation, we address the challenges by proposing a novel framework for solid model representation based on subdivision process. We call our approach Multiresolution Solid Objects, or MSO. Within the MSO framework…
This paper presents DigitalSculpture, an interactive sculpting environment founded upon iso-surfaces extracted from recursively subdivided, 3D irregular grids. Our unique implicit surface arises from an interpolatory, volumetric subdivision scheme…
In this paper, we propose novel trivariate spline-based solid subdivision schemes over arbitrary tetrahedral meshes in 3D space. The motivation of the proposed solid subdivision schemes are to represent solid objects with complex topology and heterogeneous material properties. The subdivision…
This paper presents a new, volumetric subdivision scheme for interpolation of arbitrary hexahedral meshes. To date, nearly every existing volumetric subdivision scheme is approximating, i.e., with each application of the subdivision algorithm…
Despite the growing interest in subdivision surfaces within the computer graphics and geometric processing communities, subdivision approaches have been receiving much less attention in solid modeling. This paper presents a powerful new framework for a subdivision scheme…
Subdivision has gained popularity in computer graphics and shape modeling during the past two decades, yet volumetric subdivision has received much less attention. In this paper, we develop a new subdivision scheme which can interpolate…
During the past twenty years, much research has been undertaken to study surface representations based on B-splines and box splines. In contrast, volumetric splines have received much less attention as an effective and powerful solid modeling tool. In this paper, we propose…
Reconstruction of missing or damaged portions of images is an ancient practice used extensively in artwork restoration. Recently, a few digital inpainting models based on the use of partial differential equations have been proposed. Unfortunately, these algorithms are computationally expensive…