Browsing by Author "Mahdavi-Amiri, Ali"
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- ItemOpen Access√3 Multiresolution by Local Least Squares: The Diagrammatic Approach(2015-10-19) Bartels, Richard; Mahdavi-Amiri, Ali; Samavati, FaramarzIn [2, 3, 20, 21] the authors explored a construction to produce multiresolutions from given subdivisions. Certain assumptions carried through that work, two of which we wish to challenge: (1) that multiresolutions for irregular meshes have to be constructed on the fly rather than being prepared beforehand and (2) that the connectivity graph of the coarse mesh would have to be a subgraph of the connectivity graph of the fine mesh. Kobbelt's √3 subdivision [11] lets us engage both of these assumptions. With respect to (2), the √3, post-subdivision connectivity graph shares no interior edges with the pre-subdivision connectivity graph. With respect to (1), we observe that subdivision does not produce an arbitrary connectivity graph. Rather, there are local regularities that subdivision imposes on the fine mesh that are exploitable to establish, in advance, the decomposition and reconstruction filters of a multiresolution for an irregular coarse mesh.
- ItemOpen AccessACM: Atlas of Connectivity Maps(2015-05-05) Mahdavi-Amiri, Ali; Samavati, FaramarzSemiregular models are an important subset of the graphical models used in computer graphics. They are typically obtained by applying repetitive regular refinements on an initial arbitrary model and, as a result, their connectivity exhibits a high degree of regularity. Although data structures exist for regular or irregular models, a data structure designed to take advantage of this semiregularity is desirable. We introduce such a data structure called the atlas of connectivity maps (ACM), which efficiently represents semiregular models resulting from various types of refinements. This atlas maps the connectivity information of vertices and faces onto separate 2D domains called connectivity maps, and handles connectivity queries within each connectivity map using simple algebraic operations or between connectivity maps using a set of linear transformations. We demonstrate the effectiveness of ACM for use in subdivision, multiresolution, and Digital Earth applications. In addition, the generality of ACM has been examined on a variety of face-types (e.g. triangles, hexagons, quads) as well as uniform and adaptive refinements. We compare the performance of ACM to various data structures including the standard half-edge, and show that the performance of ACM is better than these available data structures in supporting important queries such as neighborhood finding and hierarchical traversal.
- ItemOpen AccessCover-it: An Interactive System for Covering 3D Printed Objects(2014-11-03) Mahdavi-Amiri, Ali; Whittingham, Philip; Samavati, FaramarzThe ubiquity of 3D printers has made it possible to print various types of objects, from toys to mechanical objects. However, most available 3D printers are single or double colors. Even printers that can produce objects with multiple colors do not offer the ability to cover the object with a desired material, such as a piece of cloth or fur. In this paper, we propose a system that produces simple 2D patches that can be used as a reference to cover the 3D printed object. The 2D patches are created by optimizing a fitness function that measures a number of criteria such as planarity of patches, smoothness of patch boundaries, and visibility of the seams on the 3D print. The system allows for user interactions to correct and modify the patches, and provides guidelines on how to wrap the printed object via small curves illustrating the patch boundaries etched on the printed object as well as an animation showing how the 2D patches should be folded together.
- ItemOpen AccessData Management Possibilities for Aperture 3 Hexagonal Discrete Global Grid Systems(2016-08-22) Mahdavi-Amiri, Ali; Alderson, Troy; Samavati, FaramarzIn a Digital Earth framework, data sets are gathered from different sources in three main forms: imagery/elevation, vector, and quantitative data sets. In order to efficiently work with these data sets in a Digital Earth framework, effective methods to represent and transmit these data sets are required. While these representations may be different for each type of data set, they must all preserve the actual data as much as possible in order to accurately address queries. Furthermore, they also need to be compatible with the underlying structure of the Digital Earth framework. In this paper, we describe several data representations for an Aperture 3 Hexagonal Discrete Global Grid System which is a common approach to build a Digital Earth framework. We also discuss how they can be used to transmit data sets or address specific queries.
- ItemOpen AccessGFFD: General Free Form Deformations using Partition Unity Parametrics(2017-04-08) Mahdavi-Amiri, Ali; Samavati, FaramarzFree Form Deformations (FFD) have been successfully employed to deform 2D or 3D shapes to manipulate them and obtain a desired shape. In this deformation, a lattice of control points is placed on the given shape and by moving control points, the given shape is deformed according to a set of underlying smooth basis function (e.g. BSpline, NURBS). In this paper, we attempt to generalize Free Form Deformations (GFFD) by using more general basis functions called Partition Uniform Parametrics or PUPs. We provide a comparison of GFFD in which PUPs are employed as the basis functions with BSpline, Bezier, and NURBS basis functions. Although this work is in its preliminary stages, we believe that there are many directions to improve and extend the current idea. We eventually discuss these ideas in the paper.
- ItemOpen AccessHierarchical Grid Conversion(2016-04-01) Mahdavi-Amiri, Ali; Harrison, Erika; Samavati, FaramarzHierarchical grids appear in various applications in computer graphics such as subdivision and multiresolution surfaces, and terrain models. Since the different grid types perform better at different tasks, using simple conversions, we can switch between the grid types to take advantages of each grid for better supporting advanced applications. In this paper, we introduce some simple conversions between grids. To describe their usage, we define new regular and semiregular refinements. We also describe how patch-based data structures can be used for hexagonal cells and semiregular refinements.
- ItemOpen AccessRIAS: Repeated Invertible Averaging for Surface Multiresolution of Arbitrary Degree(2020-02-11) Alderson, Troy F.; Mahdavi-Amiri, Ali; Samavati, FaramarzIn this paper, we introduce two local surface averaging operators with local inverses and use them to devise a method for surface multi-resolution (subdivision and reverse subdivision) of arbitrary degree. Similar to previous works by Stam, Zorin, and Schröder that achieved forward subdivision only, our averaging operators involve only direct neighbours of a vertex, and can be configured to generalize B-Spline multi-resolution to arbitrary topology surfaces. Our subdivision surfaces are hence able to exhibit Cd continuity at regular vertices (for arbitrary values of d) and appear to exhibit C1 continuity at extraordinary vertices. Smooth reverse and non-uniform subdivisions are additionally supported.
- ItemOpen AccessA Survey of Digital Earth Representation and Visualization(2015-04-07) Mahdavi-Amiri, Ali; Alderson, Troy; Samavati, FaramarzThe creation of a digital representation of the Earth and its associated data is a complex and difficult task. The incredible size of geospatial data and differences between data sets pose challenges related to big data, data creation, and data integration. Advances in globe representation and visualization have made use of Discrete Global Grid Systems (DGGSs) that discretize the globe into a set of cells to which data are assigned. DGGSs are well studied and important in GIS, OGC, and Digital Earth communities. However, DGGSs have not been introduced very well to computer graphics community. In addition, there are many advanced techniques related to geospatial data creation and representation that might be very useful to Digital Earth community. In this paper, we provide an overview of DGGSs and their use in digitally representing the Earth as well as the list of current Digital Earths and their method of Earth representation. In addition, we present key research areas and related papers in computer graphics that are useful for a Digital Earth framework. Moreover, we list a number of applications of Digital Earths and their related works.