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Physical Sciences and Mathematics Commons™
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- Computer graphics (2)
- Cubic algebraic surfaces (2)
- Free-form modeling (2)
- Interpolation (2)
- 3D imaging (1)
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- Base points (1)
- Computational geometry (1)
- Connectionist networks (1)
- Curve fitting (1)
- Example learning (1)
- Generalization (1)
- Implicit polynomial equation (1)
- Incremental rule learning (1)
- Intersection locus (1)
- Morphometric tools (1)
- Parameterization (1)
- Piecewise constructions (1)
- Polygonization algorithm (1)
- Polynomials (1)
- Power basis representation (1)
- Space curve (1)
- Space curves (1)
- Surface anatomy (1)
Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
Techniques For Cubic Algebraic Surfaces Ii, Thomas W. Sederberg
Techniques For Cubic Algebraic Surfaces Ii, Thomas W. Sederberg
Faculty Publications
A survey of some techniques that may have potential for free-form modeling with algebraic surfaces is continued. Classical results as well as several recent innovations are included. Specific attention is paid to cubic algebraic surfaces, although many of the ideas presented have application to algebraic surfaces of any degree. Topics addressed include piecewise constructions, interpolation to points and space curves, and parameterization.
Techniques For Cubic Algebraic Surfaces I, Thomas W. Sederberg
Techniques For Cubic Algebraic Surfaces I, Thomas W. Sederberg
Faculty Publications
The tutorial presents some tools for free-form modeling with algebraic surfaces, that is, surfaces that can be defined using an implicit polynomial equation f(x, y, z )=0. Cubic algebraic surfaces (defined by an implicit equation of degree 3) are emphasized. While much of this material applies only to cubic surfaces, some applies to algebraic surfaces of any degree. This area of the tutorial introduces terminology, presents different methods for defining and modeling with cubic surfaces, and examines the power basis representation of algebraic surfaces. Methods of forcing an algebraic surface to interpolate a set of points or a space curve …
Consistency And Generalization In Incrementally Trained Connectionist Networks, Tony R. Martinez
Consistency And Generalization In Incrementally Trained Connectionist Networks, Tony R. Martinez
Faculty Publications
This paper discusses aspects of consistency and generalization in connectionist networks which learn through incremental training by examples or rules. Differences between training set learning and incremental rule or example learning are presented. Generalization, the ability to output reasonable mappings when presented with novel input patterns, is discussed in light of the above learning methods. In particular, the contrast between humming distance generalization and generalizing by high order combinations of critical variables is overviewed. Examples of detailed rules for an incremental learning model are presented for both consistency and generalization constraints.
Interactive Morphometrics From Three-Dimensional Surface Images, William A. Barrett, Shawn C. Becker
Interactive Morphometrics From Three-Dimensional Surface Images, William A. Barrett, Shawn C. Becker
Faculty Publications
Techniques have been developed for extracting three-dimensional (3D) measurements directly and interactively from 3D representations of surface anatomy. In order to obtain 3D measurements the anatomical surface is interrogated directly through the use of morphometric tools. Morphometric tools include points, 3D graphical "probes", and logical sectioning functions which interact with the surface through depth buffer compositing operations. Tools are interactively positioned on or through the surface to measure surface dimensions and partial volumes, or to define intersecting functions which allow surface anatomy to be visualized in the context of surrounding anatomy. Visualization is also enhanced because tools reveal much pertaining …