Topic
Function representation
About: Function representation is a research topic. Over the lifetime, 459 publications have been published within this topic receiving 10774 citations.
Papers published on a yearly basis
Papers
1 Feb 1980
TL;DR: In this paper, a straightforward approach that does not involve delta-function techniques is used to rigorously derive a generalized electric dyadic Green's function which defines uniquely the electric field inside as well as outside the source region.
Abstract: A straightforward approach that does not involve delta-function techniques is used to rigorously derive a generalized electric dyadic Green's function which defines uniquely the electric field inside as well as outside the source region. The electric dyadic Green's function, unlike the magnetic Green's function and the impulse functions of linear circuit theory, requires the specification of two dyadics: the conventional dyadic G- e outside its singularity and a source dyadic L-which is determined solely from the geometry of the "principal volume" chosen to exclude the singularity of G- e . The source dyadic L-is characterized mathematically, interpreted physically as a generalized depolarizing dyadic, and evaluated for a number of principal volumes (self-cells) which are commonly used in numerical integration or solution schemes. Discrepancies at the source point among electric dyadic Green's functions derived by a number of authors are shown to be explainable and reconcilable merely through the proper choice of the principal volume. Moreover, the ordinary delta-function method, which by itself is shown to be inadequate to extract uniquely the proper electric dyadic Green's function in the source region, can be supplemented by a simple procedure to yield unambiguously the correct Green's function representation and associated fields.
610 citations
TL;DR: This work uses a high-level geometric language that can extend the interactive modeling system by input symbolic descriptions of primitives, operations, and predicates and supports combinations of representational styles, including constructive geometry, sweeping, soft objects, voxel-based objects, deformable and other animated objects.
Abstract: Concepts of functionally based geometric modeling including sets of objects, operations, and relations are discussed. Transformations of a defining real function are described for set-theoretic operations, blending, offsetting, bijective mapping, projection, cartesian products, and metamorphosis. Inclusion, point membership, and intersection relations are also described. We use a high-level geometric language that can extend the interactive modeling system by input symbolic descriptions of primitives, operations, and predicates. This approach supports combinations of representational styles, including constructive geometry, sweeping, soft objects, voxel-based objects, deformable and other animated objects. Application examples of aesthetic design, collisions simulation, NC machining, range data processing, and 3D texture generation are given.
514 citations
1 Oct 1972
TL;DR: A winged edge polyhedron representation is stated and a set of primitives that preserve Euler''s F-E+V = 2 equation are explained.
Abstract: A winged edge polyhedron representation is stated and a set of primitives that preserve Euler''s F-E+V = 2 equation are explained. Present use of this representation in artificial intelligence for computer graphics and world modeling is illustrated and its intended future application to computer vision is described.
396 citations
TL;DR: This paper reviews and evaluates different shape representations, geometric algorithms, and rendering methods, which use points as a universal graphics primitive, both for efficient rendering and for flexible geometry processing of highly complex 3D-models.
373 citations
Journal Article•
TL;DR: In this article, the authors consider 3D object retrieval in which a polygonal mesh serves as a query and similar objects are retrieved from a collection of 3D objects using a normalization step in which models are transformed into canonical coordinates.
Abstract: We consider 3D object retrieval in which a polygonal mesh serves as a query and similar objects are retrieved from a collection of 3D objects. Algorithms proceed first by a normalization step in which models are transformed into canonical coordinates. Second, feature vectors are extracted and compared with those derived from normalized models in the search space. In the feature vector space nearest neighbors are computed and ranked. Retrieved objects are displayed for inspection, selection, and processing. Our feature vectors are based on rays cast from the center of mass of the object. For each ray the object extent in the ray direction yields a sample of a function on the sphere. We compared two kinds of representations of this function, namely spherical harmonics and moments. Our empirical comparison using precision-recall diagrams for retrieval results in a data base of 3D models showed that the method using spherical harmonics performed better.
305 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2023 | 1 |
| 2022 | 7 |
| 2021 | 11 |
| 2020 | 12 |
| 2019 | 7 |
| 2018 | 7 |