Geometric Theory of Ray Tracing
| Autor: | Edward S. Eby |
|---|---|
| Rok vydání: | 1970 |
| Předmět: |
Riemann curvature tensor
Acoustics and Ultrasonics Geodesic Geodesic map Mathematical analysis Fundamental theorem of Riemannian geometry Curvature symbols.namesake Arts and Humanities (miscellaneous) symbols Mathematics::Differential Geometry Tensor Metric tensor (general relativity) Solving the geodesic equations Mathematics |
| Zdroj: | The Journal of the Acoustical Society of America. 47:273-275 |
| ISSN: | 0001-4966 |
| Popis: | A temporal metric tensor is defined by combining the sound‐speed function with the spatial metric tensor for a Riemannian space. Fermat's principle implies that spatial rays are temporal geodesics. Ray equations generalized to Riemannian spaces are shown to be temporal geodesic equations expressed in spatial terms. This geometric derivation leads to the consideration of geodesic deviation and its relation to three‐dimensional spreading loss. Previous results [E. S. Eby, “Frenet Formulation of Three‐Dimensional Ray Tracing,” J. Acoust. Soc. Amer. 42, 1287–1297 (1967)] are generalized to Riemannian spaces, and tensor expressions are derived for ray curvature and torsion. |
| Databáze: | OpenAIRE |
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