AN APPROACH TO THREE-DIMENSIONAL RAY TRACING

This report illustrates an approach to the general three-dimensional ray-tracing problem. A set of vector differential equations known as the Frenet Formulas is presented, and the ray equation in vector form is used to evaluate the parameters of curvature and torsion, which lead to the approximation...

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1. Verfasser:	Eby,Edward S
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Sprache:	eng
Schlagworte:	ATTENUATION DIFFERENTIAL EQUATIONS HELIXES INTENSITY MATHEMATICAL ANALYSIS Most project-2 RANGE(DISTANCE) SONAR PULSES SOUND SOUND TRANSMISSION UNDERWATER SOUND VELOCITY
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creator	Eby,Edward S
description	This report illustrates an approach to the general three-dimensional ray-tracing problem. A set of vector differential equations known as the Frenet Formulas is presented, and the ray equation in vector form is used to evaluate the parameters of curvature and torsion, which lead to the approximation of ray paths by helical segments. The only restriction on the sound velocity is that the second partial derivatives with respect to the spatial coordinates exist and are continuous. The general spreading loxs expression is discussed. (Author) Presented as a paper to a seminar on 'Sound Ray Tracing and Isointensity Contours in the Ocean', Pennsylvania State Univ., State College, Jul 65.
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A set of vector differential equations known as the Frenet Formulas is presented, and the ray equation in vector form is used to evaluate the parameters of curvature and torsion, which lead to the approximation of ray paths by helical segments. The only restriction on the sound velocity is that the second partial derivatives with respect to the spatial coordinates exist and are continuous. The general spreading loxs expression is discussed. (Author) Presented as a paper to a seminar on 'Sound Ray Tracing and Isointensity Contours in the Ocean', Pennsylvania State Univ., State College, Jul 65.</description><language>eng</language><subject>ATTENUATION ; DIFFERENTIAL EQUATIONS ; HELIXES ; INTENSITY ; MATHEMATICAL ANALYSIS ; Most project-2 ; RANGE(DISTANCE) ; SONAR PULSES ; SOUND ; SOUND TRANSMISSION ; UNDERWATER SOUND ; VELOCITY</subject><creationdate>1965</creationdate><rights>APPROVED FOR PUBLIC RELEASE</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,780,885,27567,27568</link.rule.ids><linktorsrc>$$Uhttps://apps.dtic.mil/sti/citations/AD0619973$$EView_record_in_DTIC$$FView_record_in_$$GDTIC$$Hfree_for_read</linktorsrc></links><search><creatorcontrib>Eby,Edward S</creatorcontrib><creatorcontrib>NAVY UNDERWATER SOUND LAB NEW LONDON CONN</creatorcontrib><title>AN APPROACH TO THREE-DIMENSIONAL RAY TRACING</title><description>This report illustrates an approach to the general three-dimensional ray-tracing problem. A set of vector differential equations known as the Frenet Formulas is presented, and the ray equation in vector form is used to evaluate the parameters of curvature and torsion, which lead to the approximation of ray paths by helical segments. The only restriction on the sound velocity is that the second partial derivatives with respect to the spatial coordinates exist and are continuous. The general spreading loxs expression is discussed. 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A set of vector differential equations known as the Frenet Formulas is presented, and the ray equation in vector form is used to evaluate the parameters of curvature and torsion, which lead to the approximation of ray paths by helical segments. The only restriction on the sound velocity is that the second partial derivatives with respect to the spatial coordinates exist and are continuous. The general spreading loxs expression is discussed. (Author) Presented as a paper to a seminar on 'Sound Ray Tracing and Isointensity Contours in the Ocean', Pennsylvania State Univ., State College, Jul 65.</abstract><oa>free_for_read</oa></addata></record>
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subjects	ATTENUATION DIFFERENTIAL EQUATIONS HELIXES INTENSITY MATHEMATICAL ANALYSIS Most project-2 RANGE(DISTANCE) SONAR PULSES SOUND SOUND TRANSMISSION UNDERWATER SOUND VELOCITY
title	AN APPROACH TO THREE-DIMENSIONAL RAY TRACING
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