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ON RULED SURFACES AND THE DEVELOPMENT OF DEVELOPABLE SURFACES

V Villoria San Miguel

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Abstract

Ruled and developable surfaces have important applications in the solution of the many technical problems which are encountered, for example, in ships surfaces, which are assimilated by regions to developable or almost developable surface. In this article an analysis is made of: i) ruled surfaces and their computer representation; and ii) developable surfaces, examining the most elemental forms for their generation, the curvature of their lines in development, geodesic curvature and their geodesic lines, and their development on a plane.

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What this paper is about

Ruled and developable surfaces have important applications in the solution of the many technical problems which are encountered, for example, in ships surfaces, which are assimilated by regions to developable or almost developable surface. In this article an analysis is made of: i) ruled surfaces and their computer representation; and ii) developable surfaces, examining the most elemental forms for their generation, the curvature of their lines in development, geodesic curvature and their geodesic lines, and their development on a plane.

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Available abstract

Ruled and developable surfaces have important applications in the solution of the many technical problems which are encountered, for example, in ships surfaces, which are assimilated by regions to developable or almost developable surface. In this article an analysis is made of: i) ruled surfaces and their computer representation; and ii) developable surfaces, examining the most elemental forms for their generation, the curvature of their lines in development, geodesic curvature and their geodesic lines, and their development on a plane.

Key concepts: Developable surface, Ruled surface, Geodesic, Curvature, Geometry, Development (topology), Surface (topology), Plane (geometry)

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