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2008•Computer Engineering and Applications JournalRequires access

Developable B-spline surface for interpolating two planar curves and it's convexity analysis

Fang Kui, Tang Tuo, TAN Jianrong

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Abstract

When the two B-spline boundary curves of the ruled surface are in two arbitrary planes,a necessary and sufficient condition for the (n,n) degree developable B-spline ruled surface is obtained,and the (2,2) degree developable B-spline surfaces are constructed.Through the analysis of the convexity of the B-spline ruled surface,a necessary and sufficient condition for the convex (n,n) degree developable B-spline ruled surface is obtained.

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What this paper is about

When the two B-spline boundary curves of the ruled surface are in two arbitrary planes,a necessary and sufficient condition for the (n,n) degree developable B-spline ruled surface is obtained,and the (2,2) degree developable B-spline surfaces are constructed.Through the analysis of the convexity of the B-spline ruled surface,a necessary and sufficient condition for the convex (n,n) degree developable B-spline ruled surface is obtained.

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Available abstract

When the two B-spline boundary curves of the ruled surface are in two arbitrary planes,a necessary and sufficient condition for the (n,n) degree developable B-spline ruled surface is obtained,and the (2,2) degree developable B-spline surfaces are constructed.Through the analysis of the convexity of the B-spline ruled surface,a necessary and sufficient condition for the convex (n,n) degree developable B-spline ruled surface is obtained.

Key concepts: Developable surface, Convexity, Mathematics, B-spline, Spline (mechanical), Geometry, Surface (topology), Regular polygon

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