Generating B-spline curves with points, normals and curvature constraints: a constructive approach

Authors:
Abdulwahed Abbas;Ahmad Nasri;Takashi Maekawa
Affiliations:
The University of Balamand, Department of Computer Science, Tripoli, Lebanon;American University of Beirut, Department of Computer Science, Beirut, Lebanon;Yokohama National University, Department of Mechanical Engineering, Yokohama, Japan
Venue:
The Visual Computer: International Journal of Computer Graphics
Year:
2010

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Abstract

This paper presents a constructive method for generating a uniform cubic B-spline curve interpolating a set of data points simultaneously controlled by normal and curvature constraints. By comparison, currently published methods have addressed one or two of those constraints (point, normal or cross-curvature interpolation), but not all three constraints simultaneously with C2 continuity. Combining these constraints provides better control of the generated curve in particular for feature curves on free-form surfaces. Our approach is local and provides exact interpolation of these constraints.