Blending Extension of Non-Adjacent Cubic Bézier Curves and Surfaces

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This research focuses on developing a method for blending extensions of cubic Bézier curves and surfaces while maintaining G2 continuity.
Designed three auxiliary extension curves with specific continuity conditions: G1, G2, and G0 at connection points.
Utilized a potential function to blend the auxiliary curves into a shape-adjustable extension curve.
Generalized the curve blending extension method to surfaces to address the extension problem between non-adjacent bicubic Bézier surfaces.
Constructed extension curves and surfaces that maintain good smoothness properties.
Numerical experiments confirm the effectiveness of the proposed method on curves and surfaces with different geometric features.
Results demonstrate versatility and adaptability in shape adjustment capabilities.

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Explores blending extension techniques for curves and surfaces, suggesting improved smoothness.

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Yan et al. (2024) studied this question.

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