Blending Extension of Non-Adjacent Cubic Bzier Curves and Surfaces

Key Points

• 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.