Shape blending of curves and surfaces with geometric continuity

摘要

Linear interpolation between G{sup}1 piecewise continuous curves may result in geometrically non-continuous curves. This affects the continuity of the shapes created in a shape-blending process. Similar effects also affect the continuity of the ruled surfaces constructed with G{sup}1 continuous curves. This paper presents an approach for maintaining G{sup}1 continuity of the blended curves by adjusting the positions of the junction points of the curve segments. Criterion for G{sup}1 continuity of ruled surfaces are studied and the sufficient conditions for G{sup}1 continuity are identified. G{sup}1 continuity of composite surfaces in a shape-blending process is also studied. An approach is proposed to maintain the G{sup}1 continuity of Bezier surfaces pairs in a shape-blending process by adjusting the control points along the common boundary of the resulting surface-pair. This is extended for retaining G{sup}1 continuity of shape-blended Bezier surfaces sharing a common corner.