Localized G-splines for quad & T-gon meshes.

Area of Science:

• Computer-Aided Design (CAD)
• Geometric Modeling
• Computer Graphics

Background:

• Traditional B-spline surfaces often require regular quadrilateral meshes.
• T-gons and irregular nodes in control nets pose challenges for smooth surface generation.
• Existing methods struggle with juxtaposed T-gons and irregular nodes, limiting design flexibility.

Purpose of the Study:

• To develop novel B-spline surface constructions that handle T-gons and irregular nodes.
• To ensure geometric continuity and good highlight line quality in complex mesh configurations.
• To enhance flexibility in polyhedral design using associated smooth surfaces.

Main Methods:

• Introduction of piecewise polynomial, geometrically continuous surface constructions.
• Utilizing T-gons and irregular nodes within tensor-product B-spline control nets.
• Developing G1-continuous caps of bi-4 degree and near-G1 caps of bi-3 degree for T-gons.

Main Results:

• Achieved good highlight line distributions even with irregular nodes adjacent to T-gons.
• Demonstrated reduced quad-meshing requirements and increased design flexibility.
• Successfully covered T-gons with G1-continuous bi-4 degree caps and near-G1 bi-3 degree caps.

Conclusions:

• The proposed surfaces effectively manage complex mesh structures like T-gons and irregular nodes.
• This approach enhances the design space for polyhedral modeling with smooth surfaces.
• The method preserves desirable surface quality metrics, such as highlight line distribution.