Smooth Bi-3 spline surfaces with fewest knots

Converting a quadrilateral input mesh into a C1 surface with one bi-3 tensorproduct spline patch per facet is a classical challenge. We give explicit local averaging formulas for the spline control points. Where the quadrilateral mesh is not regular, the patches have two internal double knots, the least number and multiplicity to always allow for an unbiased G1 construction. Key words: spline surfaces, bicubic, construction, geometry continuity, Catmull-Rom splines.

• Type: Journal
• Year: 2011
• Where: CAD
• Authors: Jianhua Fan, Jörg Peters
• Keywords: CAD 2011, Explicit Local Averaging, Tensorproduct Spline Patch, Theoretical Computer Science, Unbiased G1 Construction