Cubic mean value coordinates

• DOI: 10.1145/2461912.2461917
• Publication Date: 2013-07-16T18:06:45Z
• Authors: Xian-Ying Li; Tao Ju; Shi-Min Hu
• Keywords: Barycentric coordinate system; Biharmonic equation; Transfinite number; Polygon (computer graphics); Interpolation

We present a new method for interpolating both boundary values and gradients over 2D polygonal domain. Despite various previous efforts, it remains challenging to define closed-form interpolant that produces natural-looking functions while allowing flexible control of constraints. Our builds on an existing transfinite continuous domain, which in turn extends the classical mean value interpolant. re-derive from property biharmonic functions, prove indeed matches gradient constraints when is piece-wise linear. then give formula (as generalized barycentric coordinates) represented as polynomials up degree 3 (for values) 1 normal derivatives) each polygon edge. demonstrate flexibility efficiency our coordinates two novel applications, smooth image deformation using curved cage networks adaptive simplification meshes.