Injective hierarchical free-form deformations using THB-splines

The free-form deformation (FFD) method deforms geometry in n-dimensional space by employing an n-variate function to deform (parts of) the ambient space. The original method pioneered by Sederberg and Parry in 1986 uses trivariate tensor-product Bernstein polynomials in R3 and is controlled as a Bézier volume. We propose an extension based on truncated hierarchical B-splines (THB-splines). This offers hierarchical and local refinability, an efficient implementation due to reduced supports of THB-splines, and intuitive control point hiding during FFD interaction. Additionally, we address the issue of fold-overs by efficiently checking the injectivity of the hierarchical deformation in real-time.