Injective hierarchical free-form deformations using THB-splines. (July 2018) - Reis, João Pedro Duro; Kosinka, Jiří
Abstract: 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 R 3 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. Highlights: We present a real-time FFD method based on THB-splines. It comes with an intuitive user interface with features such as control point hiding and region of influence highlighting. Our method provides efficient injectivity checking resulting in interactive fold-over prevention.