Injective hierarchical free-form deformations using THB-splines. (July 2018)

• Record Type: Journal Article
• Authors: Reis, João Pedro Duro; Kosinka, Jiří
• Is Part Of: Computer aided design. Volume 100(2018)
• Page Start: 30
• Page End: 38
• Publication Date: 2018-07
• Subjects: Free-form deformation -- Model deformation -- Truncated hierarchical B-spline -- Computer aided design -- Injective deformation; Computer-aided design -- Periodicals; Engineering design -- Data processing -- Periodicals; Computer graphics -- Periodicals; Conception technique -- Informatique -- Périodiques; Infographie -- Périodiques; Computer graphics; Engineering design -- Data processing; Periodicals; Electronic journals; 620.00420285
• DOI: 10.1016/j.cad.2018.02.005
• Languages: English
• ISSNs: 0010-4485

Abstract

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.