Can bi-cubic surfaces be class A?

• Published in: Computer graphics forum Vol. 34; no. 5; pp. 229 - 238
• Main Authors: Karčiauskas, Kęstutis, Peters, Jörg
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.08.2015
• Subjects: Analysis; Automobile industry; Automotive components; Automotive industry; Categories and Subject Descriptors (according to ACM CCS); Highlight lines; I.x.y [Computer Graphics]: Generation-Surface generation; Image processing systems; Product design; Seams; Smoothness; Splines; Studies; Tolerances; Topological manifolds
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/cgf.12711

'Class A surface’ is a term in the automotive design industry, describing spline surfaces with aesthetic, non‐oscillating highlight lines. Tensor‐product B‐splines of degree bi‐3 (bicubic) are routinely used to generate smooth design surfaces and are often the de facto standard for downstream processing. To bridge the gap, this paper explores and gives a concrete suggestion, how to achieve good highlight line distributions for irregular bi‐3 tensor‐product patch layout by allowing, along some seams, a slight mismatch of normals below the industry‐accepted tolerance of one tenth of a degree. Near the irregularities, the solution can be viewed as transforming a higher‐degree, high‐quality formally smooth surface into a bi‐3 spline surface with few pieces, sacrificing formal smoothness but qualitatively retaining the shape.