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Can bi‐cubic surfaces be class A?
Author(s) -
Karčiauskas Kęstutis,
Peters Jörg
Publication year - 2015
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.12711
Subject(s) - tensor product , bicubic interpolation , spline (mechanical) , smoothness , surface (topology) , computer science , degree (music) , class (philosophy) , automotive industry , mathematics , geometry , pure mathematics , mathematical analysis , spline interpolation , structural engineering , computer vision , engineering , artificial intelligence , physics , acoustics , aerospace engineering , bilinear interpolation
'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.