Optimal fitting of strain-controlled flattenable mesh surfaces. Issue 9 (December 2016)

• Record Type: Journal Article
• Authors: Zhang, Yunbo; Wang, Charlie; Ramani, Karthik
• Is Part Of: International journal of advanced manufacturing technology. Volume 87:Issue 9/12(2016)
• Page Start: 2873
• Page End: 2887
• Publication Date: 2016-12
• Subjects: Surface approximation -- Flattenable mesh surface -- Optimization -- Stretching controlled -- Coarse-to-fine fitting; Manufacturing processes -- Periodicals; Production engineering -- Periodicals; 670.427
• DOI: 10.1007/s00170-016-8669-2
• Languages: English
• ISSNs: 0268-3768

Abstract

Abstract A flattenable mesh surface is a polygonal mesh surface that can be unfolded into a planar patch without stretching any polygon. This paper presents a new method for computing a slightly stretched flattenable mesh surfaceM from a piecewise-linear surface patchP ∈R 3, where the shape approximation error betweenM andP is minimized and the strain of stretching onM is controlled. Prior approaches result in either a flattenable surface that could be quite different from the input shape or a (discrete) developable surface has relative simple shape. The techniques investigated in this paper overcome these difficulties. First, we introduce a new surface modeling method to conduct a sequence of nearly isometric deformations to morph a flattenable mesh surface to a new shape which has a better approximation of the input surface. Second, in order to get better initial surfaces for fitting and overcome topological obstacles, a shape perturbation scheme is investigated to obtain the optimal surface fitting result. Last, to improve the scalability of our optimal surface fitting algorithm, a coarse-to-fine fitting framework is exploited so that very dense flattenable mesh surfaces can be modeled and boundaries of the input surfaces can be interpolated.