Freeform texture representation and characterisation based on triangular mesh projection techniques

• Published in: Measurement : journal of the International Measurement Confederation 2016-10, Vol.92, p.172-182
• Main Authors: Abdul-Rahman, Hussein S., Lou, Shan, Zeng, Wenhan, Jiang, Xiangqian, Scott, Paul J.
• Format: Article
• Language: English
• Subjects: Freeform surfaces; Geometrical metrology; Non-Euclidean geometry; Surface characterisation; Surface metrology; Texture representation; Triangular meshes
• ISSN: 0263-2241; 1873-412X
• DOI: 10.1016/j.measurement.2016.06.005

•The paper proposes a new framework for calculating the texture for freeform surfaces represented by 3D triangular meshes.•The paper proposes a new method of representing the texture of freeform surfaces based on mesh projection techniques.•The paper investigates a number of mesh projection algorithms that would minimise the metric distortion.•The paper extends four surface height parameters from the regular case to the 3D triangular mesh case. Texture characterisation for freeform non-Euclidean surfaces is becoming increasingly important due to the widespread of the use of such surfaces in different applications, e.g. the additive manufacturing. Four main steps are required to analyse and characterise those surfaces which include new surface representation, surface filtration and decomposition, texture representation methods and finally the calculation of the surface parameters. Recently, the representation, as well as the filtration and decomposition, of freeform surfaces have been investigated and some algorithms have been proposed. This paper, however, shed the light on how to represent the texture of freeform non-Euclidean surfaces before calculating the parameters. A novel model for freeform surface parameterisation is introduced; this new model proposes the use of a projection algorithm before the actual calculation of the parameters. Different projection algorithms have been adopted from the mesh projection techniques found in the field of computer graphics. The results of applying those algorithms to represent the texture of both simulated and bio-engineering surfaces are shown, also a comparison between those algorithms has been carried out. Furthermore, examples of calculating some of the surface parameters for freeform surfaces are given.