Representation of a complex three-dimensional (3D) shape requires extensive computer-aided design data consisting of millions (or tens of millions) of approximated discontinuous points. The quantity of data makes it difficult or impossible to efficiently optimize the entire shape. We present a vehicle-modeling function in the form of an exponential function to smoothly express the complex two-dimensional and 3D curved shapes of an automobile. This modeling function can modify and optimize the shape with fewer design variables compared with ordinary point-fitting methods. The subsectional parts of the vehicle-modeling function are defined as section functions by classifying each subsection of the automobile configuration as a section box model. The proposed approach is suitable for remodeling existing automobiles and for newly designed automobiles. The entire 3D aerodynamic shape of an automobile can be created using a set of the proposed modeling functions, which define a combination of section boxes. A 3D aerodynamic shape was developed to verify that the optimization of the shape was practical. This capability may help to reduce the developmental time or cost of automobiles and similarly complex systems. In addition, the proposed approach can be expanded to other fields of engineering.

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