ABSTRACT
As one of the most important research topics in computer graphics, curves and surfaces have been applied in footwear manufacture for a long time. With the deepening application of curves and surfaces, the related theories and algorithms have been
7.1 Curves and Surfaces ..................................................................................... 147 7.1.1 Nonparametric Representation of Curves and Surfaces ................... 148 7.1.2 Parametric Representation of Curves and Surfaces ......................... 148 7.1.3 Comparison of Parametric and Nonparametric Representations ..... 148 7.1.4 Applications ...................................................................................... 149
7.2 Reverse Engineering ..................................................................................... 149 7.3 Processing of Point Clouds ........................................................................... 150
7.3.1 Denoising of Noisy Point Clouds ...................................................... 150 7.3.2 Point Cloud Transformation ............................................................. 153 7.3.3 Registration of Point Clouds ............................................................. 155
7.3.3.1 Coarse Registration Using PCA ......................................... 156 7.3.3.2 Fine Registration Using ICP .............................................. 156
7.4 Surface Reconstruction ................................................................................. 157 7.5 Shape Deformation ....................................................................................... 160 7.6 Dimensional Measurements ......................................................................... 162
7.6.1 Foot Dimension Definitions .............................................................. 163 7.6.2 Determination of Dimensions........................................................... 164
7.7 Models Geometric Fitting ............................................................................. 167 7.7.1 Ray-Based Difference Computation ................................................. 167 7.7.2 Rotation Using Genetic Algorithm ................................................... 168
7.8 Summary ...................................................................................................... 169 Questions ................................................................................................................ 170 References .............................................................................................................. 170
more and more mature. According to the definition of mathematical expressions of curves and surfaces, generally speaking, there are two kinds of representations: parametric and nonparametric (Foley et al. 1993). Furthermore, nonparametric representation is divided into two subcategories: explicit and implicit equations.
