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Shape transformation technique

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Free Form Deformation (FFD) technique is one of techniques in computer graphics, and developed by professor Sederberg of Brigham Young University. In the original FFD technique, control lattice points are defined around a 3D object (Figure 1, left). aBy moving the control lattice points, the 3D object is smoothly deformed (Figure 1, right).

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Figure 1. Deformation of a 3D object by Free Form Deformation technique

We think the deformed grid rather than deformed object more interesting. It is because the deformed grid is a function representing the differences between the 2 forms. If the original form and the target form are digital models of the human body, and if the digital model consists of the same number of data points of the same topology, then we can calculate the movement of the control points that deforms the original form into the target form.

Figure 2 shows an example of the foot deformation. A digital model consisting of 174 data points, each of which is defined based on the anatomical correspondence, was made for each foot. If the 2 forms are similar, only small movement is enough to deform the original form into the target form. If the 2 forms are different, large movement is necessary to deform the original form into the target form. Therefore, we can define a morphological distance as the sum of movements of all the control points.

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Figure 2. Deformed grid that deforms the original foot form (blue) into the target foot form (red)

Since the deformed grid carrys the information on the differences between the 2 forms, it is possible to apply the deformed grid to designing product forms. Supppose there is a "standard" body form (upper left in Figure 3), the product that fit to the "standard"body form (lower left in Figure 2), and a "non standard" body form (upper right), and there is no product that fit to "non standard" body form. First, calculate the deformed grid that deforms the "standard" body shape into the "non-standard" body shape. By deforming the product shape that fit to the "standard" body shape using the deformed grid, we can obtain a product shape that fit to the "non-standard" body shape.

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Figure 3. Application of the deformed grid to designing product shape