Implementation of virtual ruler for interactive object design system

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The investigation based on the 3D data acquisition system brought the following results :Curved surfaces might be classified depending on the Gaussian or Mean curvature, while the maximum and minimum curvatures, k1 and k2, respectively, serves as the better index for the classification.The classification based on the sign of k1 and k2 shows the characteristics that the convex, hyper and concave surfaces appear in this order regarding the size of areas.If k1 and k2 are closed to zero, appropriate threshold value might help greatly reduce the number of triangular patches by introducing the cylindrical surface.Further results are regarding on the curve that should be generated by our virtual rulers :The curvature change of Clothoid curves is linear and appropriate as the guide curves for the design purpose, while there is heavy restriction that the curves do not in general pass through the arbitrarily given three points. We inevitably have to use composite curves, this makes the design pr … More ocess awkward.Bezier (sub) segment may be easily utilized by a virtual ruler, the obtained segment could not be used directly for the design purpose due to their unwanted change in their curvature.As the trade off curve between Clothoid and Bezier curves, Bezier spiral is useful. This curve is the best for virtual ruler curves.To apply Bezier spirals for the design, the order should be three (or the number of control points should be four) to realize the consistency with the widely used spline rulers.If we set the second control point in the middle position between the first and the third control points, the area where Bezier spiral exist may be analytically obtained.If the second control point is between the first and the third control points (not in the middle point in general) the possible Bezier spiral may be numerically derived. These spirals are the target curves by virtual rulers.These results yield the prototype of the virtual ruler that should be used in interactive design work. Less