Implementation of virtual ruler for interactive object design system

基于3D数据采集系统的研究得出了以下结果：曲面可以根据高斯曲率或平均曲率进行分类，而最大和最小曲率k1和k2分别作为分类的较好指标。基于k1和k2的符号的分类显示了凸、超和凹曲面按面积大小依次出现的特征。如果k1和k2接近于零，适当的阈值可以通过引入圆柱曲面来大大减少三角面片的数目，进一步的结果是关于我们应该生成的曲线。虚拟标尺：回旋曲线的曲率变化是线性的，并且适合作为用于设计目的的引导曲线，同时存在曲线通常不通过任意给定的三个点的严格限制。我们不可避免地要使用复合曲线，这使得设计过程中， ...更多信息 Bezier（子）段可以很容易地被虚拟标尺利用，由于其曲率的不必要的变化，所获得的段不能直接用于设计目的。作为回旋曲线和Bezier曲线之间的折衷曲线，Bezier螺旋线是有用的。此曲线最适合虚拟标尺曲线。要将贝塞尔曲线应用于设计，其阶数应为三（或者控制点的数量应该是四个）来实现与广泛使用的样条标尺的一致性，如果我们将第二个控制点设置在第一个和第三个控制点之间的中间位置，如果第二控制点在第一和第三控制点之间（通常不在中间点），则可以数值地导出可能的Bezier螺旋。这些螺旋线是虚拟标尺的目标曲线，这些结果产生了虚拟标尺的原型，应该在交互设计工作中使用。少

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