基于四元素插值的空间曲线边界约束变形方法

曲线形状的变形技术在计算机动画和产品造型设计中有着重要的应用。以单位球面四元素插值为基础建立非线性的局部变换，通过在中间帧重构方程引进边界控制条件，提出了具有边界约束的空间曲线和平面曲线形状的变形方法。该方法在曲线形状渐变序列中具有保周长的线性变化，适合一般曲线的渐变和骨架行走的特征。还给出了建立渐变序列的边界曲线算法，通过实例说明了造型和编辑边界曲线能得到良好的拼接效果。实验表明,该算法在空间曲线变形中具有良好的视觉效果和应用前景，算法具有简易性和统一性。

3D-Curves shape blending with constrained boundary based on quaternion interpolation

Curve shape blending plays an important role in animation and products modeling. In this paper, we presented an approach of 3D-Curves and 2D-Curves shape blending with constrained boundary, by structuring nonlinear local interpolation with quaternion and using boundary control conditions in restructuring equation of in-between shapes. The approach preserves linear of perimeters of curves blending sequences, and it fits general curves blending and skeleton moving. We gave algorithm of boundary curve, and excellent results of blending surfaces were shown by examples. Experimental results indicate that our method can generate visual-pleasing blending sequences of 3D-Curves, and promising applications. Our approach has advantages over others such as simplicity and uniformity.