可拉伸的ARAP++曲面参数化算法

Surface Stretchable Parameterization Algorithm Base on ARAP++Method

为了能够得到有效的三角网格参数化结果,基于ARAP方法提出了一种可拉伸的曲面参数化方法。该方法可针对高曲率的三角网格进行处理,消除重叠,从而得到可拉伸的平面和球面参数化结果。它建立在平面ARAP++方法的局部优化和全局求解的框架下,通过调整Jacobian矩阵奇异值的拉伸算子,来控制参数化的角度面积和拉伸扭曲。利用数值实验将该方法与其它方法的3种扭曲度量和运行时间进行对比,将平面和球面参数化方法都应用到模型的纹理映射中。研究结果表明,该算法可以通过平面上的Jacobian矩阵直接推广到球面参数化,便捷高效,应用灵活,可取得很好的视觉效果。

In order to obtain the valid results,a novel stretch surface parameterization method base on the ARAP method was proposed.It could be applied to the triangular mesh with high-curvature,and the stretchable surface parameterization for triangular meshes without overlapping was obtained.It was established on the local optimization and overall situation solution based on the 2D plane ARAP++method.By adjusting the exponent of singular value of Jacobian matrix,the angle,area and stretch distortion of surface parameterization were controlled.method is efficient and convergent,can extend to spherical method directly.Numerical results demonstrate that it outperforms several popular methods on the distortion of angle area and stretch.Furthermore,planar and spherical method can achieve better visualization in texture mapping.The results show that our plane method can be directly extended to spherical parameterization,which is convenient,efficient and flexible.