Membrane Interpolation To find the value of f, Solve the following minimization problem the gradient operator min V subject to Dirichlet boundary conditions cc可视计算研究中心
• To find the value of f ,Solve the following minimization problem: • subject to Dirichlet boundary conditions: Membrane Interpolation 11 2 min f f f = f * the gradient operator
Solution Euler-Lagrange Equation In our case: F=V2=(2+f 2) The equation is af d af d af f 0 OF =0 and d af d 2fx=2 So we get 72/,a2f==0 cc可视计算研究中心 Visual Computing Research Center
Solution :Euler-Lagrange Equation 12
Laplace Equation Solution Laplace equation with Dirichlet boundary conditions A=0e9,/a=/|a Laplacian operator this method produces an unsatisfactory due to over-blurring cc可视计算研究中心 Visual Computing Research Center
• Solution: Laplace Equation with Dirichlet boundary conditions • this method produces an unsatisfactory due to over-blurring Laplace Equation 13 Laplacian operator
Guided Interpolation v: guided field v may be gradient of a function g cc可视计算研究中心
• v: guided field • v may be gradient of a function g Guided Interpolation 14