Convex approximation means on-negative basis or shape functions which have a variation diminishing approximation and yield non-negative mass matrices for dynamic analysis.The B-spline or NURBS basis functions used in isogeometric analysis are naturally convex.Nonetheless,the commonly used moving least square or reproducing kernel meshfree approximants are non-convex.Therefore,the construction of convex meshfree approximations is an important recent topic for meshfree methods.