Curvature spectrum is a useful feature in surface classification but is difficult to apply to cases with high noise typical e.g. to natural resource point clouds. We propose two methods to estimate the mean and the Gaussian curvature with filtering properties specific to triangulated surfaces. Methods completely filter a highest shape mode away but leave single vertical pikes only partially dampened. Also an elaborate computation of nodal dual areas used by the Laplace-Beltrami mean curvature can be avoided. All computation is based on triangular setting, and a weighted summation procedure using projected tip angles sums up the vertex values. A simplified principal curvature direction definition is given to avoid computation of the full second fundamental form. Qualitative evaluation is based on numerical experiments over two synthetical examples and a prostata tumor example. Results indicate the proposed methods are more robust to presence of noise than other four reference formulations.