This volume constitutes the thoroughly refereed post-conference proceedings of the 9th International Conference on Mathematical Methods for Curves and Surfaces, MMCS 2016, held in Tønsberg, Norway, in June 2016. The 17 revised full papers presented were carefully reviewed and selected from 115 submissions. The topics range from mathematical theory to industrial applications.

Computational assessment of curvatures and principal directions of implicit surfaces from 3D scalar data.- Coefficient-based spline data reduction by hierarchical spaces.- A Versatile Strategy for the Implementation of Adaptive Splines.- Machinability of surfaces via motion analysis.- Simplicial Complex Entropy.- Precise Construction of Micro-structures and Porous Geometry via Functional Composition.- Partially Nested Hierarchical Refinement of Bivariate Tensor-product Splines with Highest Order Smoothness.- Regression analysis using a blending type spline construction.- On the Coupling of Decimation Operator with Subdivision Schemes for Multi-scale Analysis.- Translation surfaces and isotropic transport nets on rational minimal surfaces.- Towards Subdivision Surfaces C2 Everywhere.- Adaptivity with B-spline Elements.- Reconstructing sparse exponential polynomials from samples:   Stirling numbers and Hermite interpolation.- Reparameterization and Adaptive Quadrature for the Isogeometric Discontinuous Galerkin Method.- Deconfliction and Surface Generation from Bathymetry Data Using LR B-splines.- Application of Longest Common Subsequence Algorithms to Meshing of Planar Domains with Quadrilaterals.- Order-randomized Laplacian mesh smoothing.