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In this note we shall introduce a simple, effective numerical method forsolving partial differential equations for scalar and vector-valued datadefined on surfaces. Even though we shall follow the traditional way toapproximate the regular surfaces under consideration by triangular meshes, thekey idea of our algorithm is to develop an intrinsic and unified way to computedirectly the partial derivatives of functions defined on triangular meshes. Weshall present examples in computer graphics and image processing applications.

A new intrinsic numerical method for PDE on surfaces