An algorithm for the automatic reconstruction of triangular mesh surface model form range images is presented. The optimal piecewise linear surface approximation problem is defined as: given a set S of points uniformly sampled from a vibrate function f(x,y) on a rectangular grid of dimension W X H, find a minimum triangular mesh approximating the surface with vertices anchored at a subset S' of S, such that the deviation at any sample point is within a given bound of (epsilon) > 0. The algorithm deploys a multi- agent resource planning approach to achieve adaptive, accurate and concise piecewise linear approximation using the L-(infinity) norm. The resulting manifold triangular mesh can be directly used as 3D rendering model for visualization with controllable and guaranteed quality. Due to this dual optimality, the algorithm achieves both storage efficiency and visual quality. The error control scheme further facilitates the construction of models in multiple levels of details, which is desirable in animation and virtual reality moving scenes. Experiments with various benchmark range images form smooth functional surfaces to satellite terrain images yield succinct, accurate and visually pleasant triangular meshes. Furthermore, the independence and multiplicity of agents suggest a natural parallelism for triangulation computation, which provides a promising solution for the real-time exploration of large data sets.