Parametric deformable models have been extensively and very successfully used for reconstructing free-form curves and surfaces, and for tracking non-rigid deformations, but they require previous knowledge of the topological type of the data, and good initial curve or surface estimates. With deformable models, it is also computationnally expensive to check for and to prevent self-intersections while tracking. The implicit simplicial model that we introduce in this paper are implicit curves and surfaces defined by piece-wise linear functions. This represnetation allows for local deformations, control of the topological type and prevention of self-interesections during tracking.