This paper presents an efficient compression algorithm for animated three-dimensional (3D) meshes. First, a segmentation approach is applied to achieve the motion estimation. The main idea is to exploit the temporal coherence of the geometry component by using the heat diffusion properties. The motion of the resulting regions is accurately described by 3D affine transforms. These transforms are computed at the first frame to match the subsequent ones. Second, in order to achieve a good compression performance, an efficient rate control mechanism is proposed to quantize the temporal prediction errors. At this stage, a rate-distortion model is used for quantizing the residual information. Comparative coding tests, for irregular 3D mesh sequences, were conducted to evaluate the coding efficiency of the proposed compression scheme. Simulation results show very promising performances.