Point sample, as a fundamental primitive for geometric modeling and image synthesis, has recently gained increasing attentions in computer graphics community. As more and more high precision and detailed geometric models are required in many graphics applications, the scale and complexity of the 3D model data have dramatically increased, thanks to the emergence of various advanced 3D acquiring technologies and new modeling tools. In this situation, polygonal meshes, the traditional geometric representation, are not suitable for representing the large and complex 3D models any more, and people start to directly represent 3D models by points. There are two main reasons: (1) polygon meshes need record the connectivity information between vertices, and storing and maintaining the connectivity information are both memory consuming and computationally expensive. This problem will be even more severely, when the scale and complexity of a mesh is increased further. (2) On the contrary, representing and processing 3D models via point samples are particularly flexible and easy, since there is no need to maintain the global consistency of topology of the surface points. Therefore, it is great significant to study the point based representation and processing method for geometric modeling and image synthesis.The 3D models we studied are generally a set of dense sampled points on a solid object's surface. Each sampled point records its position and some other optional attributes, such as normal, color, and materials et al. In this thesis, we first review the development of the point based graphics including some significant previous works. And then present a set of new algorithms on geometric modeling and rendering for point models, which are suitable for processing the widely used large scale and complex 3D point sampled models.First of all, we present a novel implicit surface reconstruction algorithm from scattered points of a 3D solid object. In this algorithm, we propose to use the local bilateral filter function near the surface of the point model as the surface reconstruction function. The function value at a given position near the model surface is computed directly by the bilateral filter function of the nearest K-neighbors. Compared with previous methods, our algorithm doesn't need solve any linear system or non-linear equations and doesn't need any internal or external support points, it is very fast. In addition, it can handle the noising data and preserve sharp features, since the function is based on a bilateral filter. Experiment results show that it can reconstruct high quality surfaces for complex 3D objects.