The three-dimensional geometric modeling in computer graphics is concerned with the representation, specification, and manipulation of free-form curves, surfaces, and volumes. This research explores a model for constructing representations of complex three-dimensional surfaces of real-world objects, such as sculptures in a museum, from sample points acquired with a special 3-D camera, and for synthesizing computer-generated pictures from this model. The difficulty of this problem comes from the complexity of the surface characteristics of such objects, which involve complicated irregular shapes and rich textures. This thesis presents a new three-dimensional surface model - three-dimensional fuzzy disk model, for computer graphics display. This model allows any curved surface to be approximated by a number of overlapping disks. A new blending method has been developed to generate smoothly curved surfaces from the overlapping disks. The shape of a blending surface can be controlled by varying some geometric parameters. This three-dimensional fuzzy disk representation is organized into a multi-resolution structure which allows adaptive refinement of surfaces details and supports coarse-to-fine display process. A scan-line rendering algorithm has been developed to synthesize images from the new model. We also present a simpler, less accurate, but more efficient approximation to the original model. In addition, we present a fast shadow penumbra approximation algorithm capable of generating soft shadows.