It is widely appreciated that 3D structures may be computed from multiple 2D images of the same scene given point correspondences between images. Of greater interest, however, is the generation of surfaces that give a compact representation of the geometric model. Assuming we are dealing with smooth surfaces, we show that B-spline is a good choice for this purpose and we describe how to construct it by approximating the 3D data points. The crucial step is the parameterization of the 3D points in a 2D domain. By studying the geometric constraints of multiple views, we show that the original images can be used for parameterization. The implications of the B-spline surfaces for improving the quality of texture mapping is discussed.