AbstractVisualization for medical volumetric data by using of computer-aided design and application techniques has become an important method to aid diagnosis and treatment, which has attracted a wide field of research and application. For implementing 3-D reconstruction of medical images, the problem of constructing a parametric triangular patch to smoothly connect three surface patches is studied in this paper, which has premise of image segmentation and triangular surfaces. We present a new method to define boundary conditions, which are defined by the new method have the same parameter space if the three given surface patches can be converted into the same form through parameter transformation. Consequently, any of the classic methods for constructing functional triangular patches can be used directly to construct a parametric triangular patch to connect given surface patches with G1 continuity. Reconstruction effects prove this method easy to get satisfied results with good quality in a short time, a...