A new interpolatory subdivision scheme for surface design is presented. The scheme is designed for general triangulations of control points and includes a tension parameter for design flexibility. The resulting surface is C¹ for a specified range of the tension parameter, with a few exceptions. The scheme is based on the local four-point interpolatory subdivision scheme for curves. The scheme is applied to a general triangulation of control points, transforming each triangular face into a patch consisting of four triangular faces interpolating the old control points. The scheme is interpolatory, meaning that the original control points are preserved in the limit. The tension parameter controls the smoothness of the surface, with smaller values producing tighter surfaces. The scheme is extended to allow for local and directional tension control by assigning tension values to individual control points and using a tension matrix. The scheme is implemented in a software package that allows for the manipulation of control points and tension parameters. Examples demonstrate the scheme's ability to produce smooth surfaces with varying tension. The scheme is tested on various control polyhedra, including a fish-like shape and a head-like shape, showing the effectiveness of the scheme in producing smooth surfaces. The scheme is also tested with local and directional tension changes, showing the flexibility of the scheme in controlling the smoothness of the surface. The scheme is compared to other subdivision schemes, showing its advantages in terms of flexibility and smoothness. The scheme is also analyzed for convergence and smoothness, showing that it produces a C¹ surface for a specified range of the tension parameter. The scheme is also tested for irregular vertices, showing that the surface is not C¹ near such vertices. The scheme is also tested for different types of control points, showing its versatility in surface design. The scheme is implemented on a SUN 3/50 workstation and tested with various input files. The scheme is found to be efficient in terms of memory and computation, with a data structure that allows for general triangulation. The scheme is also tested with different types of control points, showing its versatility in surface design. The scheme is found to be effective in producing smooth surfaces with varying tension. The scheme is also tested with different types of control points, showing its versatility in surface design. The scheme is found to be effective in producing smooth surfaces with varying tension.A new interpolatory subdivision scheme for surface design is presented. The scheme is designed for general triangulations of control points and includes a tension parameter for design flexibility. The resulting surface is C¹ for a specified range of the tension parameter, with a few exceptions. The scheme is based on the local four-point interpolatory subdivision scheme for curves. The scheme is applied to a general triangulation of control points, transforming each triangular face into a patch consisting of four triangular faces interpolating the old control points. The scheme is interpolatory, meaning that the original control points are preserved in the limit. The tension parameter controls the smoothness of the surface, with smaller values producing tighter surfaces. The scheme is extended to allow for local and directional tension control by assigning tension values to individual control points and using a tension matrix. The scheme is implemented in a software package that allows for the manipulation of control points and tension parameters. Examples demonstrate the scheme's ability to produce smooth surfaces with varying tension. The scheme is tested on various control polyhedra, including a fish-like shape and a head-like shape, showing the effectiveness of the scheme in producing smooth surfaces. The scheme is also tested with local and directional tension changes, showing the flexibility of the scheme in controlling the smoothness of the surface. The scheme is compared to other subdivision schemes, showing its advantages in terms of flexibility and smoothness. The scheme is also analyzed for convergence and smoothness, showing that it produces a C¹ surface for a specified range of the tension parameter. The scheme is also tested for irregular vertices, showing that the surface is not C¹ near such vertices. The scheme is also tested for different types of control points, showing its versatility in surface design. The scheme is implemented on a SUN 3/50 workstation and tested with various input files. The scheme is found to be efficient in terms of memory and computation, with a data structure that allows for general triangulation. The scheme is also tested with different types of control points, showing its versatility in surface design. The scheme is found to be effective in producing smooth surfaces with varying tension. The scheme is also tested with different types of control points, showing its versatility in surface design. The scheme is found to be effective in producing smooth surfaces with varying tension.