Abstract: A method of and a system for generating free-form surfaces with NURBS boundary Gregory patches and the formed surface is G1 continuous with adjacent surfaces while the inner areas of the formed surface are C1 continuous.

Abstract: A free-form surface generating method. There is a generating of a continuity condition by detecting a continuity on a common boundary of two free-form surfaces based on tangent vectors on a NURBS common boundary curve and tangent vectors on boundary curves continuous to end points of the NURBS common boundary curve. Next, one of a plurality of predetermined joining processes is selected in accordance with the continuity condition. Then, internal control points of each of the two free-form surfaces are generated based on the selected joined with continuity on the common boundary are generated.

Abstract: A method of generating a free-form surface includes calculating cross boundary derivatives on all the boundary curves forming a face, and storing the results in a memory device (STEP 1), determining whether the cross boundary derivatives calculated at STEP 1 are all polynomials or not, and if there is a rational function, go to STEP 3, if they are all polynomials, go to STEP 4 (STEP 2), creating the control points of a rational surface by using the cross boundary derivatives (STEP 3), and creating the control points of a polynomial surface by using the cross boundary derivatives (STEP 4).

Abstract: A 3-dimensional (3-D) Computer Aided Design (CAD) System generates a fillet surface which smoothly connects two surfaces to each other. This is accomplished by sliding a circle on a normal plane of a user-designated spine curve which is in contact with two surfaces. Then, the fillet surface is approximated by Gregory patches which are generated from trajectories of two tangent points between the circle and the two surfaces. The fillet surface thus expressed by the Gregory patches is easily and efficiently processed in computers such as those in 3D CAD systems. Because the fillet surface is generated along the spine curve, various fillet surfaces, including that generated by the conventional rolling-ball blending method, can be generated to satisfy various needs of designers of 3-D CAD Systems.