Abstract: A method of modeling a 3-dimensional object including performing one of a rounding operation generating the 3-dimensional object from a control grid and an inverse rounding operation generating a control grid from the 3-dimensional object depending on which one of the control grid and the 3-dimensional object is newly provided, the control grid including a plurality of edges and a plurality of vertexes, the 3-dimensional object including a plurality of boundary curves and a plurality of curved surfaces deforming the control grid by shifting the plurality of vertexes, performing the rounding operation when the control grid is deformed so as to introduce the deformation of the control grid to the 3-dimensional object, attaching a weight to one of the plurality of vertexes of the control grid to deform a corresponding one of the plurality of curved surfaces of the 3-dimensional object, attaching a weight to one of the plurality of edges of the control grid to deform a corresponding one of the plurality of bounda

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 solid modeling method for modeling solids which include free-form surfaces calculates intersecting portions of two solids and storing calculated results as first data, stores free-form shapes of the two solids as second data, approximates free-form surface portions of the two solids by polyhedrons so as to describe the two solids in a form of polyhedrons, obtains a union, a difference or an intersection of the two solids by carrying out set operations on the polyhedrons, and returns the polyhedrons obtained by the set operations into solids including free-form surfaces based on the stored first and second data.