Method of forming curved surfaces and the apparatus

Claim 1

A method of interactively generating electronic data which is representative of a curved surface and visually displaying the surface to an operator, wherein the method comprises the following steps of: (a) selectively generating data representative of a desired deformation area including an action point on a surface to be deformed; (b) selectively determining a vector field function F i representative of a relative deformation rate at each point within the deformation area; (c) selectively designating a deformation vector V i * representative of a deformation quantity and a deformation direction at the action point within the deformation area; (d) electronically calculating a position vector representative of a deformation quantity of a curved surface at each point within the deformation area on the basis of the deformation vector V i * and the vector field function F i ; (e) electronically calculating a position vector P i * representative of a deformed curved surface on the basis of the position vector representative of the deformation quantity of the curved surface and a position vector P i-1 * representative of the surface to be deformed; and (f) visually displaying to an operator the deformed curved surface represented by the position vector P i * from a preselected point of view.

Claim 2

A method of interactively generating electronic data which is representative of a curved surface and visually displaying the surface to an operator, wherein the method comprises the following steps of: (a) selectively generating data representative of a desired deformation area including an action point on a surface to be deformed; (b) selectively determining a vector field function F i representative of a relative deformation rate at each point within the deformation area; (c) selectively designating a deformation vector V i * representative of a deformation quantity and a deformation direction at the action point within the deformation area; (d) electronically calculating a position vector representative of a deformation quantity of a curved surface at each point within the deformation area on the basis of the deformation vector V i * and the vector field function F i ; (e) electronically calculating a position vector P i * representative of a deformed curved surface on the basis of the position vector representative of the deformation quantity of the curved surface and a position vector P i-1 * representative of the surface to be deformed; and (f) visually displaying to an operator the deformed curved surface represented by the position vector P i * from a preselected point of view.

Claim 6

A method of interactively, generating and visually displaying electronic data representative of a curved surface, which comprises the following steps of: (a) selectively, electronically generating data representative of a desired deformation area including an action point on a non-deformed surface; (b) selectively, electronically generating transformed position data by transforming each position at each deformation point within the deformation area in accordance with a predetermined position transformation function having a selectable position transformation coefficient K; (c) electronically calculating a vector field function F i representative of a relative deformation rate at each position on a curved surface on the basis of the transformed position data; (d) electronically generating data representative of a deformation vector V i * representative of a deformation quantity and a deformation direction at the action point within the deformation area; (e) electronically calculating a position vector representative of a deformation quantity of a curved surface at each point within the deformation area by multiplying the deformation vector by the vector field function F i ; (f) electronically calculating a position vector representative of a transformed curved surface on the basis of the position vector representative of a deformation quantity of the curved surface and the position vector representative of the non-deformed surface; and (g) electronically, visually displaying said curved surface to an operator.

Claim 7

A method of interactively, generating and visually displaying electronic data representative of a curved surface, which comprises the following steps of: (a) selectively, electronically generating data representative of a desired deformation area including an action point on a non-deformed surface; (b) selectively, electronically generating transformed position data by transforming each position at each deformation point within the deformation area in accordance with a predetermined position transformation function having a selectable position transformation coefficient K; (c) electronically calculating a vector field function F i representative of a relative deformation rate at each position on a curved surface on the basis of the transformed position data; (d) electronically generating data representative of a deformation vector V i * representative of a deformation quantity and a deformation direction at the action point within the deformation area; (e) electronically calculating a position vector representative of a deformation quantity of a curved surface at each point within the deformation area by multiplying the deformation vector by the vector field function F i ; (f) electronically calculating a position vector representative of a transformed curved surface on the basis of the position vector representative of a deformation quantity of the curved surface and the position vector representative of the non-deformed surface; and (g) electronically, visually displaying said curved surface to an operator.