Method of forming curved surfaces and the apparatus

• US 4,885,702 A
• Filed: 11/09/1988
• Issued: 12/05/1989
• Est. Priority Date: 07/27/1985
• Status: Expired due to Term

• Current Assignee: Sony Corporation (Sony Group Corp.)
• Original Assignee: Sony Corporation (Sony Group Corp.)
• Inventors: Ohba, Akio
• Primary Examiner(s): Clark, David L.
• Application Number:
  US07/268,773
• Time in Patent Office: 391 Days
• Field of Search: 364/518, 364/521, 364/414, 364/470, 364/519, 364/520, 364/522, 340/729, 340/747
• US Class Current: 345/419
• CPC Class Codes: G06T 15/00 3D [Three Dimensional] image rendering
• CPC Class Codes: G06T 3/047 Fisheye or wide-angle transformations

Abstract

A method and apparatus for interactively generating and visually displaying deformed, free curved surfaces using a computer aided display apparatus by designating a desired deformation area, including an action point, on a non-deformed surface, determining a vector field function Fi (deformation rate) at each point within the deformation area; designating a deformation vector V_i * (deformation quantity and direction) at the action point; adding the position vector P_i-1 * (non-deformed curved surface) to the position vector V_i * * F_i (deformation quantity) to generate a position vector P_i * (deformed curved surface); and visually displaying the deformed curved surface represented by the position vector P_i *.

Claims

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.

2. The method of generating data representing a curved surface as set forth in claim 1, wherein the position vector representative of a deformation quantity of the curved surface is obtained by multiplying the deformation vector V_i * by the vector field function F_i ;

and the position vector P_i * representative of a deformed curved surface is obtained by adding the position vector P_i-1 * representative of the non-deformed surface to the position vector representative of a deformation quantity of the curved surface, as expressed by a following recurrence formula;

space="preserve" listing-type="equation">P.sub.i *=P.sub.i-1 *+V.sub.i * * F.sub.i (P.sub.i-1 *, CP.sub.i *)

where CP_i * denotes a position vector at the action point.

3. The method of electronically generating data representing a curved surface as set forth in claim 2, further comprising the steps of:

(a) repeatedly electronically calculating the recurrence formula step by step to generate electronic data representative of a deformed curved surface;

(b) electronically storing data representative of deformation parameters set in calculating the recurrence formula at each deformation step and data representative of the deformation vector and the vector field function in a command list memory;

(c) electronically storing data representative of the position vector P_i * representative of the deformed curved surface is stored in a curved surface data memory; and

(d) selectively electronically reproducing data representative of any given deformed curved surface obtained at each of the deformation steps on the basis of the deformation parameters stored in the command list memory and the position vector P_i * stored in the curved surface data memory, when they are read from the memories in a first predetermined sequence.

4. The method of electronically generating data representing a curved surface as set forth in claim 3, wherein the deformation calculation is executed in accordance with the following steps of:

(a) the vector field function F_i at each of the deformation steps is set on first coordinates; and

(b) both the deformation parameters set at each of the deformation steps and stored in the command list memory and the position vectors P_i * stored in the curved surface data memory are read for deformation calculations in a second predetermined sequence.

5. 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.