Computational Geometry Using Control Geometry Having At Least Two Dimensions

• US 20070152999A1
• Filed: 03/01/2007
• Published: 07/05/2007
• Est. Priority Date: 07/23/1998
• Status: Active Grant

• Current Assignee: Cad-Sense LLC
• Original Assignee: Freedesign, Inc.
• Inventors: Lee, John, Hagen, Lance, Hagen, Scott, Rockwood, Alyn
• Granted Patent: US 7,417,635 B2
• Time in Patent Office: Days
• US Class Current: 345/420
• CPC Class Codes: G06T 17/30 Polynomial surface description
• CPC Class Codes: Y10S 715/964 CAD or CAM, e.g. interactive design tools

Abstract

A method and system for computer aided design (CAD) is disclosed for designing geometric objects. The present invention interpolates and/or blends between such geometric objects sufficiently fast so that real time deformation of such objects occurs while deformation data is being input. Thus, a user designing with the present invention obtains immediate feedback to input modifications without separately entering a command for performing such deformations. The present invention utilizes novel computational techniques for blending between geometric objects, wherein weighted sums of points on the geometric objects are used in deriving a new blended geometric object. The present invention is particularly useful for designing the shape of surfaces. Thus, the present invention is applicable to various design domains such as the design of, e.g., bottles, vehicles, and watercraft. Additionally, the present invention provides for efficient animation via repeatedly modifying surfaces of an animated object such as a representation of a face.

Claims

1. A method for determining a blended geometric object, comprising:

providing, for each of a plurality of parameterized geometric objects S_i, i=1, . . . , N, N≧

2, a mapping f_Si from a parametric space, PS, to a common geometric space GS containing the S_i wherein (A1) and (A2) hold;

(A1) at least one of the plurality of parameterized geometric objects, S_i0, has a dimension greater than or equal to 2;

(A2) for each S_i there is a portion P_i of S_i wherein f_Si is continuous at points of f_Si<sup>−

1</sup>(P_i);

computing, a function S at each of a plurality of points q in PS, for obtaining a corresponding point S(q) in GS, wherein (B1) and (B2) hold;

(B1) S(q) is dependent upon

$f_{S_{i_0}}<br><br>\left(q\right)$

and at least one f_Sj(q) for j≠

i₀, and wherein

$S<br><br>\left(f_{S_{i_0}}^{-1}<br><br>\left(P_{i_0}\right)\right)\subseteq <br><br>P_{i_0},S<br><br>\left(f_{S_j}^{-1}<br><br>\left(P_j\right)\right)\subseteq <br><br>P_j;<br><br>$

and

(B2) S is continuous at f

$f_{S_{i_0}}^{-1}<br><br>\left(P_{i_0}\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{and}<br><br>\text{\hspace{1em}<br><br>}<br><br>f_{S_j}^{-1}<br><br>\left(S_j\right);<br><br>$

displaying a representation of said corresponding points S(q) as a representation of a geometric object that blends between S_i0 and S_j.

2. The method as claimed in claim 1, wherein:

(a) each said mapping f_Si is a parametric mapping for parameterizing the S_i;

(b) each said S_i is a surface;

(c) each said P_i is a curve for one of the S_i;

(d) said points, S(q), are contained within a surface defined by said function S, wherein said curves P_i are included in a perimeter of said surface.

3. The method as claimed in claim 2, wherein each of said P_i is interpolated through a plurality of points.

4. The method as claimed in claim 1, wherein points of said parametric space PS are represented as a tuple of a predefined number of coordinates, wherein each coordinate has a predetermined range.

5. The method as claimed in claim 1, wherein said computing step includes determining S(q) as a function of at least a weighted sum of

$f_{s_{i_0}}$

( q )

and f_Sj(q).

6. The method as claimed in claim 5, wherein said step of computing includes determining, for at least some of said points S(q), one or more corresponding weights of said weighted sum, wherein each weight, w, scales a point of one of said geometric objects S_i.