Computational Geometry Using Control Geometry Having At Least Two Dimensions

• US 20070176923A1
• Filed: 04/09/2007
• Published: 08/02/2007
• Est. Priority Date: 07/23/1998
• Status: Active Grant

• Current Assignee: Cad-Sense LLC
• Original Assignee: Freedesign, Inc.
• Inventors: Lee, John, Hagen, Lance, Rockwood, Alyn, Hagen, Scott
• Granted Patent: US 7,636,091 B2
• Time in Patent Office: Days
• US Class Current: 345/420
• CPC Class Codes: B66D 3/006 Power actuated devices operating on ropes, cables, or chains for hauling in a mainly horizontal direction B66D3/003 takes precedence
• 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 modifying a representation of a surface by a user, comprising:

graphically displaying a first surface having a first curve approximately contained in the first surface;

graphically displaying a second curve whose points are indicative of tangents to said first surface at or approximately at each point on said first curve;

changing, relative to said first curve, a position of a portion of said second curve for changing a contour of said first surface.

2. The method as claimed in claim 1, wherein each point on said first curve is within a predetermined distance of said first surface.

3. The method as claimed in claim 2, wherein said predetermined distance is in a range of 10⁻

3 to 10<sup>−

6</sup>.

4. The method as claimed in claim 1, wherein said first curve is a profile curve interpolated from at least two points on said first surface.

5. The method as claimed in claim 1, wherein points of a surface between said first and second curves are used in determining points of one or more of said first surface and said second surface.

6. The method as claimed in claim 1, further including a step of interpolating points of said first curve from surface tangents to points on said first surface.

7. The method as claimed in claim 1, wherein said changing step includes changing one of a direction and a magnitude of a vector representing a tangent to said first surface.

8. A method for modifying a representation of a N dimensional geometric object by a user of a computational system, wherein N is greater than or equal to two, comprising:

graphically displaying, on said computational system, a first geometric object having a dimension of N, and wherein there is a lower dimensional second geometric object embedded within said first geometric object;

graphically displaying a third geometric object whose points are indicative of rates of change of one or more measurements of said first geometric object at points of said second geometric object; and

changing, relative to said second geometric object, one or more geometric features of said third geometric object for affecting one or more geometric features of said first geometric object.

9. A method as claimed in claim 8, wherein:

for each of said first, second and third geometric objects, the dimension of the geometric object is the minimal number of linearly independent vectors required to represent all points of the geometric object.

10. A method as claimed in claim 8, wherein the one or more geometric features of said first and third geometric objects include one or more of:

a tangent direction, a tangent vector magnitude, and a curvature measurement.