SURFACE PATCH TECHNIQUES FOR COMPUTATIONAL GEOMETRY

• US 20140354639A1
• Filed: 08/17/2014
• Published: 12/04/2014
• Est. Priority Date: 07/23/1998
• Status: Active Grant

• Current Assignee: Cad-Sense LLC
• Original Assignee: Freedesign, Inc.
• Inventors: Rockwood, Alyn P.
• Granted Patent: US 9,262,859 B2
• Time in Patent Office: Days
• US Class Current: 345/420
• CPC Class Codes: G06F 17/10 Complex mathematical operations function generation by table look-up G06F1/03; evaluation of elementary functions by calculation G06F7/544
• CPC Class Codes: G06F 2111/04 Constraint-based CAD
• CPC Class Codes: G06F 30/00 Computer-aided design [CAD]
• CPC Class Codes: G06F 30/10 Geometric CAD
• CPC Class Codes: G06T 15/10 Geometric effects
• CPC Class Codes: G06T 17/10 Constructive solid geometry [CSG] using solid primitives, e.g. cylinders, cubes
• CPC Class Codes: G06T 17/30 Polynomial surface description

Abstract

A method and system for computer aided design (CAD) is disclosed for designing geometric objects, wherein interpolation and/or blending between such objects is performed while deformation data is being input. Thus, a designer obtains immediate feedback to input modifications without separately entering a command(s) for performing such deformations. A novel N-sided surface generation technique is also disclosed herein to efficiently and accurately convert surfaces of high polynomial degree into a collection of lower degree surfaces. E.g., the N-sided surface generation technique disclosed herein subdivides parameter space objects (e.g., polygons) of seven or more sides into a collection of subpolygons, wherein each subpolygon has a reduced number of sides. More particularly, each subpolygon has 3 or 4 sides. The present disclosure is particularly useful for designing the shape of surfaces. Thus, the present disclosure is applicable to various design domains such as the design of, e.g., bottles, vehicles, and watercraft. Additionally, the present disclosure provides for efficient animation via repeatedly modifying surfaces of an animated object such as a representation of a face.

Claims

1. (canceled)

2. The method for deforming a computer display of a three dimensional surface during a continuous input by a user for such deformation, comprising performing the following step by computer equipment:

displaying, on a computer display, at least one three dimensional geometric surface, which is represented by first data providing a parameterization of the at least one geometric surface, wherein the at least one geometric surface has an at least a two dimensional area as a pre-image in the parameterization;

accessing respective data representing one or more additional geometric object space surfaces used in determining shape modified instances of the at least one geometric surface, each of the one or more additional geometric object space surfaces having a corresponding common portion with the at least one geometric surface;

for at least one point on, or effectively on, the at least one geometric surface, a step of receiving a selection by a user for selecting the at least one point or a corresponding related extent associated with the at least one point, the corresponding related extent being indicative of an extent of one of the additional geometric object space surfaces having the point;

iteratively performing the steps A1 through A4 following so that the user perceives a substantially real time deformation of the at least one geometric surface during a continuous series of user inputs to the computer equipment, wherein each of the user inputs is for entering a corresponding change to one of;

a location for the at least one point, or the corresponding related extent therefor;

(A1) receiving a next one of the user inputs by the computer equipment;

(A2) deriving, using the next one of the user inputs received, data representing a modified version of the one additional geometric object space surfaces having the at least one point,

wherein;

(a) the modified version of the one additional geometric object space surface includes the corresponding change, and,

(b) for the one additional geometric object space surface, when neither of (i) and (ii) following are selected by the user for contributing to the real time deformation;

(i) a user designated another point for the one additional geometric object space surface, and

(ii) a corresponding second related extent indicative of an extent of the one additional geometric object space surface, the corresponding second related extent for the another point,

then at least one of;

(1) the another point, and

(2) the corresponding second related extent associated with the another point

remains unchanged and also corresponds with the modified version;

(A3) subsequently, determining data representing one of the shape modified instances of the at least one geometric surface, using data representing a modified collection of the one or more additional geometric object space surfaces, wherein the modified version of the one additional geometric object space surface is provided in the modified collection;

wherein the step of determining data representing the one shape modified instance includes a substep of combining terms for determining points of the one shape modified instance, wherein for each pre-image point in a plurality of points distributed throughout the at least two dimensional area, and for each surface (S) of the modified collection, there is a corresponding one of the terms for determining a point, p, of the one shape modified instance, the point p having the pre-image point as a pre-image;

wherein each term (T), for the surface S, is determined by computing a multiplicative product of;

(a) a corresponding weighting, and (b) data representing a particular point of the surface S, wherein the particular point has the pre-image point, for the corresponding term T, as a pre-image, and

wherein for the surface S being the modified version of the one additional geometric object space surface, the corresponding weightings, used in determining the terms for the modified version, are such that each weighting (w), of the correspond weightings, is determined by the computer equipment computing a corresponding distance value of the pre-image point, for the term to which the weighting W corresponds, from a pre-image of the corresponding common portion in a pre-image parameterization space for the one additional geometric object space surface; and

(A4) displaying the one shape modified instance of the at least one geometric surface on a computer display.

3. The method of claim 2, wherein the corresponding related extent for the at least one point is such that:

i) the corresponding related extent has a parametric direction substantially identical to a parametric tangency direction of the at least one geometric surface at the at least one point according to the parameterization of the at least one geometric surface, and

ii) a length of the corresponding related extent for the at least one point is representative of how closely a contour of the at least one geometric surface follows the parametric tangency direction as the contour extends away from the at least one point.

4. The method of claim 2 further including:

adding an additional boundary to the at least one geometric surface or a specified one of the shape modified instances by the user selecting points therefor;

subsequently, generating a further geometric object space surface for the additional boundary; and

subsequently, iteratively performing the steps A1 through A4 using the further geometric object space surface as one of the additional geometric object space surfaces.

5. The method of claim 4, wherein the step of adding an additional boundary includes:

receiving a user input by the computer equipment identifying a point, q, for the at least one geometric surface or the specified one modified instance; and

subsequently, generating the additional boundary, wherein a boundary of the at least one geometric surface is modified to connectedly extend between the user identified point, q, and another user identified point for the at least one geometric surface such that the additional boundary is interpolated from the at least one geometric surface or the specified one modified instance so that a tolerance between the at least one geometric surface or the specified one modified instance and the additional boundary is below a predetermined maximum tolerance.

6. The method of claim 2, wherein each of the one or more additional geometric object space surfaces has a pre-image parameterization space, and further including a step of obtaining, for each weighting (Wtg) for the terms for determining points of the one shape modified instance, a corresponding value of a blending function, wherein the corresponding value is used for determining the weighting Wtg.

7. The method of claim 2, wherein the weightings W vary monotonically with their corresponding distance values, each of which is indicative of a spacing between (i) the pre-i image point, for the term to which the weighting W corresponds, and (ii) the pre-image of the corresponding common portion in the pre-image parameterization space for the additional geometric object space surface.

8. The method of claim 2, wherein the user input moves the least one marker point along the boundary curve C containing the at least one marker point, and further including changing the one shape modified instance of the at least one geometric surface as a result of the user input.

9. The method of claim 2, wherein the user input is generated from the user dragging a graphical representation of the at least one marker point.

10. The method of claim 2, further including maintaining a predetermined constraint for the marker related extent, E, for the at least one marker point, wherein the constraint includes one of:

(a) constraining the extent E to a predetermined range of directions;

(b) constraining the extent E to a predetermined range of magnitudes;

(c) constraining the extent E to lie in a plane with another of the marker related extents included in the at least one additional object space surface;

(d) constraining the extent E to a predetermined range of curvatures; and

(e) constraining the extent E to transform identically with another of the marker related extents included in the at least one additional object space surface.