Relational modeling of trimmed nurbs surfaces

Details Relational modeling of trimmed nurbs surfaces Relational modeling of trimmed nurbs surfaces

1999-04-21

2004-01-27

Razavi, Michael (Department: 2672)

Computer graphics processing and selective visual display system

Computer graphics processing

Graphic manipulation

C345S619000, C345S621000, C345S622000, C345S623000, C345S624000

Reexamination Certificate

active

06683620

ABSTRACT:

FIELD OF THE INVENTION
The present invention relates to computer modeling of geometric shapes and, in particular, to modeling NURBS surfaces.
BACKGROUND OF THE INVENTION
Computer generated 3-D animations enrich a wide range of human experience, captivating audiences at the movie theaters, gluing gamers to their personal computers, and embarking home buyers on virtual tours of new homes. To generate 3-D animations, a 3-D designer creates 3-D computer models of the entities using computer aided design systems (CAD). These models are used to emulate the movement, color, and shape of animated entities, from a dancing baby to space ships trekking through the universe.
3-D models are often composed of graphical components that represent the shapes and surfaces that make up modeled objects. A graphical component is a set of data, procedures, or a combination thereof used to represent a geometry, such as curve or a surface, or a feature of the geometry, such as a curve defining a boundary of a surface.
A CAD system generates a graphical component when, for example, the system receives user input that specifies the definition of a graphical component. The CAD system generates the graphical component as specified by the user input. With earlier CAD systems, designers would determine the position of new components in relation to one or more components already in existence, and input data specifying the position. For example, a CAD system receives user input from a designer that specifies the creation of a line B, and in particular, specifies an endpoint for line B at a particular position. The user has selected the endpoint because it coincides with the endpoint of a line A. In response, the CAD system generates line B with the specified endpoint.
While the position of the endpoint of line B was captured, the intended relationship between line A and line B was not. Thus graphical components generated through earlier CAD systems are essentially independent entities, whose relationship from the perspective of the CAD system were incidental to the manner and order created, and not described to the CAD system. If line A was displaced through a revision, then line B may no longer join line A. To maintain the intended relationship between components, the designer may have to revise each of the related components.
Having to change all components in a relationship when one of those components is revised can be cumbersome, especially for more complex components such as surfaces. For example, a designer may specify a particular surface (blend surface) to provide a blend between two other surfaces (blended surfaces). In the earlier CAD systems, when the designer specified a revision to one of the blended surfaces, the designer would also have to modify the blend surface to maintain the intersection between it and the blended surfaces. In CAD systems, intersections between surfaces account for much of the complexity in the CAD system, and in particular, its user interface.
Capturing the intended relationships between graphical components is especially important to computer generated animation. Without information describing these relationships between graphical components, the computer may not automatically maintain the relationships when revising graphical components.
RELATIONAL MODELING
A solution to the problem of capturing the relationship between graphical components is relational modeling. In relational modeling, graphical components may defined in terms of other graphical components, and the types of operations needed to create the graphical components, including operations that may applied to the other graphical components.
FIG. 1
shows an example of a surface created through relational modeling, and the graphical components used to model the surface. Surface
110
is defined as a loft through a set of lines, and in particular, lines
112
,
114
,
116
,
118
,
122
, and
124
.
Surface component
120
is a graphical component used to model surface
110
. Similarly, curve components
152
,
154
,
156
,
158
,
162
, and
164
are used to model lines
112
,
114
,
116
,
118
,
122
and
124
. Just as lines
112
,
114
,
116
,
118
,
122
and
124
are used to define surface
110
, curve component
152
,
154
,
156
,
158
,
162
, and
164
are used to define surface component
120
. Surface component
120
is defined in terms graphical components used to define curves that define surface
110
. These graphical components include curve components
152
,
154
,
156
,
158
,
162
, and
164
. Surface component
120
is also associated with operations (e.g. functions, methods) that are applied to curve components
152
,
154
,
156
,
158
, and
162
in order to, for example, recalculate data used to define a surface.
The following terms are useful to describing graphical components used in relational modeling. A “surface” component is a graphical component used to model a surface. A particular graphical component is said to “depend” on another graphical component when the particular graphical component is defined in terms of the other graphical component. Thus surface component
120
is said to depend on curve components
152
,
154
,
156
,
158
,
162
, and
164
because surface component
120
is defined by the curve components.
Graphical components are referred to as being “related” when one of the graphical components depends on the other graphical component. A graphical component that depends on another graphical component is referred to as a “relational” graphical component. Thus, surface component
120
is a relational graphical component. A “relational model” is set of related graphical components used to model a particular geometry. Thus, surface component
120
and curve components
152
,
154
,
156
,
158
,
162
, and
164
are related, and form a relational model used to depict surface
110
.
Because surface component
120
is a relational model, it may be revised through the graphical components on which it depends. Thus surface component
120
may be revised by modification to one of curves
112
,
114
,
116
,
118
,
122
, and
124
. After such a revision, surface
110
may be recalculated and redisplayed to fit the revised curve.
Typically, a graphical component that depends on another contains a reference to the other graphical component. A reference used to refer to another graphical component on which a particular graphical depends is referred to as a relational reference. When a graphical component in an relational model is altered, any graphical component that contains a reference to the altered graphical component may be altered, recalculated, and re-displayed. Thus, when curve component
162
is altered, surface component
120
may be altered and recalculated.
NURBS SURFACES
Surfaces are often modeled through a type of graphical component referred to as a Nonuniform Rational B-spline (NURBS) surface component. NURBS surface components are able to describe smooth shapes, are intuitively editable by a user, and are efficiently calculated by a computer. Surfaces described by NURBS surface components are referred to as NURBS surfaces.
However, one drawback to NURBS surface components is that they require four distinct boundaries. Thus, surface
110
may be described using a NURBS surface component because it has four distinct boundaries, lines
112
,
114
,
116
, and
118
.
FIG. 2
, on the other hand, shows a surface
210
, which may not be described using NURBS surface components. Surface
210
has one boundary, curve
212
, not four.
DEFINING SURFACES WITHOUT FOUR SIDES USING NURBS
One approach to overcoming the four-boundary limitation and to building non-four sided surfaces using NURBS surface components involves applying a trimming curve to the NURBS surface, where the trimming curve is defined to be on the NURBS surface. A trimming curve is a closed loop that defines a pattern on a surface. A trimmed surface is a surface that, when rendered, is “trimmed” by a trimming curve. That is, either the portion of the trimmed surface that extends beyond the closed lo

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