Computer graphics processing and selective visual display system – Computer graphics processing – Adjusting level of detail
Reexamination Certificate
2000-10-10
2003-05-27
Vo, Cliff N. (Department: 2671)
Computer graphics processing and selective visual display system
Computer graphics processing
Adjusting level of detail
C345S520000
Reexamination Certificate
active
06570568
ABSTRACT:
FIELD OF THE INVENTION
This invention relates to the field of computer graphics. More specifically the invention relates to the simplification of geometric models for the purpose of display.
BACKGROUND OF THE INVENTION
In the field of mechanical computer aided design (MCAD), geometric models are sometimes simultaneously represented by wire-frame and surface descriptions. For example, a model may be displayed by using a surface description to render the surface and a wire-frame description to show sharp edges, as in FIG.
2
. The simultaneous use of surface and wire-frame descriptions of geometric models is also used for display purposes in other fields in MCAD. One such field is the application of numerical analysis to geometric models.
Numerical methods are frequently used to simulate the response of geometric models to a diverse variety of imposed environments. In one popular numerical method known as the finite element method, geometric models are represented by an assembly of subdivisions called finite elements. Finite elements are interconnected at point locations called nodes. Within a finite element, the value of a dependent variable is completely determined by the value of the dependent variable at nodes of the element. The use of the finite element method to simulate real-world problems is commonly referred to as finite element analysis. An assembly of finite elements is referred to as a finite element mesh. The finite element mesh serves as an alternate representation of the original real or abstract geometric model.
It is common practice to use graphical representations of the finite element mesh and one or more computed results to examine a solution obtained from a finite element analysis. For finite element meshes composed of 2-dimensional or 3-dimensional elements embedded in the 3-dimensional Euclidean space, graphical representations can be used to simultaneously communicate the structure of the finite element mesh, the surface of the finite element mesh (or geometric model) and the scalar magnitude of a solution component. Here polygons (usually triangles) are used to represent the surface of the mesh, line segments are used to represent the boundaries of individual elements, and color is used to represent the scalar magnitude of the solution component (e.g., temperature). Typically, the graphical result is obtained by combining a surface rendering with a line segment rendering. The surface rendering is used to represent the mesh surface and a scalar magnitude either representing or derived from a solution component. The shading is performed by applying shading algorithms. These shading algorithms use as input the geometry of the mesh surface and the color derived from the scalar magnitude of the solution component. The line segment rendering is generated from the edges of individual finite elements in the finite element mesh. The scalar magnitude of the solution component is frequently represented by a single color selected from a banded color map. The banded color map represents a contiguous range of scalar values with a single color. The final rendering usually takes one of two forms. One rendering mode, referred to as the iso mode, is used to represent scalar values attached to nodes and intra-finite element transitions from a color representing one scalar value to a color representing another scalar value. The other rendering mode, referred to as the finge mode, is used to represent scalar values attached to 2-dimensional faces in the mesh. The fringe mode uses one color corresponding to the scalar value to represent the face.
Most of the existing techniques for visualizing surface descriptions of the geometric models utilize triangle meshes. The geometry of a triangle mesh refers to the pair (K, V), where K is a simplicial complex of degree
2
specifying the connectivity of the mesh simplices, and V={v
1
, . . . , v
m
} is the set of vertex positions v
i
=(x
i
, y
i
, z
i
) defining the shape of the mesh in R
3
. In the FEM applications, there are either discrete scalar attributes D associated with the faces of the mesh, or scalar attributes S associated with the vertices of the mesh. In the FEM analysis, model descriptions also involve a wire-frame description of a geometric model (finite element mesh). A wire-frame description is represented by a subcomplex L⊂K, where L is a degree
1
subcomplex of K. The visualization task is to render either the triple (N, L, V) or one of the quadruples K, L, V, D) (for the fringe rendering mode) or K, L, V, S) (for the iso rendering mode). For example,
FIG. 2
is a visualization of some triple (K, L, V).
The graphical detail contained in a visualization is not always required for display. Furthermore, graphical detail may be reduced to increase the display rate by decreasing the required graphics processing. A variety of simplification techniques aimed at reducing the amount of graphics processing and increasing display rates by sacrificing geometric detail have been covered in the literature (see, for example, Garland and Heckbert, “
Survey of Polygonal Surface Simplification Algorithms
”, Multiresolution Surface Modeling Course, SIGGRAPH-97). These simplification reduce the graphics processing to increase the frame rates by rendering representations containing lower levels of geometric detail than the original geometric model. Factors such as the size in screen space of the rendered model distance from the viewer, relative importance of the model requested frame rate, relative motion between the viewer and the model, are used to select a simplified representation of the original model. All of these techniques attempt to produce a simplified model that, when rendered, retains as much image fidelity as possible with a rendering of the original model.
There exist several techniques that address the simplification of meshes. In most approaches, the initial meshes are replaced by approximations with fewer faces which produce visually similar results, thereby improving rendering efficiency. Rossignac and Borrel (“Multi-resolution 3D approximations for rendering complex scenes”,
Modeling in Computer Graphics
, 455-465 (Springer-Verlag 1993) and U.S. Pat. No. 5,448,686) proposed one of the earliest simplification algorithms. Their algorithm divides the model into cells of a uniform rectangular grid, and replaces all vertices within the grid cell by a single representative vertex.
The edge collapse operation has been used extensively in simplification, and it generally produces higher quality results. Garland and Heckbert (“Surface simplification using quadric error metrics”,
Computer Graphics Proceedings, Animal Conference Series
, 1997, 209-216) maintain a 4 by 4 symmetric matrix at each vertex that allows to track square distances to the faces of the original model. They subsequently generalized the quadric error metric to support simplification of surfaces with color and texture (“Simplifyng surfaces with color and texture using quadric error metrics”, IEEE
Visualization
'98
Proceedings
, October 1998, 263-269). Lindstrom and Turk (“Fast and memory efficient polygonal simplification”, IEEE
Visualization '
98
Proceedings
, October 1998, 279-286) determine the vertex placement by minimizing the quadratic volume, boundary, and triangle shape objective functions, with the cost of edge collapse determined by the volume and boundary functions. Lindstrom (“Out-of-core simplification of large polygonal models”,
Computer Graphics Proceedings, Annual Conference Series
, 2000, 259-262) has proposed a method extending the vertex clustering scheme of Rossignac and Borrel by using quadric error metrics to select the representative vertex for each cell in the uniform grid.
PROBLEMS WITH THE PRIOR ART
Standard techniques exist to simultaneously display wire-frame and surface descriptions of geometric models. However, as the complexity of the geometric model increases, the number of polygons and line segments that need to be rendered to convey the surface description and the wire-frame
Horn William P.
Klosowski James T.
Lecina Gerard
Suits Frank
Valuyeva Julia Anatolyevna
Herzberg Louis P.
Vo Cliff N.
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