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PI: Fuhua (Frank) Cheng Department of Computer Science University of Kentucky Lexington, KY 40506
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Project Assistants:
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Co-PI: Brian A. Barsky Computer Science Division - EECS University of California Berkeley, CA 94720
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1. Introduction
The universal availability of computer networks is rapidly changing many
of the ways in which information and goods are developed and delivered.
In design and manufacturing, networks provide an environment which allows
the integration of activities across the corporation throughout the period
of product design and development. In the future, manufacturing will
almost certainly rely heavily on access between collaborators and services
which is integrated, distributed, and highly networked.
Advances in computer network methodology also are rapidly changing the
methods for the development and dissemination of computer assisted tools
and techniques. In a network enriched product development environment,
geographically separated researchers should be able to collaborate with
more facility and ease.
Computer aided techniques for modeling and design are rapidly becoming
important tools for modern industrial design and manufacturing.
In many applications, computer models are replacing physical models
because they are cheaper to construct, easier to change, and simpler
to analyze. Computer generated images increase productivity by allowing
swift and accurate visualization during design. This permits not only
rapid prototyping but early detection of errors, which in turn, decreases
the fabrication of erroneous components as well as costly redesign during
manufacturing. Factory automation is being revolutionized by this
methodology.
Geometric design and modeling is a major research and development area
in computer aided design. The automobile, aerospace, and shipbuilding
industries rely heavily on applications of many techniques developed in
this area. These techniques are also finding their way into many new areas.
But, despite these advances, the techniques in geometric design and modeling
are nonetheless far from completely developed. Research in this area is
constantly extensively conducted so that new computational and visualization
techniques can be developed to further facilitate the modeling and design
process.
In this project we propose to develop and deliver CAD/CAM software systems
which support such methodologies. These issues require the development
of network CAD/CAM interfaces and collaborative design paradigms for
the following components of an object-oriented geometric modeling tool kit.
Four particular areas of research in solid and geometric modeling
included in the above tool kit will be investigated during the tenure
of this project. They are:
To visualize an object for which we have a set of range data points from
its boundary surfaces, a typical approach is to generate a mesh
representation of the object and render this mesh representation.
This technique is also frequently used in reverse engineering.
One of the most important issues that needs to be addressed here is
the extraction of special features from the data points.
These special features allow the decomposition of the mesh representation
into smooth components that can be represented by smooth surfaces.
The major objective is to develop a range data based mesh generation
technique which preserves all the features of the original object
(such as sharp edges and sharp corners), and, for each smooth patch,
generate a surface representation.
The approach is comprised of four steps. The first step is standard:
topology mesh construction [HDD92, HDD93, HDD94].
Next, Gaussian mapping is used to develop a technique which identifies
special existing features. Under Gaussian mapping, sharp points and
edges are denoted as singular and defined as follows.
The third step is to search and identify the location of these special
vertices and edges that define special features of the object.
An initial estimate may be made by comparing tangent planes for each
data point. A refining technique such as the one used by Hoppe, DeRose,
et. al [HDD92, HDD93] will be used to refine the location of these
vertices and edges, as well as the other data points, while still
maintaining the topology of the data points.
The last step is to generate a smooth surface representation for each
patch that is bounded by the sharp edges and boundary edges of the
original object. A surface interpolation technique that interpolates a
surface through a set of network curves of arbitrary topology will be
developed. To avoid having patches of very small sizes, the refining
technique used in step three should be capable of removing vertices and
edges from the mesh representation without changing its shape or topology.
It should be pointed out that the second and third tasks can be subsumed
by task one or, actually, any visualization process as an alternative
input phase for objects whose boundary representation is not available
or, simply, to make the input phase more flexible.
To complete this topic, we must develop algorithms to:
Triangulations play an important role in finite element mesh analysis,
approximation theory, numerical analysis and computer-aided geometric
design. Delaunay triangulation is often used but does not optimally
satisfy angle criteria. Thus there may be tetrahedra of poor shape in
a 3D Delaunay triangulation. Local transformations such as those of
Joe [Joe98] have proved acceptable and desirable, but could be improved.
Beginning with either Joe's triangulations or standard Delaunay
triangulations, final solutions will be formulated using:
At this point, genetic operators, such as adaptive polyhedron crossover
and mutation will be developed for use in genetic algorithms.
All algorithms will be tuned to existing commercial data sets and
compared with the standard triangulation techniques.
First, we will develop modeling and rendering techniques for visualizing
the melting process of an object in 3D space. The problem will be studied
in a general setting so that objects with different melting points,
absorptivity, and viscosity can be considered. The causes of the melting
can be point-heat sources, line-heat sources, face-heat sources,
or ambient temperature. Boundaries of objects are defined by piecewise
surfaces (for example: including polyhedra and free-form surfaces).
Modeling of the deformation of an object during the melting process focuses
on understanding and simulating the physics of the melting process and
comprises the initial portion of this investigation.
The second part, rendering of a time-dependent shape representation,
emphasizes the development of efficient time-dependent surface evaluation
algorithms.
Object deformation during melting involves:
At present, the most efficient and numerically stable NURB surface
rendering technique is a two-stage Cox-de Boor recurrence based
tessellation approach [LC93, LC96]. However, for time-dependent shape
representations, it is not known if the incremental factor is also
considered. Thus, rendering time-dependent shape representations will
incorporate developing an incremental method for the surface scheme for
continuous deformation, as well as performing a comparison on forward
differencing [LSP87, SC88], knot insertion [RHD89], and the two-stage
Cox-de Boor recurrence based tessellation [LC93] for time-dependent shape
representations.
In order to complete this topic, we first need:
In contemporary modeling systems, curves are usually represented by
spline forms, and surfaces are often represented as triangular meshes
or spline surfaces. For a complex scene, or an object defined by data
from a laser scanning system, there could be a mesh of extreme complexity
or a vast amount of control vertices which make it is too expensive to
store, transmit, or render. We propose developing modeling, rendering and
animation techniques for such complex scenes or objects.
Our investigation of this problem is divided into three sections.
For this we need to :
We shall develop a method which extends Finkelstein and Salesin's
multiresolution editing for endpoint-interpolating B-spline curves to
that of uniform , nonuniform, and NURBS B-spline curves or surfaces.
Then we shall develop an algorithm for multiresolution smoothing for
these curves or surfaces based upon arbitrary meshes.
Computer Supported
Cooperative Work (CSCW) has been studied intensely in recent years.
Infrastructure level in enabling
techniques, such as data sharing, concurrency control and coordination
control, etc. have been addressed frequently. The system architecture
aspect, however, is often left out. While the enabling techniques are
general, they ought to be
organized under a proper system architecture to fulfill the requirement of
collaboration on a specific application.
In the field of collaborative engineering, including collaborative CAD,
efforts have been made to develop the the enabling techniques suitable to
the engineering context.
We will analyze the requirements and properties of a
collaborative CAD system from the system architecture point of view
and present a conceptual model that fulfills these requirements.
Issues that should be considered in the implementation of this architecture
are also discussed.
These should be implemented as platform-independent applications which can
be accessed from anywhere over the World Wide Web. With the use of applets
written in "Java" [AG96] the research teams from Tsinghua University
and the United States will be able to collaborate over the web.
2. Research Objectives
Detailed descriptions of the work to be undertaken in each of these
areas appears in the sequel.
2.1 Feature extraction and shape reconstruction of unorganized range data:
Definition. A surface point is called a "singular point" if in each
of the point's neighborhoods there is a curve passing through the point
whose image (excluding the point) under the Gaussian mapping consists of
at least two disjoint connected closed regions of the unit sphere.
Definition. A surface edge is a "singular edge" if each point of the
edge is a singular point.
It is easy to see that a Gaussian mapping maps a cone, excluding the tip,
to a circle on the unit sphere. Each curve through the tip (excluding the
tip itself) is mapped to two distinct closed subsets of the circle.
Hence the tip of a cone is a singular point. Therefore, by examining
the distribution of the unit normal vectors on the unit sphere,
one can estimate the number of sharp vertices and sharp edges in each
region.
as well as an object-oriented implementation of this technique as part
of a mesh representation generation process.
2.2 Local and random search algorithms for 3D triangulation:
For each method,
a) representations for feasible solutions,
need to be defined. Then search mechanisms need to be developed for
the local search along the lines of Kernighan and Lin's classic min-cut
heuristic [KL70]. Next, these can be applied to simulated annealing
triangulation algorithms.
b) search techniques for neighborhoods, and
c) evaluation methods for gains in cost
2.3 Physically based modeling and rendering of melting process:
An idea similar to Terzopoulos and Qin's dynamic NURBS [TQ94] will be
used in the development of the surface representation scheme for
continuous deformation.
Then, an object-oriented implementation that will
must be developed and delivered.
render the results on screen to visualize the melting process
2.4 Modeling, rendering and animation technology based on wavelets:
3. Introduction to Conceptual Model