ACM SIGGRAPH
Articles |
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T. Sederberg, D.Cardon, G.Finnigan, N.North, J. Zheng, T.
Lyche (2004)
"T-spline
simplification and local refinement"
ACM Transactions on Graphics
(SIGGRAPH 2004),
Vol.23, No.3.
A
typical NURBS surface model has a large percentage of superfluous control
points that significantly interfere with the design process. This paper presents
an algorithm for eliminating such superfluous control points, producing a T-spline. The paper also presents a new
T-spline
local refinement algorithm and answers two fundamental open questions on T-spline
theory.
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T. Sederberg, J. Zheng, A. Bakenov, A. Nasri (2003)
"T-splines
and T-NURCCs"
ACM Transactions on Graphics
(SIGGRAPH 2003),
Vol.22, No.3, pp 477-484.
This paper presents a generalization
of non-uniform B-spline surfaces called T-splines. T-splines permit T-junctions
in their control grid, and thus support many valuable operations. T-NURCCs (Non-Uniform
Rational Catmull-Clark Surfaces with T-junctions) are a superset of both T-splines
and Catmull- Clark surfaces. Thus, a modeling program for T-NURCCs can handle any
NURBS or Catmull-Clark model as special cases.
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T. Sederberg, J. Zheng, D. Sewell, M. Sabin (1998)
"Non-uniform recursive subdivision
surfaces"
ACM SIGGRAPH 1998 Proceedings, pp 387-394.
This paper
develops rules for non-uniform Doo-Sabin and Catmull-Clark surfaces
that generalize non-uniform tensor product Bspline surfaces to arbitrary
topologies. This added flexibility allows, among other things, the
natural introduction of features such as cusps, creases, and darts,
while else where maintaining the same order of continuity as their uniform
counterparts.
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Refereed
International Journal
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W. Chen, J. Zheng,
Y.Cai
(2009)
"Kernel modeling for molecular surfaces using a uniform solution"
Computer-Aided Design,
2009.
This paper
proposes to use rational Bézier surfaces as a uniform approach to model all
three types of molecular surfaces: van der Waals surface, solvent accessible
surface and solvent excluded surface. The solution consists of three steps:
topology modeling, boundary modeling and surface modeling. First, using
weighted
α-shape, topology modeling creates two networks to describe the
neighboring relationship of the molecular atoms. Second, boundary modeling
derives all boundary arcs from the networks. Third, surface modeling
constructs all three types of molecular surfaces patch-by-patch based on the
networks and the boundary arcs. For SES, the singularity is specially
treated to avoid self-intersections. Instead of approximation, the proposed
solution can produce precise shapes of molecular surfaces. Since rational
Bézier representation is much simpler than trimmed NURBS, computational load
can be significantly saved when dealing with molecular surface modeling.
This research shows that the rational Bézier representations, more
specifically, bi-cubic or 2×4 rational Bézier surfaces, are sufficient for
kernel modeling of molecular surfaces and related applications. |
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W.Yang, J. Zheng,
J.Cai, S.Rahardja, C.Chen
(2009)
"Natural
and seamless image composition with color control"
IEEE Transactions on
Image Processing, Vol.18. No.11.
While the
state-of-the-art image composition algorithms subtly handle the object
boundary to achieve seamless image copy-and-paste, it is observed that they
are unable to preserve the color fidelity of the source object, often
require quite an amount of user interactions, and often fail to achieve
realism when there exists salient discrepancy between the background
textures in the source and destination images. These observations motivate
our research towards color controlled natural and seamless image composition
with least user interactions. In particular, based on the Poisson image
editing framework, we first propose a variational model that considers both
the gradient constraint and the color fidelity. The proposed model allows
users to control the coloring effect caused by gradient domain fusion.
Second, to have less user interactions, we propose a distance-enhanced
random walks algorithm, through which we avoid the necessity of accurate
image segmentation while still able to highlight the foreground object.
Third, we propose a multiresolution framework to perform image compositions
at different subbands so as to separate the texture and color components to
simultaneously achieve smooth texture transition and desired color control.
The experimental results demonstrate that our proposed framework achieves
better and more realistic results for images with salient background color
or texture differences, while providing comparable results as the
state-of-the-art algorithms for images without the need of preserving the
object color fidelity and without significant background texture
discrepancy.
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J. Zheng
(2009)
"C1
NURBS representation of G1
composite rational Bezier curves"
Computing, Vol.86. No2.
This paper is concerned with the
re-representation of a G1 composite rational Bezier curve.
Although the rational Bezier curve segments that form the composite curve
are G^1 continuous at their joint points, their homogeneous representations
may not be even C0 continuous in the homogeneous space. In this
paper, an algorithm is presented to convert the G1 composite
rational Bezier curve into a NURBS curve whose nonrational homogeneous
representation is C1 continuous in the homogeneous space. This
re-representation process involves reparameterization using Moebius
transformations, smoothing multiplication and parameter scaling
transformations. While the previous methods may fail in some situations, the
method proposed in this paper always works.
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Y.Wang, J. Zheng
(2009)
"Tubular
triangular mesh parameterization and applications"
Computer Animation and Virtual
Worlds, Vol 20.
Triangular
meshes are a popular geometric representation for 3D models used in computer
graphics. Parameterization is a process that establishes a mapping between
the surface of a model and a suitable domain. This paper considers the
problem of parameterizing triangular meshes that have tubular shapes. Unlike
an open mesh that is of plane topological type, a tubular mesh gives rise to
some special issues in parameterization due to its mesh structure. This
paper presents an edge-based parameterization method, in which the edges
rather than the vertices of the mesh are treated as the target for
parameterization. It first parameterizes the edges on the two boundaries of
the tubular mesh, then parameterizes the internal edges based on the mean
value coordinates, and finally computes the parameters of the mesh vertices.
The method does not need cutting of the mesh. It improves conventional
cutting-based algorithms, which cut the mesh to make it a disk
topologically, and overcomes the problems of cutting paths that are the
zigzag paths leading to suboptimal parameterizations and the difficulty in
finding good cutting paths. Some applications such as surface fitting and
texture mapping are also provided.
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W. Guan, J. Cai, J. Zheng,
C.W.Chen
(2008)
"Segmentation-based
view-dependent 3D graphics model transmission"
IEEE Transactions on
Multimedia, Vol.10. No.5, pp.724-734.
For wireless
network based graphics applications, a key challenge is how to efficiently
transmit complex 3-D models over bandwidth-limited wireless channels. Most
existing 3-D mesh transmission systems do not consider such a view-dependent
delivery issue, and thus transmit unnecessary portions of 3-D mesh models,
which leads to the waste in precious wireless network bandwidth. In this
paper, we propose a novel view-dependent 3-D model transmission scheme,
where a 3-D model is partitioned into a number of segments, each segment is
then independently coded using the MPEG-4 3DMC coding algorithm, and finally
only the visible segments are selected and delivered to the client.
Moreover, we also propose analytical models to find the optimal number of
segments so as to minimize the average transmission size. Simulation results
show that such a view-based 3-D model transmission is able to substantially
save the transmission bandwidth and therefore has a significant impact on
wireless graphics applications.
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S. Raman, J. Zheng
(2008)
"Efficient
terrain triangulation and modification algorithms for game applications"
International Journal of
Computer Games Technology, Vol.8. No.3, pp.1-5.
An efficient
terrain generation algorithm is developed, based on constrained conforming
Delaunay triangulation. The density of triangulation in different regions of
a terrain is determined by its flatness, as seen from a height map, and a
control map. Tracks and other objects found in a game world can be applied
over the terrain using the "stenciling" and "stitching" algorithms. Using
user controlled parameters, varying levels of detail can be preserved when
applying these objects over the terrain as well. The algorithms have been
incorporated into 3dsMax as plugins, and the experimental results
demonstrate the usefulness and efficiency of the developed algorithms. |
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W. Chen, Y. Cai, J. Zheng
(2008)
"Constructing triangular meshes of minimal area"
Computer-Aided Design and
Applications, Vol.5. No.1-4, pp.508-518.
This paper is
concerned with the problem of constructing an aesthetically pleasing
triangular mesh with a given closed polygonal contour in three dimensional
space as boundary. Triangular meshes of minimal area from all triangular
meshes with the prescribed boundary are suggested as the candidates for this
problem. An iterative algorithm of constructing such a triangular mesh from
a given polygonal boundary is presented. Experimental examples show that the
proposed algorithm is reliable and effective. Some related theoretical
issues, possible extensions and applications are also discussed. |
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I. Chandrasekaran, Y. Cai, C.Cao,
B. Lu, J. Zheng
(2007)
"Virtual
reality prototyping of bio-molecules"
Virtual and Physical
Prototyping, Vol.2. No.1, pp.37-49.
Modelling,
sharing and transmission of three-dimensional (3D) graphics data of
biomolecules are essential in many bio visualization tasks from
collaborative research and education to molecular simulation and drug
discovery. In the current paper, modelling and representing of bio-molecular
structure for virtual and physical rapid prototyping is presented. Our aim
is to devise a uniform solution for visualizing, browsing, interacting and
prototyping of bio-molecules in various environments including internet,
immersive virtual reality (VR), and rapid manufacturing. To do so, we use
non uniform rational B-spline surfaces (NURBS) to represent protein
secondary structure and surface structure. NURBS protein structures are then
tessellated to form bio-molecular graphics models. Their triangular mesh
representation is next extracted from their scene graph. A geometric
optimization process is followed to make data compatible for their
formatting in compact and consistent VR standard to support protein internet
browsing, protein VR visualization, protein 3D rapid prototyping and crystal
sub-surface laser engraving. |
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J. Zheng, Y.Y. Cai (2006)
"Interpolation
over arbitrary topology meshes using a two-phase subdivision scheme"
IEEE Transactions on Visualization
and Computer Graphics, Vol.12. No.3, pp.301-310.
This paper presents a two-phase process, based on a topological modification of the control mesh and a subsequent
Catmull-Clark subdivision, to construct a smooth surface that interpolates some or all of the vertices of a mesh with arbitrary topology. It is also possible to constrain the surface to have specified tangent planes at an arbitrary subset of the vertices to be
interpolated. The method has following features: (1) it is guaranteed to always work and the computation is numerically stable; (2) there is no need to solve a system of linear equations and the whole
computation complexity is O(K) where K is the number of the vertices; and (3) each vertex can be associated with a scalar shape handle for local shape control. These features make interpolation using
Catmull-Clark surfaces simple and thus make the new method itself suitable for interactive freeform shape design.
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Y.Y.Cai, B.Lu, J. Zheng, L.
Lin (2006)
"Immersive
protein gaming for bio edutainment"
Simulation and Gaming, Vol.37. No.4, pp.466-275.
Learning
through playing is one of the natural ways for
knowledge and skill acquisition. Games have long been used as a tool for
education, from concept building to problem solving. Through fun learning,
students may further develop their curiosities and interest in their study. This paper addresses the issue of learning biomolecular
structures by Virtual Reality (VR) gaming. A bio edutainment system is developed
for protein structure learning. It consists of mainly three components: visualization, modeling and interaction, on top of various supporting
technologies such as Graphics and Networking. Via virtual reach-in and hands-on,
students can interact with amino acid sequences, protein a-helices, b-sheets and
other protein structural information.
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B.Lu, Z.Fan, J. Zheng, L. Lin (2006)
"Bio-native
shape modeling and virtual reality for bio education"
International Journal of Image and
Graphics, Vol.6. No.2, pp.251-265.
Bio structural
and functional research and education is playing an increasingly important role
in today's post-genome era. Protein geometry and shape modeling is thus a
fundamental issue for protein visualization. The number of protein structure
determined by X-ray crystallography or Nuclear Magnetic Resonance (NMR) is
expanding in an exponential rate. Recent technology advancement has also made it
possible for the determination of larger and more complicated protein
structures. A generic and automatic shape modeling for protein structures is
therefore highly desired for effective and efficient protein visualization. We
propose a bio-native geometric modeling technique in this paper for constructing
protein secondary structure. Our emphasis is placed on the shape compatibility
with the protein conformation property. Efforts are also mage handle smooth
sweeping for complex protein structures. We describe as well a virtual reality
application for protein structure education based on our bio-native shape
modeling and visualization techniques developed in this work.
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J. Zheng, Y.Y. Cai (2005)
"Making
Doo-Sabin surface interpolation always work over irregular meshes"
The Visual Computer, Vol.21,
No.4., pp 242-251
This paper presents
a reliable method for constructing a control mesh whose Doo-Sabin subdivision
surface interpolates the vertices of a given mesh with arbitrary topology. The
method improves on existing techniques in two respects: (1) it is guaranteed to
always work
for meshes of arbitrary topological type; (2) there is no need to solve a system
of linear equations to obtain the control points. Extensions to include normal
vector interpolation and/or shape adjustment are also discussed.
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J. Zheng (2005)
"Minimizing
the maximal ratio of weights of a rational Bezier curve"
Computer Aided Geometric Design, Vol.
22, No. 3, pp 275-280
This paper presents
a solution to the problem of reparameterizing a rational curve by a Moebius
transformation such that the maximal ratio of weights in the reparameterized
representation is minimized. The problem is reduced to solving a linear
programming problem, which can be solved directly and simply. The result can be
used to reparameterize rational curves so as to yield tight bounds on
derivatives.
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W.Li, S.Xu, J.Zheng, G.Zhao
(2004)
"Target
curvature driven fairing algorithm for planar cubic B-spline curves"
Computer Aided Geometric Design, Vol. 21., No.5., pp.499-513.
This paper proposes
to use target curvature plots to identify bad points or bad curve segments of a
given B-spline curve. Then the control points of the curve are modified by a
local constrained optimization, which involves the shape fairness and the
coherence to the original design. The target curvature plots are prescribed by
designers according to their design intention.
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X.Song, T.Sederberg, J.Zheng, R.Farouki, J.Hass
(2004)
"Linear
perturbation methods for topologically consistent representations of free-form
surface intersection"
Computer Aided Geometric Design, Vol. 21, No.3.
By applying
displacement maps to slightly perturb two free-form surfaces, one can ensure exact
agreement between the images in 
of parameter-domain approximations to their curve of intersection. Thus, at the
expense of slightly altering the surfaces in the vicinity of their intersection,
a perfect matching of the surface trimming curves is guaranteed. This exact
agreement of contiguous trimmed surfaces is essential to achieving topologically
consistent solid model constructions through Boolean operations, and has a
profound impact on the efficiency and reliability of applications such as
meshing, rendering, and computing volumetric properties.
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J. Zheng, T. Sederberg, R. Johnson
(2004)
"Least squares methods for solving
differential equations using Bezier control points"
Applied Numerical Mathematics,
Vol. 48, No.2
This paper investigates the use of the control points of the
Bernstein- Bezier form for numerically solving differential equations. Two least squares
type schemes based on degree raising and subdivision are proposed. The convergence of the methods applied to two-point boundary value
problems is analyzed.
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T. Sederberg, J. Zheng, Song
X. (2004)
"A conjecture on tangent
intersections of surface patches"
Computer Aided Geometric Design,
Vol.21, No.1
This paper provides
some evidences to show that if two surface patches intersect with G1
continuity along an entire curve, the probability is one that the curve is
rational. This idea has significance for surface intersection algorithms. |
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J. Zheng, Wang G.Z. (2003)
"Perturbing Bezier coefficients for
best constrained degree reduction in L2-norm"
Graphical Models, Vol.65,
No.6., pp 351-368
This paper shows how the Bézier coefficients of a given degree n polynomial
are perturbed, based on minimizing a weighted Euclidean norm, so that it can be reduced to a degree m (<n)
polynomial with the constraint that continuity of a prescribed order is
preserved at the two endpoints. Then the paper proves that the problem of finding a best L2-approximation
over the interval [0,1] for constrained degree reduction is equivalent to that
of finding a minimum perturbation vector in a certain weighted Euclidean norm.
The relevant weights are derived.
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J. Zheng, T. Sederberg (2003)
"Gaussian and mean curvatures of rational Bezier patches"
Computer Aided Geometric Design, Vol. 20, No. 6, pp 297-301
This paper derives
formulae for Gaussian and mean curvatures for rational Bézier surface patches.
The formulae are expressed in terms of simple geometric quantities (lengths and
areas) obtained from the control mesh. These formulae provide more geometric
intuition and are easier to compute than the generic formulae from differential
geometry. Both the tensor product and triangular patch cases are addressed. |
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T. Sederberg, J. Zheng, Song
X. (2003)
"Knot intervals and multi-degree
splines"
Computer Aided Geometric Design,
Vol.20, No.7, pp 455-468.
This paper studies the merits of using knot interval notation for B-spline
curves. Using knot interval notation, the paper introduces MD-splines, which are
B-spline-like curves that are comprised of polynomial segments of various
degrees (MD stands for "multi-degree"). The paper focuses on MD-splines
of degree 1, 2, and 3, as well as degree 1 and n.
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J. Zheng, T. Sederberg (2001)
"A direct approach to computing
the mu-basis of planar rational curves"
Journal of Symbolic Computation,
Vol.31, No.5, pp 619-629.
This paper presents
an O(n2) algorithm, based on Gröbner basis techniques,
to compute the 
-basis of a degree n planar rational curve. The prior method involved
solving a set of linear equations whose complexity by standard numerical methods
was O(n3). |
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Chen F., J. Zheng, T. Sederberg (2001)
"The
mu-basis of a rational ruled
surface"
Computer Aided Geometric Design,
Vol.18, No.1, pp 61-72.
This
paper presents a simple
algorithm for computing the -basis for a rational ruled
surface. The -basis consists of two polynomials p(x,y,z,s)
and q(x,y,z,s) that are linear in x,y,z
and degree
and m-
in s respectively, where m is the degree of the implicit equation.
The implicit equation of the surface is then obtained by merely taking the
resultant of p and q with respect to s. This
implicitization algorithm is faster and/or more robust than previous methods. |
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J. Zheng, T. Sederberg (2000)
"Estimating tessellation parameter
intervals for rational curves and surfaces"
ACM Transactions on Graphics,
Vol.19, No.1, pp 56-77.
This paper presents a method for determining
a priori
a constant parameter interval for tessellating a rational curve or surface such
that the deviation of the curve or surface from its piecewise linear
approximation is within a specified tolerance. The parameter interval is
estimated based on information about second-order derivatives in the homogeneous
coordinates, instead of using affine coordinates directly.
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T. Sederberg, J. Zheng, K.
Klimaszewski,
T. Dokken (1999)
"Approximate implicitization using
monoid curves and surfaces"
Graphical Models and Image
Processing, Vol.61, No.4, pp 177-198.
This paper presents an approach to finding an approximate implicit equation and
an approximate inversion map of a rational parametric curve or surface. High accuracy of the approximation is achieved with a
small number of low-degree curve segments or surface patches. By
using monoid curves and surfaces, the method eliminates the undesirable
singularities and "phantom" branches normally associated with implicit
representation. The monoids are expressed in exact implicit and parametric
equations simultaneously, and upper bounds are derived for the approximate
errors.
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Wang G.Z., J. Zheng (1997)
"Bounds on the moving control points
of hybrid curves"
Graphical Models and Image
Processing, Vol.59, No.1, pp 19-25. This
paper provides several methods to
estimate the error bounds for the approximation to the moving control point of
the hybrid curves. When the given rational Bézier curves satisfies the
convergent conditions for moving control point of the hybrid curve, the polynomial Bézier curves
that approximate the rational Bézier curve can
be obtained by replacing the moving control point with the special point.
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J. Zheng, Wang G.Z., Liang Y. (1995)
"GCn continuity conditions for
adjacent rational parametric surfaces"
Computer Aided Geometric Design,
Vol.12, No.2, pp 111-129. This
paper derives the constraints on the homogeneous surface belonging to a certain
rational surface that are both necessary and sufficient to ensure
that the rational surface is nth-order geometric continuous. This gives
up the strong restriction that requires the homogeneous surface to be as smooth
as the rational surface. Further the conditions for the rectangular rational Bézier
patches are developed, and some simple and practical sufficient conditions are
presented which might give a valid means for the construction of GCn
connecting surfaces.
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J. Zheng, Wang G.Z., Liang Y. (1992)
"Curvature continuity between
adjacent rational Bezier patches"
Computer Aided Geometric Design,
Vol.9, No.5, pp 321-335.
This paper discusses
the curvature continuity between two adjacent rational Bézier surfaces. The necessary and sufficient
conditions are derived, and further, a series of simple sufficient conditions
are developed. With them one can both check the geometric continuity between two
surfaces and construct a rational surface possessing curvature continuity with a
given rational patch along a certain boundary. |
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Refereed Book Chapters |
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J. Zheng, T. Sederberg,
Chionh E.-W., D. Cox (2003)
"Implicitizing rational surfaces
with base points using the method of moving surface"
Topics in Algebraic Geometry and
Geometric Modeling, Contemporary Mathematics Series, Vol. 334, Ron
Goldman and Rimvydas Krasauskas, eds., AMS, pp 151-168. ISBN 0-8218-3420-7.
The method of moving planes and moving quadrics can express the
implicit equation of a parametric surface as the determinant of a matrix M.
The rows of M correspond to moving planes or moving quadrics that follow the
parametric surface. Previous papers on the method of moving surfaces have shown that a simple base point
has the effect of converting one moving quadric to a moving plane. A much more general version of the method of moving surfaces is
presented in this paper that is capable of dealing with multiple base points.
This is a unifying approach whereby tensor product surfaces, pure degree surfaces, and
"corner-cut"
surfaces, can all be implicitized under the same framework and do not need to be treated as distinct cases. The central idea in this
approach is that if a surface has a base point of multiplicity k, the moving surface blending functions must have the same base
point, but of multiplicity k-1. |
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T. Sederberg, J. Zheng (2002)
"Algebraic methods for computer
aided geometric design"
Handbook of Computer Aided Geometric
Design, G. Farin, J. Hoschek, M.-S. Kim, eds., Elsevier, North-Holland,
pp.363-387.
ISBN: 0-444-51104-0.
The concepts and methods of algebra and algebraic geometry have found
significant applications in many disciplines. This chapter presents a collection of
gleanings from algebra or algebraic geometry that
hold practical value for the field of computer aided geometric design. We focus on the insights, algorithm
enhancements and practical capabilities that algebraic methods have contributed to
CAGD. Specifically, we examine resultants and Gröbner basis, and discuss their
applications in implicitization, inversion, parametrization and intersection algorithms. Other topics of CAGD research work using algebraic methods
are also outlined. |
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T. Sederberg, J. Zheng (2001)
"Towards the
mu-basis of a rational
surface"
Mathematical Methods for Curves and
Surfaces , T. Lyche and L. L. Schumaker, eds., Vanderbilt University Press,
TN, pp 467-476.
ISBN: 0-8265-1378-6. This
paper makes some contributions in defining the mu-basis of a rational
surface, and it proves some important properties of the proposed basis. The
concepts are based on syzygy modules.
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Book
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Wang G.J.,
Wang G.Z., J. Zheng (2001)
Computer Aided
Geometric Design
CHEP-Beijing,
Springer-Heiderberg, July 2001. ISBN: 7-04-010019-3.
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