Bio Sketch 
I am now an
associate professor in School of Computer Science and
Technology of Shandong University. In 07/2008, I
received my Ph.D degree in the Department of Computer
Science and Technology at Tsinghua University, China. I
received my B.Sc. and M. Sc in Computer Science and
Technology from Shandong University in 2000 and 2003,
respectively. 
Research
Interests 
Constrained Surface
Mapping
Extremal
Quasiconformal Mapping
Surface
Registration and Analysis
Freeform
Surface Parameterization


Publications 

Y.J. Yang, W. Zeng, XiangXu
Meng. Conformal freeform surfaces. ComputerAided Design,
2016, 81:4860.
Abstract:
The conformality of freeform surfaces
highly affects their rendering and tessellation results. To
improve the conformality of freeform surfaces, a novel freeform
surface representation named hierarchical freeform surfaces is
presented in this paper. The conformality energy of hierarchical
freeform surfaces is first formulated and its numerical
approximation is then constructed using the composite Simpson’s
rule. By constructing the parameterization of the initial
freeform transformation using the Ricci flow method, the optimal
freeform transformation is obtained by the Levenberg–Marquardt
method, which is further interleaved with the freeform
refinement procedure to generate a hierarchical freeform surface
with bounded conformality deviations. Examples are given to show
the performance of our algorithm for rendering and tessellation
applications. 

W. Zeng, Y.J. Yang and
Muhammad Razib. GraphConstrained Surface Registration Based on
Tutte Embedding. The 7th International Workshop on Biomedical
Image Registration, 2016.
Abstract:
This work presents an efficient method to
compute the registration between surfaces with consistent graph
constraints based on Tutte graph embedding. Most natural objects
have consistent anatomical structures, extracted as isomorphic
feature graphs. For genus zero surfaces with ≥ 1 boundaries, the
graphs are planar and usually 3connected. By using Tutte
embedding, each feature graph is embedded as a convex
subdivision of a planar convex domain. Using the convex
subdivision as constraint, surfaces are mapped onto convex
subdivision domains and the registration is then computed over
them. The computation is based on con
strained harmonic maps to minimize the stretching energy, where
curvy graph constraints become linear ones. This method is
theoretically rigorous. The algorithm solves sparse linear
systems and is computationally efficient and robust. The
resulting mappings are proved to be unique and diffeomorphic.
Experiments on various facial surface data demonstrate its
efficiency and practicality. 

Y.J. Yang,
W. Zeng, TianQi Song.Optimizing
Conformality of NURBS Surfaces by General Bilinear
Transformations. ComputerAided Design,2015,46(6):12–25.SCI,EI
Abstract:
The conformality of NURBS surfaces greatly
affects the results of rendering and tessellation applications.
To improve the conformality of NURBS surfaces, an optimization
algorithm using general bilinear transformations is presented in
this paper. The conformality energy is first formulated and its
numerical approximation is then constructed using the composite
simpson’s rule. The initial general bilinear transformation is
obtained by approximating the conformal mapping of its 3D
discretized mesh using a least square method, which is further
optimized by the Levenberg–Marquardt method. Examples are given
to show the performance of our algorithm for rendering and
tessellation applications. 

Y.J. Yang,
W. Zeng. Optimizing Equiareality of
NURBS Surfaces using Composite Mobius Transformations.
Journal of Computational and Applied Mathematics(CAM),2015,279:112.SCI,EI
Abstract:
The equiareality of NURBS surfaces greatly
affects the results of visualization and tessellation
applications, especially when dealing with extruding and
intruding shapes. To obtain more equiareal parameterizations of
NURBS surfaces than the Mobius based method, an optimization
algorithm is presented in this paper based on the more flexible
composite reparameterization functions. For fixed knots, the
optimal composite reparameterization can be obtained using the
LevenbergMarquardt method. For a given tolerance, a uniform
subdivision scheme is interleaved with the optimization
procedure and this process finishes until the change of the
equiareal deviation energy is less than the given tolerance.
Examples are given to show the performance of our algorithm for
visualization and tessellation applications. 

W. Zeng, Y.J. Yang. Colon
Flattening by LandmarkDriven Optimal Quasiconformal Mapping.
MICCAI 2014. Abstract:
In virtual colonoscopy, colon conformal
flattening plays an important role, which unfolds the colon wall
surface to a rectangle planar image and preserves local shapes
by conformal mapping, so that the cancerous polyps and other
abnormalities can be easily and thoroughly recognized and
visualized without missing hidden areas. In such maps, the
anatomical landmarks (taeniae coli, flexures, and haustral
folds) are naturally mapped to convoluted curves on 2D domain,
which poses difficulty for comparing shapes from geometric
feature details. Understanding the nature of landmark curves to
the whole surface structure is meaningful but it remains
challenging and open. In this work, we present a novel and
effective colon flattening method based on quasiconformal
mapping, which straightens the main anatomical landmark curves
with least conformality (angle) distortion. It provides a
canonical and straightforward view of the long, convoluted and
folded tubular colon surface. The computation is based on the
holomorphic 1form method with landmark straightening
constraints and the quasiconformal optimization, and has linear
time complexity due to the linearity of 1forms in each
iteration. Experiments on various colon data demonstrate the
efficiency and efficacy of our algorithm and its practicability
for polyp detection and findings visualization; furthermore, the
result reveals the geometric characteristics of anatomical
landmarks on the colon surfaces. 

W. Zeng, Y.J. Yang.
Surface Matching and Registration by Landmark CurveDriven
Canonical Quasiconformal Mapping. ECCV 2014.
Abstract:
This work presents a novel surface
matching and registration method based on the landmark
curvedriven canonical surface quasiconformal mapping, where an
open genus zero surface decorated with landmark curves is mapped
to a canonical domain with horizontal or vertical straight
segments and the local shapes are preserved as much as possible.
The key idea of the canonical mapping is to minimize the
harmonic energy with the landmark curve straightening
constraints to generate a quasiholomorphic 1form which is zero
in one parameter along landmark and results in a quasiconformal
mapping. The mapping exists and is unique and intrinsic to
surface and landmark geometry. The novel shape representation
provides a conformal invariant shape signature; we use this as
Teichm¨uller coordinates to construct a subspace of the
Teichm¨uller space which considers geometry feature details and
therefore increases the discriminative ability for matching.
Furthermore, we present a novel and efficient registration
method for surfaces with landmark curve constraints by computing
an optimal mapping over the canonical domains with straight
segments, where the curve constraints become linear forms. Due
to the linearity of 1form and harmonic map, the algorithms are
easy to compute, efficient and practical. Experiments on human
face and brain surfaces demonstrate the efficiency and efficacy
and shows the potential for broader shape analysis applications. 

Y.J. Yang, W. Zeng,
J.F. Chen. Equiareal parameterizations of NURBS surfaces.
Graphical Models (GMOD),2014,76(1):4355.
(SCI,EI, impact factor: 0.697)
Abstract:
The equiareality of
freeform surfaces greatly affects the results of visualization
and tessellation applications, especially when dealing with
extruding and intruding shapes. To improve the equiareality of
given freeform surfaces, an optimization algorithm using the
Mobius transformations is presented in this paper. The optimal
Mobius transformation is obtained by computing the intersection
of two planar algebraic curves, whose coefficients are computed
explicitly for Bezier and Bspline surfaces, while numerically
for NURBS surfaces. Examples are given to show the performance
of our algorithm for visualization and tessellation
applications. 

C.L.
Yang, W.Z.
Wang, Y.J.
Yang, L. Lu, Z.J.
Zhu, B.H. Zhu, W.
Zeng. Weak visibility polygons of NURBS curves inside simple
polygons. Journal of Computational and Applied
Mathematics,2014,256(115). (SCI:EI, impact factor 0.989)
Abstract:
Visibility computation plays an important
role in applications such as architectural design, art gallery
patrolling and virtual worlds. In this paper, we present an
algorithm to compute the weak visibility polygons (WVP) of Non
Uniform Rational Bspline (NURBS) curves inside simple polygons.
The NURBS curve is first subdivided into triangular curves. We
then compute the WVP of each triangular curve by shearing that
of its triangle hull. Finally, all triangular curves’ WVPs are
merged together to obtain the WVP of the NURBS curve. Analysis
and examples are given to show the performance of our algorithm. 

Y.J. Yang, , W. Zeng, C.L.
Yang, B.L. Deng, X.X. Meng,S.S. lyengar. An algorithm to improve
parameterizations of rational Bezier surfaces using rational
bilinear reparameterization. ComputerAided Design,2013,45(3):628–638.(SCI:
102GY; EI:20130215873983,impact factor 1.264)
Abstract:
The representation of rational Bezier
surfaces greatly affects the results of rendering and
tessellation applications. The uniformity and orthogonality of
isoparameter curves are two key properties of the optimal
parameterization. The only rational Bezier surfaces with uniform
isoparameter curves are bilinear surfaces, while the control
points of the rational Bezier surfaces with orthogonal
isoparameter curves satisfy a symmetrical condition. Moreover,
the only rational Bezier surfaces with uniform and orthogonal
isoparameter curves are rectangles. To improve the uniformity
and orthogonality of isoparameter curves for general Bezier
surfaces, an optimization algorithm using the quadratic
transformations is presented, which can produce a better
parameterization with the cost of degree elevation. Examples are
given to show the performance of our algorithm for rendering and
tessellation applications. 

Y.J. Yang, W. Zeng, C.L.
Yang, X.X. Meng, J.H. Yong, B.L. Deng. G^{1} continuous
approximate curves on NURBS surfaces. ComputerAided Design,2012,44(9):824–834.
(SCI: 966SW; EI: 20122315101838, impact factor 1.264)
Abstract:
Curves on surfaces play an
important role in computer aided geometric design. In this
paper, we present a parabola approximation method based on the
cubic reparameterization of rational Bezier surfaces, which
generates G^{1} continuous approximate curves lying
completely on the surfaces by using isoparameter curves of the
reparameterized surfaces. The Hausdorff distance between the
approximate curve and the exact curve is controlled under the
userspecified tolerance. Examples are given to show the
performance of our algorithm. 

Y.L. Yang, Y.J. Yang, M.
Niloy, H. Pottmann. Shape space exploration of constrained
meshes. ACM transaction on Graphics (TOG),2011,30(6).
(SCI: 856YP; EI: 20114914575468, impact factor 3.489).
SIGGRAPH ASIA 2011.
Abstract:
We present a general
computational framework to locally characterize any shape space
of meshes implicitly prescribed by a collection of nonlinear
constraints. We computationally access such manifolds, typically
of high dimension and codimension, through first and second
order approximants, namely tangent spaces and quadratically
parameterized osculant surfaces. Exploration and navigation of
desirable subspaces of the shape space with regard to
application specific quality measures are enabled using
approximants that are intrinsic to the underlying manifold and
directly computable in the parameter space of the osculant
surface. We demonstrate our framework on shape spaces of planar
quad (PQ) meshes, where each mesh face is constrained to be
(nearly) planar, and circular meshes, where each face has a
circumcircle. We evaluate our framework for navigation and
design exploration on a variety of inputs, while keeping context
specific properties such as fairness, proximity to a reference
surface, etc. 

H. C. Song, J.H. Yong, Y. J.
Yang, X.M. Liu. Algorithm for orthogonal projection of
parametric curves on Bspline surfaces. ComputerAided Design,
2011,43:381393.(SCI: 743KT; EI: 20111013734335,impact
factor 1.264)
Abstract:
This paper proposes an algorithm for calculating the orthogonal
projection of parametric curves onto Bspline surfaces. It
consists of a second order tracing method with which we
construct a polyline to approximate the preimage curve of the
orthogonal projection curve in the parametric domain of the base
surface. The final 3D approximate curve is obtained by mapping
the approximate polyline onto the base surface. The Hausdorff
distance between the exact orthognal projection curve and the
approximate curve is controlled under the userspecified
distance tolerance. And the continuity of the approximate curve
is approximate continuous. Experiments demonstrate that our
algorithm is faster than the existing first order algorithms. 

Y.J. Yang, W. Zeng, H.
Zhang, J. C. Paul and J. H. Yong. Projection of Curves on
BSpline Surfaces Using Quadratic Reparameterization. Journal
of Graphical Models (GMOD), 72(5): 4759, 2010. (SCI: 695WI;
EI: 20104013272039,impact factor 1.0)
Abstract:
Curves on surfaces play an
important role in computer aided geometric design. In this
paper, we present a hyperbola approximation method based on the
quadratic reparameterization of Bézier surfaces, which generates
reasonable low degree curves lying completely on the surfaces by
using isoparameter curves of the reparameterized surfaces. The
Hausdorff distance between the projected curve and the original
curve is controlled under the userspecified distance tolerance.
The projected curve is approximate continuous. Examples are
given to show the performance of our algorithm. 

Y. J. Yang, S. Cao, J. H.
Yong, H. Zhang, J. C. Paul, J. G. Sun. Approximate
computation of curves on Bspline surfaces. ComputerAided
Design, 2008, 40(2):223234. (SCI: CAIDA5; EI:080611089859,impact
factor 1.264)
Abstract:
Curves on surfaces play an
important role in computeraided geometric design. Because of
the considerably high degree of exact curves on surfaces,
approximation algorithms are preferred in CAD systems. To
approximate the exact curve with a reasonably low degree curve
which also lies completely on the Bspline surface, an algorithm
is presented in this paper. The Hausdorff distance between the
approximate curve and the exact curve is controlled under the
userspecified distance tolerance. The approximate curve is
approximate continuous. Examples are given to show the
performance of our algorithm. 

Y. J. Yang, J. H.
Yong, J. G. Sun. An algorithm for tetrahedral mesh generation
based on conforming constrained Delaunay tetrahedralization.
Computers & Graphics, 2005, 29(4): 606615. (SCI: 971CG, EI:
8765028,impact factor 1.0)
Abstract:
An unstructured tetrahedral mesh
generation algorithm for 3D model with constraints is presented.
To automatically generate a tetrahedral mesh for model with
constraints, an advancing front algorithm is presented based on
conforming constrained Delaunay tetrahedralization (CCDT). To
reduce the number of visibility tests between vertices with
respect to model faces as well as the computation of constrained
Delaunay tetrahedra, a sufficient condition for DT (constrained
Delaunay tetrahedralization whose simplexes are all Delaunay)
existence is presented and utilized coupled to uniform grid and
advancing front techniques in our algorithm. The mesh generator
is robust and exhibits a linear time complexity for mechanical
models with uniform density distribution. 

Y. J. Yang, J. H. Yong, H.
Zhang, J.C. Paul, J.G. Sun. A rational extension of Piegl's
method for filling nsided holes. ComputerAided Design,
2006, 38(11): 11661178. (SCI: 098FP, EI: 063910135166,impact
factor 1.234)
Abstract:
Nsided hole filling plays an important
role in vertex blending. To deal with the case that the corner
is surrounded by rational surfaces (i.e. NURBS surfaces), an
algorithm to fill an nsided hole with
G^{1}
continuous NURBS patches that interpolate the given
boundary curves and approximate the given crossboundary
derivatives is presented based on Piegl's method. The NURBS
surfaces joining along inner or boundary curves have normal
vectors that do not deviate more than the userspecified angular
tolerance . The boundaries as well as crossboundary derivatives
all can be NURBS curves. No restrictions are imposed on the
number of boundary curves, and the crossboundary derivatives
can be specified independently.


Y. J. Yang,
TingTing Cui, ChengLei Yang, XiangXu Meng, Wei Zeng.
Bezier surfaces with orthogonal
isoparameter curves, GDC 2013, Dalian,
China.
Abstract:
The
representation of Bezier surfaces greatly affects the results of
rendering and tessellation applications. The orthogonality of
isoparameter curves is one of the most important properties of
the surface parameterization in differential geometry. The only
rational bilinear surface with orthogonal isoparameter curves
is a rectangle. For Bezier surfaces of degree 2 × 2, we derive
the explicit orthogonality condition of their control points, by
using which a scheme to construct surfaces with orthogonal
isoparameter curves is then presented. Also the possible
extension of the construction scheme for Bezier surfaces of any
degree is discussed. Examples are given to show the performance
of our algorithm for rendering and tessellation applications. 

Y. J. Yang, J. H. Yong, H.
Zhang, J.C. Paul, J.G. Sun. Optimal parameterizations of Bezier
surfaces. 2nd International Symposium on Visual Computing, Reno
(Nevada), USA. LNCS 4291, pp. 672681. 2006. (EI:065010308619)
Abstract:
The presentation of Bezier surfaces
affects the results of rendering and tessellating applications
greatly. To achieve optimal parameterization, we present two
reparameterization algorithms using linear Mobius
transformations and quadratic transformations, respectively. The
quadratic reparameterization algorithm can produce more
satisfying results than the Mobius reparameterization algorithm
with degree elevation cost. Examples are given to show the
performance of our algorithms for rendering and tessellating
applications. 

Y. J. Yang,
H. Zhang, J. H. Yong, J.C. Paul, J.G. Sun. Constrained Delaunay
Triangulation Using Delaunay Visibility. 2nd International
Symposium on Visual Computing, Reno (Nevada), USA. LNCS 4291,
pp. 682691. 2006. (EI:065010308619)
Abstract:
An algorithm for constructing constrained
Delaunay triangulation (CDT) of a planar straightline graph
(PSLG) is presented. Although the uniform grid method can reduce
the time cost of visibility determinations, the time needed to
construct the CDT is still long. The algorithm proposed in this
paper decreases the number of edges involved in the computation
of visibility by replacing traditional visibility with Delaunay
visibility. With Delaunay visibility introduced, all strongly
Delaunay edges are excluded from the computation of visibility.
Furthermore, a sufficient condition for DT (CDT whose triangles
are all Delaunay) existence is presented to decrease the times
of visibility determinations. The mesh generator is robust and
exhibits a linear time complexity for randomly generated PSLGs. 
