September 28 Budi Purnomo 
PolyCubeMaps Tarini, Hormann, Cignoni, and Montani Proceedings of SIGGRAPH 2004. pp. 853860. Standard texture mapping of realworld meshes suffers from the presence of seams that need to be introduced in order to avoid excessive distortions and to make the topology of the mesh compatible to the one of the texture domain. In contrast, cube maps provide a mechanism that could be used for seamless texture mapping with low distortion, but only if the object roughly resembles a cube. We extend this concept to arbitrary meshes by using as texture domain the surface of a polycube whose shape is similar to that of the given mesh. Our approach leads to a seamless texture mapping method that is simple enough to be implemented in currently available graphics hardware. 
October 5 Joe Hennessey 
Laplacian
Surface Editing Olga Sorkine, Daniel CohenOr, Yaron Lipman, and Marc Alexa Symposium on Geometry Processing 2004. Surface editing operations
commonly require geometric details of the surface to be preserved as
much as possible. We argue that geometric detail is an intrinsic
property of a surface and that, consequently, surface editing is best
performed by operating over an intrinsic surface representation. We
provide such a representation of a surface, based on the Laplacian of
the mesh, by encoding each vertex relative to its neighborhood. The
Laplacian of the mesh is enhanced to be invariant to locally linearized
rigid transformations and scaling. Based on this Laplacian
representation, we develop useful editing operations: interactive
freeform deformation in a region of interest based on the
transformation of a handle, transfer and mixing of geometric details
between two surfaces, and transplanting of a partial surface mesh onto
another surface. The main computation involved in all operations is the
solution of a sparse linear system, which can be done at interactive
rates. We demonstrate the effectiveness of our approach in several
examples, showing that the editing operations change the shape while
respecting the structural geometric detail

October 12 Peter Yee 
Mesh Editing with PoissonBased Gradient
Field Manipulation Yizhou Yu, Kun Zhou, Dong Xu Xiaohan Shi, Hujun Bao, Baining Guo, HeungYeung Shum ACM SIGGRAPH 2004 In this paper, we introduce a
novel approach to mesh editing with the Poisson equation as the
theoretical foundation. The most distinctive feature of this approach
is that it modifies the original mesh geometry implicitly through
gradient field manipulation. Our approach can produce desirable and
pleasing results for both global and local editing operations, such as
deformation, object merging, and smoothing. With the help from a few
novel interactive tools, these operations can be performed conveniently
with a small amount of user interaction. Our technique has three key
components, a basic mesh solver based on the Poisson equation, a
gradient field manipulation scheme using local transforms, and a
generalized boundary condition representation based on local frames.
Experimental results indicate that our framework can outperform
previous related mesh editing techniques.

October 19 Jim Houser 
Multiichart
Geometry Images Sander, Wood, Gortler, Snyder, and Hoppe Proceedings of the Eurographics/ACM SIGGRAPH Symposium on Geometry Processing. pp. 146155. 2003. We introduce multichart geometry
images, a new representation for
arbitrary surfaces. It is created by resampling a surface onto a
regular 2D grid. Whereas the original scheme of Gu et al. maps the
entire surface onto a single square, we use an atlas construction to
map the surface piecewise onto charts of arbitrary shape. We
demonstrate that this added flexibility reduces parametrization
distortion and thus provides greater geometric fidelity, particularly
for shapes with long extremities, high genus, or disconnected
components. Traditional atlas constructions suffer from discontinuous
reconstruction across chart boundaries, which in our context create
unacceptable surface cracks. Our solution is a novel zippering
algorithm that creates a watertight surface. In addition, we present a
new atlas chartification scheme based on clustering optimization.

October 26 Matthew Bolitho 
Smooth
Geometry Images Losasso, Hoppe, Schaefer, and Warren Proceedings of the Eurographics/ACM SIGGRAPH Symposium on Geometry Processing. pp. 138145. 2003. Previous parametric
representations of smooth genuszero surfaces
require a collection of abutting patches (e.g. plines, NURBS,
recursively subdivided polygons). We introduce a simple construction
for these surfaces using a single uniform bicubic Bspline. Due to its
tensorproduct structure, the spline control points are conveniently
stored as a geometry image with simple boundary symmetries. The bicubic
surface is evaluated using subdivision, and the regular structure of
the geometry image makes this computation ideally suited for graphics
hardware. Specifically, we let the fragment shader pipeline perform
subdivision by applying a sequence of masks (splitting, averaging,
limit, and tangent) uniformly to the geometry image. We then extend
this scheme to provide smooth levelofdetail transitions from a
subsampled base octahedron all the way to a finely subdivided, smooth
model. Finally, we show how the framework easily supports scalar
displacement mapping.

November 2 Pavan Piratla 
Global
conformal surface parameterization Xianfeng Gu and ShingTung Yau Proceedings of the Eurographics/ACM SIGGRAPH Symposium on Geometry Processing. pp. 127137. 2003. We solve the problem of computing global conformal parameterizations for surfaces with nontrivial topologies. The parameterization is global in the sense that it preserves the conformality everywhere except for a few points, and has no boundary of discontinuity. We analyze the structure of the space of all global conformal parameterizations of a given surface and find all possible solutions by constructing a basis of the underlying linear solution space. This space has a natural structure solely determined by the surface geometry, so our computing result is independent of connectivity, insensitive to resolution, and independent of the algorithms to discover it. Our algorithm is based on the properties of gradient fields of conformal maps, which are closedness, harmonity, conjugacy, duality and symmetry. These properties can be formulated by sparse linear systems, so the method is easy to implement and the entire process is automatic. We also introduce a novel topological modification method to improve the uniformity of the parameterization. Based on the global conformal parameterization of a surface, we can construct a conformal atlas and use it to build conformal geometry images which have very accurate reconstructed normals. 
November 9 Chris Niski 
Spherical
Parametrization and Remeshing Emil Praun and Hugues Hoppe ACM SIGGRAPH 2003, 340349. The traditional approach for
parametrizing a surface involves cutting it into charts and mapping
these piecewise onto a planar domain. We introduce a robust technique
for directly parametrizing a genuszero surface onto a spherical
domain. A key ingredient for making such a parametrization practical is
the minimization of a stretchbased measure, to reduce scaledistortion
and thereby prevent undersampling. Our second contribution is a scheme
for sampling the spherical domain using uniformly subdivided polyhedral
domains, namely the tetrahedron, octahedron, and cube. We show that
these particular semiregular samplings can be conveniently represented
as completely regular 2D grids, i.e. geometry images. Moreover, these
images have simple boundary extension rules that aid many processing
operations. Applications include geometry remeshing, levelofdetail,
morphing, compression, and smooth surface subdivision.

November 16 Ashley Fernandes 
Isocharts:
Stretchdriven Mesh Parameterization using
Spectral Analysis We describe a fully automatic
method, called isocharts, to create texture atlases on arbitrary
meshes. It is the first
to consider stretch not only when parameterizing charts, but also when forming charts. The output atlas bounds stretch by a userspecified constant, allowing the user to balance the number of charts against their stretch. Our approach combines two seemingly incompatible techniques: stretchminimizing parameterization, based on the surface integral of the trace of the local metric tensor; and the "isomap " or MDS (multidimensional scaling) parameterization, based on an eigenanalysis of the matrix of squared geodesic distances between pairs of mesh vertices. We show that only a few iterations of nonlinear stretch optimization need be applied to the MDS param eterization to obtain lowstretch atlases. The close relationship we discover between these two parameterizations also allows us to apply spectral clustering based on MDS to partition the mesh into charts having low stretch. We also novelly apply the graph cut algorithm in optimizing chart boundaries to further minimize stretch, follow sharp features, and avoid meandering. Overall, our algorithm creates texture atlases quickly, with fewer charts and lower stretch than previous methods, providing improvement in applications like geometric remeshing. We also describe an extension, signalspecialized atlas creation, to efficiently sample surface signals, and show for the first time that considering signal stretch in chart formation produces better texture maps.

November 23 Yuan Chen 
SignalSpecialized
Parameterization for Piecewise Linear Reconstruction Geetika Tewari, John Snyder, Pedro V. Sander, Steven J. Gortler, Hugues Hoppe Proceedings of the Eurographics/ACM SIGGRAPH Symposium on Geometry Processing. pp 5766. 2004. We
propose a metric for surface parameterization specialized to its signal
that can be used to create more efficient, highquality texture maps.
Derived from Taylor expansion of signal error, our metric predicts the
signal approximation error  the difference between the original
surface signal and its reconstruction from the sampled texture. Unlike
previous methods, our metric assumes piecewiselinear reconstruction,
and thus makes a good approximation to bilinear reconstruction employed
in graphics hardware. We achieve significant savings in texture area
for a desired signal accuracy compared to the signalspecialized
parameterization metric proposed by Sander et al. in the 2002
Eurographics Workshop on Rendering.

November 30 Jonathan Bilodeau 
Crossparameterization
and compatible remeshing of 3D models Kraevoy and Scheffer Proceedings of SIGGRAPH 2004. pp. 861869 Many geometry processing applications, such as morphing, shape blending, transfer of texture or material properties, and fitting template meshes to scan data, require a bijective mapping between two or more models. This mapping, or crossparameterization, typically needs to preserve the shape and features of the parameterized models, mapping legs to legs, ears to ears, and so on. Most of the applications also require the models to be represented by compatible meshes, i.e. meshes with identical connectivity, based on the crossparameterization. In this paper we introduce novel methods for shape preserving crossparameterization and compatible remeshing. Our crossparameterization method computes a lowdistortion bijective mapping between models that satisfies user prescribed constraints. Using this mapping, the remeshing algorithm preserves the userdefined feature vertex correspondence and the shape correlation between the models. The remeshing algorithm generates output meshes with significantly fewer elements compared to previous techniques, while accurately approximating the input geometry. As demonstrated by the examples, the compatible meshes we construct are ideally suitable for morphing and other geometry processing applications. 
December 7 Nat Duca 
Interpolating
and Approximating Implicit Surfaces From Polygon Soup Chen Shen, James F. OBrien, and Jonathan R. Shewchuk ACM SIGGRAPH 2004 This paper describes a method for
building interpolating or approximating implicit surfaces from
polygonal data. The user can choose to generate a surface that exactly
interpolates the polygons, or a surface that approximates the input by
smoothing away features smaller than some userspecified size. The
implicit functions are represented using a moving leastsquares
formulation with constraints integrated over the polygons. The paper
also presents an improved method for enforcing normal constraints and
an iterative procedure for ensuring that the implicit surface tightly
encloses the input vertices.
