203 research outputs found
Free-boundary conformal parameterization of point clouds
With the advancement in 3D scanning technology, there has been a surge of
interest in the use of point clouds in science and engineering. To facilitate
the computations and analyses of point clouds, prior works have considered
parameterizing them onto some simple planar domains with a fixed boundary shape
such as a unit circle or a rectangle. However, the geometry of the fixed shape
may lead to some undesirable distortion in the parameterization. It is
therefore more natural to consider free-boundary conformal parameterizations of
point clouds, which minimize the local geometric distortion of the mapping
without constraining the overall shape. In this work, we develop a
free-boundary conformal parameterization method for disk-type point clouds,
which involves a novel approximation scheme of the point cloud Laplacian with
accumulated cotangent weights together with a special treatment at the boundary
points. With the aid of the free-boundary conformal parameterization,
high-quality point cloud meshing can be easily achieved. Furthermore, we show
that using the idea of conformal welding in complex analysis, the point cloud
conformal parameterization can be computed in a divide-and-conquer manner.
Experimental results are presented to demonstrate the effectiveness of the
proposed method
Interactive Geometry Remeshing
We present a novel technique, both flexible and efficient, for interactive remeshing of irregular geometry. First, the original (arbitrary genus) mesh is substituted by a series of 2D maps in parameter space. Using these maps, our algorithm is then able to take advantage of established signal processing and halftoning tools that offer
real-time interaction and intricate control. The user can easily combine these maps to create a control map – a map which controls the sampling density over the surface patch. This map is then sampled at interactive rates allowing the user to easily design a tailored resampling.
Once this sampling is complete, a Delaunay triangulation
and fast optimization are performed to perfect the final mesh.
As a result, our remeshing technique is extremely versatile and general, being able to produce arbitrarily complex meshes with a variety of properties including: uniformity, regularity, semiregularity, curvature sensitive resampling, and feature preservation. We provide a high level of control over the sampling distribution allowing the user to interactively custom design the mesh based on
their requirements thereby increasing their productivity in creating a wide variety of meshes
Density-equalizing maps for simply-connected open surfaces
In this paper, we are concerned with the problem of creating flattening maps
of simply-connected open surfaces in . Using a natural principle
of density diffusion in physics, we propose an effective algorithm for
computing density-equalizing flattening maps with any prescribed density
distribution. By varying the initial density distribution, a large variety of
mappings with different properties can be achieved. For instance,
area-preserving parameterizations of simply-connected open surfaces can be
easily computed. Experimental results are presented to demonstrate the
effectiveness of our proposed method. Applications to data visualization and
surface remeshing are explored
Constrained Texture Mapping And Foldover-free Condition
Texture mapping has been widely used in image
processing and graphics to enhance the realism of CG scenes.
However to perfectly match the feature points of a 3D model
with the corresponding pixels in texture images, the
parameterisation which maps a 3D mesh to the texture space
must satisfy the positional constraints. Despite numerous
research efforts, the construction of a mathematically robust
foldover-free parameterisation subject to internal constraints
is still a remaining issue. In this paper, we address this
challenge by developing a two-step parameterisation method.
First, we produce an initial parameterisation with a method
traditionally used to solve structural engineering problems,
called the bar-network. We then derive a mathematical
foldover-free condition, which is incorporated into a Radial
Basis Function based scheme. This method is therefore able to
guarantee that the resulting parameterization meets the hard
constraints without foldovers
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