1,138 research outputs found
3D mesh metamorphosis from spherical parameterization for conceptual design
Engineering product design is an information intensive decision-making
process that consists of several phases including design specification
definition, design concepts generation, detailed design and analysis,
and manufacturing. Usually, generating geometry models for
visualization is a big challenge for early stage conceptual design.
Complexity of existing computer aided design packages constrains
participation of people with various backgrounds in the design
process. In addition, many design processes do not take advantage of
the rich amount of legacy information available for new concepts
creation.
The research presented here explores the use of advanced graphical
techniques to quickly and efficiently merge legacy information with
new design concepts to rapidly create new conceptual product designs.
3D mesh metamorphosis framework 3DMeshMorpher was created to
construct new models by navigating in a shape-space of registered
design models. The framework is composed of: i) a fast spherical
parameterization method to map a geometric model (genus-0) onto a unit
sphere; ii) a geometric feature identification and picking technique
based on 3D skeleton extraction; and iii) a LOD controllable 3D
remeshing scheme with spherical mesh subdivision based on the
developedspherical parameterization. This efficient software framework
enables designers to create numerous geometric concepts in real time
with a simple graphical user interface.
The spherical parameterization method is focused on closed genus-zero
meshes. It is based upon barycentric coordinates with convex boundary.
Unlike most existing similar approaches which deal with each vertex in
the mesh equally, the method developed in this research focuses
primarily on resolving overlapping areas, which helps speed the
parameterization process. The algorithm starts by normalizing the
source mesh onto a unit sphere and followed by some initial relaxation
via Gauss-Seidel iterations. Due to its emphasis on solving only
challenging overlapping regions, this parameterization process is much
faster than existing spherical mapping methods.
To ensure the correspondence of features from different models, we
introduce a skeleton based feature identification and picking method
for features alignment. Unlike traditional methods that align single
point for each feature, this method can provide alignments for
complete feature areas. This could help users to create more
reasonable intermediate morphing results with preserved topological
features. This skeleton featuring framework could potentially be
extended to automatic features alignment for geometries with similar
topologies. The skeleton extracted could also be applied for other
applications such as skeleton-based animations.
The 3D remeshing algorithm with spherical mesh subdivision is
developed to generate a common connectivity for different mesh models.
This method is derived from the concept of spherical mesh subdivision.
The local recursive subdivision can be set to match the desired LOD
(level of details) for source spherical mesh. Such LOD is controllable
and this allows various outputs with different resolutions. Such
recursive subdivision then follows by a triangular correction process
which ensures valid triangulations for the remeshing. And the final
mesh merging and reconstruction process produces the remeshing model
with desired LOD specified from user. Usually the final merged model
contains all the geometric details from each model with reasonable
amount of vertices, unlike other existing methods that result in big
amount of vertices in the merged model. Such multi-resolution outputs
with controllable LOD could also be applied in various other computer
graphics applications such as computer games
Surface parameterization over regular domains
Surface parameterization has been widely studied and it has been playing a critical role in many geometric processing tasks in graphics, computer-aided design, visualization, vision, physical simulation and etc. Regular domains, such as polycubes, are favored due to their structural regularity and geometric simplicity. This thesis focuses on studying the surface parameterization over regular domains, i.e. polycubes, and develops effective computation algorithms. Firstly, the motivation for surface parameterization and polycube mapping is introduced. Secondly, we briefly review existing surface parameterization techniques, especially for extensively studied parameterization algorithms for topological disk surfaces and parameterizations over regular domains for closed surfaces. Then we propose a polycube parameterization algorithm for closed surfaces with general topology. We develop an efficient optimization framework to minimize the angle and area distortion of the mapping. Its applications on surface meshing, inter-shape morphing and volumetric polycube mapping are also discussed
Assessing the Predictability of Convection Initiation Using an Object-Based Approach
Improvements in numerical forecasts of deep, moist convection have been notable in recent years and are in large part due to increased computational power allowing for the explicit numerical representation of convection. Accurately forecasting the timing and location of convection initiation (CI), however, remains a substantial forecast challenge. This is attributed to the inherently limited intrinsic predictability of CI due to its dependence on highly non-linear moist physics and fine-scale atmospheric processes that are poorly represented in observations. Because CI is the starting point of deep, moist convection that grows upscale, even small errors in initial convective development can rapidly spread to larger scales, having potentially significant impacts on downstream forecasts. This study investigates the practical predictability of CI using the Advanced Research Weather Research and Forecasting (WRF-ARW) model with a horizontal grid spacing of 429 meters. A unique object-based method is used to evaluate very high-resolution model performance for twenty-five cases of CI across the west-central High Plains of the United States from the 2010 convective season. CI objects are defined as areas of higher observed or model simulated radar reflectivity that develop and remain sustained for a sufficient period of time. Model simulations demonstrate an average probability of detection of 0.835, but due to significant overproduction of CI, an average false alarm ratio of 0.664 and bias ratio of 2.49. The average critical success index through all simulations is 0.315. Model CI objects that are matched with observed CI objects show, on average, an early bias of about 7 minutes and distance errors of around 62 kilometers. The operational utility and inherent biases of such high-resolution simulations are discussed
Multi-directional Geodesic Neural Networks via Equivariant Convolution
We propose a novel approach for performing convolution of signals on curved
surfaces and show its utility in a variety of geometric deep learning
applications. Key to our construction is the notion of directional functions
defined on the surface, which extend the classic real-valued signals and which
can be naturally convolved with with real-valued template functions. As a
result, rather than trying to fix a canonical orientation or only keeping the
maximal response across all alignments of a 2D template at every point of the
surface, as done in previous works, we show how information across all
rotations can be kept across different layers of the neural network. Our
construction, which we call multi-directional geodesic convolution, or
directional convolution for short, allows, in particular, to propagate and
relate directional information across layers and thus different regions on the
shape. We first define directional convolution in the continuous setting, prove
its key properties and then show how it can be implemented in practice, for
shapes represented as triangle meshes. We evaluate directional convolution in a
wide variety of learning scenarios ranging from classification of signals on
surfaces, to shape segmentation and shape matching, where we show a significant
improvement over several baselines
Recommended from our members
Mathematical Imaging and Surface Processing
Within the last decade image and geometry processing have become increasingly rigorous with solid foundations in mathematics. Both areas are research fields at the intersection of different mathematical disciplines, ranging from geometry and calculus of variations to PDE analysis and numerical analysis. The workshop brought together scientists from all these areas and a fruitful interplay took place. There was a lively exchange of ideas between geometry and image processing applications areas, characterized in a number of ways in this workshop. For example, optimal transport, first applied in computer vision is now used to define a distance measure between 3d shapes, spectral analysis as a tool in image processing can be applied in surface classification and matching, and so on. We have also seen the use of Riemannian geometry as a powerful tool to improve the analysis of multivalued images.
This volume collects the abstracts for all the presentations covering this wide spectrum of tools and application domains
2D and 3D surface image processing algorithms and their applications
This doctoral dissertation work aims to develop algorithms for 2D image segmentation application of solar filament disappearance detection, 3D mesh simplification, and 3D image warping in pre-surgery simulation. Filament area detection in solar images is an image segmentation problem. A thresholding and region growing combined method is proposed and applied in this application. Based on the filament area detection results, filament disappearances are reported in real time. The solar images in 1999 are processed with this proposed system and three statistical results of filaments are presented.
3D images can be obtained by passive and active range sensing. An image registration process finds the transformation between each pair of range views. To model an object, a common reference frame in which all views can be transformed must be defined. After the registration, the range views should be integrated into a non-redundant model. Optimization is necessary to obtain a complete 3D model. One single surface representation can better fit to the data. It may be further simplified for rendering, storing and transmitting efficiently, or the representation can be converted to some other formats.
This work proposes an efficient algorithm for solving the mesh simplification problem, approximating an arbitrary mesh by a simplified mesh. The algorithm uses Root Mean Square distance error metric to decide the facet curvature. Two vertices of one edge and the surrounding vertices decide the average plane. The simplification results are excellent and the computation speed is fast. The algorithm is compared with six other major simplification algorithms.
Image morphing is used for all methods that gradually and continuously deform a source image into a target image, while producing the in-between models. Image warping is a continuous deformation of a: graphical object. A morphing process is usually composed of warping and interpolation. This work develops a direct-manipulation-of-free-form-deformation-based method and application for pre-surgical planning. The developed user interface provides a friendly interactive tool in the plastic surgery. Nose augmentation surgery is presented as an example. Displacement vector and lattices resulting in different resolution are used to obtain various deformation results. During the deformation, the volume change of the model is also considered based on a simplified skin-muscle model
- …