2,983 research outputs found
Surface Mesh Generation based on Imprinting of S-T Edge Patches
AbstractOne of the most robust and widely used algorithms for all-hexahedral meshes is the sweeping algorithm. However, for multi- sweeping, the most difficult problems are the surface matching and interval assignment for edges on the source and target surfaces. In this paper, a new method to generate surface meshes by imprinting edge patches between the source and target surfaces is proposed. The edge patch imprinting is based on a cage-based morphing of edge patches on the different sweeping layers where deformed and undeformed cages are extracted by propagating edge patches on the linking surfaces. The imprinting results in that the source or target surfaces will be partitioned with the imprinted edge patches. After partitioning, every new source surface should be matched to a new specific target surface where surface mesh projection from one-to-one sweeping based on harmonic mapping[19] can be applied. In addition, 3D edge patches are projected onto 2D computational domains where every sweeping level is planar in order to increase the robustness of imprinting. Finally, the algorithm time complexity is discussed and examples are provided to verify the robustness of our proposed algorithm
Doctor of Philosophy
dissertationVolumetric parameterization is an emerging field in computer graphics, where volumetric representations that have a semi-regular tensor-product structure are desired in applications such as three-dimensional (3D) texture mapping and physically-based simulation. At the same time, volumetric parameterization is also needed in the Isogeometric Analysis (IA) paradigm, which uses the same parametric space for representing geometry, simulation attributes and solutions. One of the main advantages of the IA framework is that the user gets feedback directly as attributes of the NURBS model representation, which can represent geometry exactly, avoiding both the need to generate a finite element mesh and the need to reverse engineer the simulation results from the finite element mesh back into the model. Research in this area has largely been concerned with issues of the quality of the analysis and simulation results assuming the existence of a high quality volumetric NURBS model that is appropriate for simulation. However, there are currently no generally applicable approaches to generating such a model or visualizing the higher order smooth isosurfaces of the simulation attributes, either as a part of current Computer Aided Design or Reverse Engineering systems and methodologies. Furthermore, even though the mesh generation pipeline is circumvented in the concept of IA, the quality of the model still significantly influences the analysis result. This work presents a pipeline to create, analyze and visualize NURBS geometries. Based on the concept of analysis-aware modeling, this work focusses in particular on methodologies to decompose a volumetric domain into simpler pieces based on appropriate midstructures by respecting other relevant interior material attributes. The domain is decomposed such that a tensor-product style parameterization can be established on the subvolumes, where the parameterization matches along subvolume boundaries. The volumetric parameterization is optimized using gradient-based nonlinear optimization algorithms and datafitting methods are introduced to fit trivariate B-splines to the parameterized subvolumes with guaranteed order of accuracy. Then, a visualization method is proposed allowing to directly inspect isosurfaces of attributes, such as the results of analysis, embedded in the NURBS geometry. Finally, the various methodologies proposed in this work are demonstrated on complex representations arising in practice and research
Geometric and photometric affine invariant image registration
This thesis aims to present a solution to the correspondence problem for the registration
of wide-baseline images taken from uncalibrated cameras. We propose an affine
invariant descriptor that combines the geometry and photometry of the scene to find
correspondences between both views. The geometric affine invariant component of the
descriptor is based on the affine arc-length metric, whereas the photometry is analysed
by invariant colour moments. A graph structure represents the spatial distribution of the
primitive features; i.e. nodes correspond to detected high-curvature points, whereas arcs
represent connectivities by extracted contours. After matching, we refine the search for
correspondences by using a maximum likelihood robust algorithm. We have evaluated
the system over synthetic and real data. The method is endemic to propagation of errors
introduced by approximations in the system.BAE SystemsSelex Sensors and Airborne System
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Sliceforms: Deployable structures from interlocking slices
A sliceform is a volumetric, honeycomb-like structure assembled from an array of cross-sectional planar slices that are interlocked via pairs of complementary slots placed along each intersection. If the slices are thin, these slotted intersections function as revolute joints, and the sliceform is foldable if the geometry of the embedded spatial linkage permits it, for example a lattice sliceform (LS) is bi-directionally flat-foldable. This thesis concerns a study of such sliceforms toward the design of novel deployable structures.
A sliceform torus, composed of two sets of inclined slices arranged at regular intervals about a central axis of symmetry, has been discovered to exhibit a surprising and intriguing folding action whereby its incomplete form can be collapsed to a flat-folded stack of coplanar slices. On deployment, the assembly expands smoothly about an arc until the slices have rotated to their design inclination, then, without reaching any apparent physical limit, abruptly โlocks outโ. With a full complement of slices, the outermost intersections can be interlocked to complete and rigidify the ring. The torus is an example of a rotational sliceform (RS), and analysis of these structures proceeds by noting that their structural geometry comprises an array of pyramidal cells that is commensurate to a spherical scissor grid. The conditions for flat-foldability are determined by examination of the intrinsic geometry of each cell; the incompatibility of the slices with apparent rigid-folding revealed by assessment of the extrinsic motion of the slices. Investigation of their compliant kinematics reveals the articulation to be a bistable transition admitted by small transverse deflections of the slices.
This structural form is generalised by development of a technique for generating sliceforms along a smooth spatial curve โ curve sliceforms (CS). Their synthesis is more involved than for an RS, but a range of sliceform โtubesโ are generated and manufactured. Each example retains the flat-foldable, deployable characteristic of an RS, despite the apparent intrinsic rigidity of each constituent skew cell. Examination of the small-scale models indicates that deployable motion is achieved via imperfect action of the slots, and a simple model of the articulation of a single cell is constructed to investigate how this proceeds, verifying that motion is kinematically admissible via local deformations
Doctor of Philosophy
dissertationThe medial axis of an object is a shape descriptor that intuitively presents the morphology or structure of the object as well as intrinsic geometric properties of the objectรขโฌโขs shape. These properties have made the medial axis a vital ingredient for shape analysis applications, and therefore the computation of which is a fundamental problem in computational geometry. This dissertation presents new methods for accurately computing the 2D medial axis of planar objects bounded by B-spline curves, and the 3D medial axis of objects bounded by B-spline surfaces. The proposed methods for the 3D case are the first techniques that automatically compute the complete medial axis along with its topological structure directly from smooth boundary representations. Our approach is based on the eikonal (grassfire) flow where the boundary is offset along the inward normal direction. As the boundary deforms, different regions start intersecting with each other to create the medial axis. In the generic situation, the (self-) intersection set is born at certain creation-type transition points, then grows and undergoes intermediate transitions at special isolated points, and finally ends at annihilation-type transition points. The intersection set evolves smoothly in between transition points. Our approach first computes and classifies all types of transition points. The medial axis is then computed as a time trace of the evolving intersection set of the boundary using theoretically derived evolution vector fields. This dynamic approach enables accurate tracking of elements of the medial axis as they evolve and thus also enables computation of topological structure of the solution. Accurate computation of geometry and topology of 3D medial axes enables a new graph-theoretic method for shape analysis of objects represented with B-spline surfaces. Structural components are computed via the cycle basis of the graph representing the 1-complex of a 3D medial axis. This enables medial axis based surface segmentation, and structure based surface region selection and modification. We also present a new approach for structural analysis of 3D objects based on scalar functions defined on their surfaces. This approach is enabled by accurate computation of geometry and structure of 2D medial axes of level sets of the scalar functions. Edge curves of the 3D medial axis correspond to a subset of ridges on the bounding surfaces. Ridges are extremal curves of principal curvatures on a surface indicating salient intrinsic features of its shape, and hence are of particular interest as tools for shape analysis. This dissertation presents a new algorithm for accurately extracting all ridges directly from B-spline surfaces. The proposed technique is also extended to accurately extract ridges from isosurfaces of volumetric data using smooth implicit B-spline representations. Accurate ridge curves enable new higher-order methods for surface analysis. We present a new definition of salient regions in order to capture geometrically significant surface regions in the neighborhood of ridges as well as to identify salient segments of ridges
AUTOMATIC IMAGE TO MODEL ALIGNMENT FOR PHOTO-REALISTIC URBAN MODEL RECONSTRUCTION
We introduce a hybrid approach in which images of an urban scene are automatically alignedwith a base geometry of the scene to determine model-relative external camera parameters. Thealgorithm takes as input a model of the scene and images with approximate external cameraparameters and aligns the images to the model by extracting the facades from the images andaligning the facades with the model by minimizing over a multivariate objective function. Theresulting image-pose pairs can be used to render photo-realistic views of the model via texturemapping.Several natural extensions to the base hybrid reconstruction technique are also introduced. Theseextensions, which include vanishing point based calibration refinement and video stream basedreconstruction, increase the accuracy of the base algorithm, reduce the amount of data that mustbe provided by the user as input to the algorithm, and provide a mechanism for automaticallycalibrating a large set of images for post processing steps such as automatic model enhancementand fly-through model visualization.Traditionally, photo-realistic urban reconstruction has been approached from purely image-basedor model-based approaches. Recently, research has been conducted on hybrid approaches, whichcombine the use of images and models. Such approaches typically require user assistance forcamera calibration. Our approach is an improvement over these methods because it does notrequire user assistance for camera calibration
์คํ์ ๊ณก์ ๋ฐ ๊ณก๋ฉด์ ์๊ฐ ๊ต์ฐจ ๊ฒ์ถ ๋ฐ ์ ๊ฑฐ
ํ์๋
ผ๋ฌธ(๋ฐ์ฌ)--์์ธ๋ํ๊ต ๋ํ์ :๊ณต๊ณผ๋ํ ์ปดํจํฐ๊ณตํ๋ถ,2020. 2. ๊น๋ช
์.Offset curves and surfaces have many applications in computer-aided design and manufacturing, but the self-intersections and redundancies must be trimmed away for their practical use.
We present a new method for offset curve and surface trimming that detects the self-intersections and eliminates the redundant parts of an offset curve and surface that are closer than the offset distance to the original curve and surface.
We first propose an offset trimming method based on constructing geometric constraint equations.
We formulate the constraint equations of the self-intersections of an offset curve and surface in the parameter domain of the original curve and surface.
Numerical computations based on the regularity and intrinsic properties of the given input curve and surface is carried out to compute the solution of the constraint equations.
The method deals with numerical instability around near-singular regions of an offset surface by using osculating tori that can be constructed in a highly stable way, i.e., by offsetting the osculating torii of the given input regular surface.
We reveal the branching structure and the terminal points from the complete self-intersection curves of the offset surface.
From the observation that the trimming method based on the multivariate equation solving is computationally expensive, we also propose an acceleration technique to trim an offset curve and surface.
The alternative method constructs a bounding volume hierarchy specially designed to enclose the offset curve and surface and detects the self-collision of the bounding volumes instead.
In the case of an offset surface, the thickness of the bounding volumes is indirectly determined based on the maximum deviations of the positions and the normals between the given input surface patches and their osculating tori.
For further acceleration, the bounding volumes are pruned as much as possible during self-collision detection using various geometric constraints imposed on the offset surface.
We demonstrate the effectiveness of the new trimming method using several non-trivial test examples of offset trimming.
Lastly, we investigate the problem of computing the Voronoi diagram of a freeform surface using the offset trimming technique for surfaces.
By trimming the offset surface with a gradually changing offset radius, we compute the boundary of the Voronoi cells that appear in the concave side of the given input surface.
In particular, we interpret the singular and branching points of the self-intersection curves of the trimmed offset surfaces in terms of the boundary elements of the Voronoi diagram.์คํ์
๊ณก์ ๋ฐ ๊ณก๋ฉด์ computer-aided design (CAD)์ computer-aided manufacturing (CAM)์์ ๋๋ฆฌ ์ด์ฉ๋๋ ์ฐ์ฐ๋ค ์ค ํ๋์ด๋ค.
ํ์ง๋ง ์ค์ฉ์ ์ธ ํ์ฉ์ ์ํด์๋ ์คํ์
๊ณก์ ๋ฐ ๊ณก๋ฉด์์ ์๊ธฐ๋ ์๊ฐ ๊ต์ฐจ๋ฅผ ์ฐพ๊ณ ์ด๋ฅผ ๊ธฐ์ค์ผ๋ก ์คํ์
๊ณก์ ๋ฐ ๊ณก๋ฉด์์ ์๋์ ๊ณก์ ๋ฐ ๊ณก๋ฉด์ ๊ฐ๊น์ด ๋ถํ์ํ ์์ญ์ ์ ๊ฑฐํ์ฌ์ผํ๋ค.
๋ณธ ๋
ผ๋ฌธ์์๋ ์คํ์
๊ณก์ ๋ฐ ๊ณก๋ฉด์์ ์๊ธฐ๋ ์๊ฐ ๊ต์ฐจ๋ฅผ ๊ณ์ฐํ๊ณ , ์คํ์
๊ณก์ ๋ฐ ๊ณก๋ฉด์์ ์๊ธฐ๋ ๋ถํ์ํ ์์ญ์ ์ ๊ฑฐํ๋ ์๊ณ ๋ฆฌ์ฆ์ ์ ์ํ๋ค.
๋ณธ ๋
ผ๋ฌธ์ ์ฐ์ ์คํ์
๊ณก์ ๋ฐ ๊ณก๋ฉด์ ์๊ฐ ๊ต์ฐจ์ ๋ค๊ณผ ๊ทธ ๊ต์ฐจ์ ๋ค์ด ๊ธฐ์ธํ ์๋ ๊ณก์ ๋ฐ ๊ณก๋ฉด์ ์ ๋ค์ด ์ด๋ฃจ๋ ํ๋ฉด ์ด๋ฑ๋ณ ์ผ๊ฐํ ๊ด๊ณ๋ก๋ถํฐ ์คํ์
๊ณก์ ๋ฐ ๊ณก๋ฉด์ ์๊ฐ ๊ต์ฐจ์ ์ ์ ์ฝ ์กฐ๊ฑด์ ๋ง์กฑ์ํค๋ ๋ฐฉ์ ์๋ค์ ์ธ์ด๋ค.
์ด ์ ์ฝ์๋ค์ ์๋ ๊ณก์ ๋ฐ ๊ณก๋ฉด์ ๋ณ์ ๊ณต๊ฐ์์ ํํ๋๋ฉฐ, ์ด ๋ฐฉ์ ์๋ค์ ํด๋ ๋ค๋ณ์ ๋ฐฉ์ ์์ ํด๋ฅผ ๊ตฌํ๋ solver๋ฅผ ์ด์ฉํ์ฌ ๊ตฌํ๋ค.
์คํ์
๊ณก๋ฉด์ ๊ฒฝ์ฐ, ์๋ ๊ณก๋ฉด์ ์ฃผ๊ณก๋ฅ ์ค ํ๋๊ฐ ์คํ์
๋ฐ์ง๋ฆ์ ์ญ์์ ๊ฐ์ ๋ ์คํ์
๊ณก๋ฉด์ ๋ฒ์ ์ด ์ ์๊ฐ ๋์ง ์๋ ํน์ด์ ์ด ์๊ธฐ๋๋ฐ,
์คํ์
๊ณก๋ฉด์ ์๊ฐ ๊ต์ฐจ ๊ณก์ ์ด ์ด ๋ถ๊ทผ์ ์ง๋ ๋๋ ์๊ฐ ๊ต์ฐจ ๊ณก์ ์ ๊ณ์ฐ์ด ๋ถ์์ ํด์ง๋ค.
๋ฐ๋ผ์ ์๊ฐ ๊ต์ฐจ ๊ณก์ ์ด ์คํ์
๊ณก๋ฉด์ ํน์ด์ ๋ถ๊ทผ์ ์ง๋ ๋๋ ์คํ์
๊ณก๋ฉด์ ์ ์ด ํ ๋ฌ์ค๋ก ์นํํ์ฌ ๋ ์์ ๋ ๋ฐฉ๋ฒ์ผ๋ก ์๊ฐ ๊ต์ฐจ ๊ณก์ ์ ๊ตฌํ๋ค.
๊ณ์ฐ๋ ์คํ์
๊ณก๋ฉด์ ์๊ฐ ๊ต์ฐจ ๊ณก์ ์ผ๋ก๋ถํฐ ๊ต์ฐจ ๊ณก์ ์ -๊ณต๊ฐ์์์ ๋ง๋จ ์ , ๊ฐ์ง ๊ตฌ์กฐ ๋ฑ์ ๋ฐํ๋ค.
๋ณธ ๋
ผ๋ฌธ์ ๋ํ ๋ฐ์ด๋ฉ ๋ณผ๋ฅจ ๊ธฐ๋ฐ์ ์คํ์
๊ณก์ ๋ฐ ๊ณก๋ฉด์ ์๊ฐ ๊ต์ฐจ ๊ณก์ ๊ฒ์ถ์ ๊ฐ์ํํ๋ ๋ฐฉ๋ฒ์ ์ ์ํ๋ค.
๋ฐ์ด๋ฉ ๋ณผ๋ฅจ์ ๊ธฐ์ ๊ณก์ ๋ฐ ๊ณก๋ฉด์ ๋จ์ํ ๊ธฐํ๋ก ๊ฐ์ธ๊ณ ๊ธฐํ ์ฐ์ฐ์ ์ํํจ์ผ๋ก์จ ๊ฐ์ํ์ ๊ธฐ์ฌํ๋ค.
์คํ์
๊ณก๋ฉด์ ์๊ฐ ๊ต์ฐจ ๊ณก์ ์ ๊ตฌํ๊ธฐ ์ํ์ฌ, ๋ณธ ๋
ผ๋ฌธ์ ์คํ์
๊ณก๋ฉด์ ๋ฐ์ด๋ฉ ๋ณผ๋ฅจ ๊ตฌ์กฐ๋ฅผ ๊ธฐ์ ๊ณก๋ฉด์ ๋ฐ์ด๋ฉ ๋ณผ๋ฅจ๊ณผ ๊ธฐ์ ๊ณก๋ฉด์ ๋ฒ์ ๊ณก๋ฉด์ ๋ฐ์ด๋ฉ ๋ณผ๋ฅจ์ ๊ตฌ์กฐ๋ก๋ถํฐ ๊ณ์ฐํ๋ฉฐ ์ด๋ ๊ฐ ๋ฐ์ด๋ฉ ๋ณผ๋ฅจ์ ๋๊ป๋ฅผ ๊ณ์ฐํ๋ค.
๋ํ, ๋ฐ์ด๋ฉ ๋ณผ๋ฅจ ์ค์์ ์ค์ ์คํ์
๊ณก์ ๋ฐ ๊ณก๋ฉด์ ์๊ฐ ๊ต์ฐจ์ ๊ธฐ์ฌํ์ง ์๋ ๋ถ๋ถ์ ๊น์ ์ฌ๊ท ์ ์ ์ฐพ์์ ์ ๊ฑฐํ๋ ์ฌ๋ฌ ์กฐ๊ฑด๋ค์ ๋์ดํ๋ค.
ํํธ, ์๊ฐ ๊ต์ฐจ๊ฐ ์ ๊ฑฐ๋ ์คํ์
๊ณก์ ๋ฐ ๊ณก๋ฉด์ ๊ธฐ์ ๊ณก์ ๋ฐ ๊ณก๋ฉด์ ๋ณด๋ก๋
ธ์ด ๊ตฌ์กฐ์ ๊น์ ๊ด๋ จ์ด ์๋ ๊ฒ์ด ์๋ ค์ ธ ์๋ค.
๋ณธ ๋
ผ๋ฌธ์์๋ ์์ ๊ณก๋ฉด์ ์ฐ์๋ ์คํ์
๊ณก๋ฉด๋ค๋ก๋ถํฐ ์์ ๊ณก๋ฉด์ ๋ณด๋ก๋
ธ์ด ๊ตฌ์กฐ๋ฅผ ์ ์ถํ๋ ๋ฐฉ๋ฒ์ ์ ์ํ๋ค.
ํนํ, ์คํ์
๊ณก๋ฉด์ ์๊ฐ ๊ต์ฐจ ๊ณก์ ์์์ ๋ํ๋๋ ๊ฐ์ง ์ ์ด๋ ๋ง๋จ ์ ๊ณผ ๊ฐ์ ํน์ด์ ๋ค์ด ์์ ๊ณก๋ฉด์ ๋ณด๋ก๋
ธ์ด ๊ตฌ์กฐ์์ ์ด๋ป๊ฒ ํด์๋๋์ง ์ ์ํ๋ค.1. Introduction 1
1.1 Background and Motivation 1
1.2 Research Objectives and Approach 7
1.3 Contributions and Thesis Organization 11
2. Preliminaries 14
2.1 Curve and Surface Representation 14
2.1.1 Bezier Representation 14
2.1.2 B-spline Representation 17
2.2 Differential Geometry of Curves and Surfaces 19
2.2.1 Differential Geometry of Curves 19
2.2.2 Differential Geometry of Surfaces 21
3. Previous Work 23
3.1 Offset Curves 24
3.2 Offset Surfaces 27
3.3 Offset Curves on Surfaces 29
4. Trimming Offset Curve Self-intersections 32
4.1 Experimental Results 35
5. Trimming Offset Surface Self-intersections 38
5.1 Constraint Equations for Offset Self-Intersections 38
5.1.1 Coplanarity Constraint 39
5.1.2 Equi-angle Constraint 40
5.2 Removing Trivial Solutions 40
5.3 Removing Normal Flips 41
5.4 Multivariate Solver for Constraints 43
5.A Derivation of f(u,v) 46
5.B Relationship between f(u,v) and Curvatures 47
5.3 Trimming Offset Surfaces 50
5.4 Experimental Results 53
5.5 Summary 57
6. Acceleration of trimming offset curves and surfaces 62
6.1 Motivation 62
6.2 Basic Approach 67
6.3 Trimming an Offset Curve using the BVH 70
6.4 Trimming an Offset Surface using the BVH 75
6.4.1 Offset Surface BVH 75
6.4.2 Finding Self-intersections in Offset Surface Using BVH 87
6.4.3 Tracing Self-intersection Curves 98
6.5 Experimental Results 100
6.6 Summary 106
7. Application of Trimming Offset Surfaces: 3D Voronoi Diagram 107
7.1 Background 107
7.2 Approach 110
7.3 Experimental Results 112
7.4 Summary 114
8. Conclusion 119
Bibliography iDocto
Efficient Point-Cloud Processing with Primitive Shapes
This thesis presents methods for efficient processing of point-clouds based on primitive shapes. The set of considered simple parametric shapes consists of planes, spheres, cylinders, cones and tori. The algorithms developed in this work are targeted at scenarios in which the occurring surfaces can be well represented by this set of shape primitives which is the case in many man-made environments such as e.g. industrial compounds, cities or building interiors. A primitive subsumes a set of corresponding points in the point-cloud and serves as a proxy for them. Therefore primitives are well suited to directly address the unavoidable oversampling of large point-clouds and lay the foundation for efficient point-cloud processing algorithms. The first contribution of this thesis is a novel shape primitive detection method that is efficient even on very large and noisy point-clouds. Several applications for the detected primitives are subsequently explored, resulting in a set of novel algorithms for primitive-based point-cloud processing in the areas of compression, recognition and completion. Each of these application directly exploits and benefits from one or more of the detected primitives' properties such as approximation, abstraction, segmentation and continuability
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