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Veltkamp R.C. — Closed Object Boundaries From Scattered Points
Veltkamp R.C. — Closed Object Boundaries From Scattered Points

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Название: Closed Object Boundaries From Scattered Points

Автор: Veltkamp R.C.

Аннотация:

This monograph is devoted to computational morphology, particularly to the construction of a two-dimensional or a three-dimensional closed object boundary through a set of points in arbitrary position.
By applying techniques from computational geometry and CAGD, new results are developed in four stages of the construction process: (a) the gamma-neighborhood graph for describing the structure of a set of points; (b) an algorithm for constructing a polygonal or polyhedral boundary (based on (a)); (c) the flintstone scheme as a hierarchy for polygonal and polyhedral approximation and localization; (d) and a Bezier-triangle based scheme for the construction of a smooth piecewise cubic boundary.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 144

Добавлена в каталог: 14.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$G^{1}$-continuity      97 109 110 119 127
$L_{2}$-distance      6
$N_{e}$      6
$N_{t}$      6
$N_{v}$      6
$\alpha$-Hull      17 43
$\alpha$-shape      17
$\beta$-skeleton      18
$\beta$-Skeleton, circle-based ($\beta_{c}$)      18 25 26
$\beta$-Skeleton, lune-based ($\beta_{l}$)      18 27
$\gamma$-graph      24 26
$\gamma$-graph, augmented      60
$\gamma$-graph, pruned      45 62
$\gamma$-graph, weighted      36
$\gamma$-indicator      47 50
$\gamma(c_{0},c_{1})$ neighborhood graph      24
$\gamma([c_{0},c_{1}],[c_{2},c_{3}])$ neighborhood graph      26
$\mathcal{O}$-notation      7
$\omega$-notation      7
$\pm$-operator      74 82
$\Theta$-notation      7
2D      6
3D      6
3D iterative extreme point fit      69
Adaptive approximation      79 87
Adjacent      9
Approximation      3 63
Approximation, adaptive      79 87
Approximation, flintstone      76 82
Approximation, optimal      67
Arc-tree      68 91
Augmented $\gamma$-graph      60
Ball      11
Ball, generalized      17
Ball, with signed radius      82
Barycentric coordinates      101
Bernstein polynomial      97 101
Bezier curve      97
Bezier ordinate      102
Bezier scheme      5 91 97 102
Bezier triangle      102
Blackbird      14
Blending function      94
BLG-tree      68
Boundary      6 38
Boundary construction problem      38 39
Boundary of a graph      45
Boundary polygon      46
Boundary polyhedron      49
Boundary segment      6
Boundary tetrahedron      49
Boundary triangle      46
Boundary, smooth      5 93
Boundary-based      65 67
Closest Pair (CP)      12
Clustering      43
Complete graph      9 45
Computational geometry      1
Computational Morphology      2 43 44
Computer Aided Geometric Design (CAGD)      1 2 5
Connected      10
Connected, n-connected      10 52
Constriction of $\gamma$-graph      45 58
Constriction, constrained      60
Constriction, minimal area change      42 58
Continuity, geometric      96 97 100 101
Continuity, parametric      96 99
Continuity, visual      96
contour      43
Control point      94 102
Control polyhedron      102
Convex Hull (CH)      14 27 39 41 45 51
Covering      66 79 87
Curvature, normal curvature vector      97 101
Curvature, principal      101
Curvature, scalar curvature      97
CYCLE      10
Cycle, Hamilton      10
Delaunay neighborhood      16 46 50
Delaunay pyramid      69 91
Delaunay tree      71
Delaunay Triangulation (DT)      15 39 42 71
Delaunay Triangulation (DT), closest point      15
Delaunay Triangulation (DT), degenerate      15 26
Delaunay Triangulation (DT), furthest point      15
Derivative vector      94
Derivative, directional      99 103
Derivative, partial      99
Disc      11
Disc, smallest bounding disc (SBD)      76
Disc, with signed radius      74
Dual      15
EDGE      9
Euclidean Minimum Spanning Tree (EMST)      12 39 45
Euler's formula      11
External structure      19 27
Face      10
Flintstone      75 77 82
Flintstone scheme      72
Flintstone tree      77 78 86
Flintstone, approximation      76 82
Flintstone, width      79 89
Forest      10
Gabriel Graph (GG)      14 18 25
Geometric continuity      96 100 101
Geometric graph      3 10
Graph      9
Graph, complete      9 18 24 25
Graph, empty      9 18 24 25
Graph, geometric      3 10
Graph, hyper-graph      10
Graph, neighborhood graph      11
Graph, spanning      9
Graph, subgraph      9
Hamilton cycle      10 38
Hamilton polygon      38 42 52
Hamilton polyhedron      39 52
Hierarchy      4 64
Hyper-graph      10 11
Infinite Strip Graph ($\infty$-SG)      12 18
Internal structure      19 26
INTRINSIC      65 67
Iterative end point fit      68
L-subdivision      15
Least-squares fit      111 116
localization      4 64 74 82
Macro triangle      116
Mathematical morphology      44
Micro triangle      116
Minimal area change constriction      41 58
Minimal area polyhedron      41
Nearest Neighbors Graph (NNG)      12 39
Neighborhood      11
Neighborhood, $\beta_{c}$      18
Neighborhood, $\beta_{l}$      18
Neighborhood, $\gamma$      24
Neighborhood, Delaunay      16
Neighborhood, empty      11
Neighborhood, Gabriel      14
Neighborhood, graph      11
Neighborhood, relative      13
Neighbors      9
Normal curvature      101
Normal curvature vector      97
Normal vector      101
Octree      71
P-interpolation      110
Parametric continuity      95 96 99
Partial derivative      99
Patch      99
Patch, Bezier      102
Patch, degenerate      104
Path      9
Path, shortest      82
PD-interpolation      110
piecewise      94 95 99 107
PN-interpolation      110
Polygon      10
Polygon, closed      10 73
Polygon, control      97
Polygon, Hamilton      38 42 43 46 52
Polygon, simple      10 46 91
Polyhedron of minimal area      41
Polyhedron, closed      10 81
Polyhedron, control      102
Polyhedron, Hamilton      39 52
Polyhedron, open      10 82
Polyhedron, simple      10 49 91
POLYLINE      10
Power basis      94
Principal curvature      101
prism      70
Prism tree      70
Pruned $\gamma$-graph      45 62
PT-interpolation      110
Quadtree      71
Reflection line      104 128
Regular parameterization      94 96 99 100
Relative Neighborhood Graph (RNG)      13 18
Removable edge      46
Removable triangle      49
Reparameterization      94 96 100
Scalar curvature      97
Scattered data points      2 5 102 109 117
Selection rule      49 52
simplex      11
Sine rule      49 50
Singularity      99
Skeleton      43 62
Smooth boundary      4 93
spanning      9 12
Specular reflection      105
Sphere decomposition      71
Sphere of Influence Graph (SIG)      13
SPLINE      95 99
Split, Clough-Tocher      116
Split, flintstone scheme      83
Split, six-split      124
Split, three-split      116 117
Split, two-split      121
stereo      31 38
Stochastic geometry      1 36
Strip      66 68
Strip tree      68 91
Subgraph      9
Surface-based      44
Tangent line      97
Tangent line, continuity      5 97 109
Tangent plane      101
Tangent plane, continuity      5 104 110 118 119 126
Tangent plane, orientation      103 110 115
Tangent vector      97 110
Total degree      98
TREE      10
Triangulation growth      40
Vertex      9
Visual continuity      97 107
Volume-based      44
Voronoi Diagram (VD)      15 43
Voronoi Diagram (VD), closest point      15
Voronoi Diagram (VD), furthest point      15
Voronoi Skeleton      43 58
Voronoi tree      43
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