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Digital manifold

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Basically, a connected set of grid points M can be viewed as a digital k-manifold if: (1) any two k-cells are (k-1)-connected, (2) every (k-1)-cell has only one or two parallel-moves, and (3) M does not contain any (k+1)-cells.
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Parallel-move is used to extend an i-cell to (i+1)-cell. In other words, if A and B are two i-cells and A is a parallel-move of B, then {A,B} is an (i+1)-cell. Therefore, k-cells can be defined recursively.
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which is defined in digital space i.e. grid cell space. A combinatorial manifold is a kind of manifold which is a discretization of a manifold. It usually means a
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Proceedings on the second ACM symposium on Solid modeling and applications, Montreal, Quebec, Canada
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Chen, L.; Zhang, J. (1993). "Digital manifolds: an intuitive definition and some properties".
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Special kind of combinatorial manifold which is defined in grid cell space
142: 18: 164:. Association for Computing Machinery. pp. 459–460. 46:but its sources remain unclear because it lacks 8: 77:Learn how and when to remove this message 7: 14: 23: 1: 173:Digital and Discrete Geometry 211: 138:Topological data analysis 99:piecewise linear manifold 32:This article includes a 61:more precise citations. 95:combinatorial manifold 93:is a special kind of 148:Discrete mathematics 103:simplicial complexes 89:In mathematics, a 34:list of references 171:Chen, L. (2014). 87: 86: 79: 202: 195:Digital geometry 190:Digital topology 176: 165: 133:Digital topology 128:Digital geometry 91:digital manifold 82: 75: 71: 68: 62: 57:this article by 48:inline citations 27: 26: 19: 210: 209: 205: 204: 203: 201: 200: 199: 180: 179: 170: 159: 156: 124: 111: 83: 72: 66: 63: 52: 38:related reading 28: 24: 17: 12: 11: 5: 208: 206: 198: 197: 192: 182: 181: 178: 177: 167: 166: 155: 152: 151: 150: 145: 140: 135: 130: 123: 120: 110: 107: 85: 84: 42:external links 31: 29: 22: 15: 13: 10: 9: 6: 4: 3: 2: 207: 196: 193: 191: 188: 187: 185: 174: 169: 168: 163: 158: 157: 153: 149: 146: 144: 141: 139: 136: 134: 131: 129: 126: 125: 121: 119: 115: 108: 106: 104: 100: 96: 92: 81: 78: 70: 67:December 2022 60: 56: 50: 49: 43: 39: 35: 30: 21: 20: 172: 161: 116: 112: 90: 88: 73: 64: 53:Please help 45: 175:. Springer. 59:introducing 184:Categories 154:References 143:Topology 122:See also 109:Concepts 101:made by 55:improve 40:, or 186:: 105:. 44:, 36:, 80:) 74:( 69:) 65:( 51:.

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list of references
related reading
external links
inline citations
improve
introducing
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combinatorial manifold
piecewise linear manifold
simplicial complexes
Digital geometry
Digital topology
Topological data analysis
Topology
Discrete mathematics
Categories
Digital topology
Digital geometry

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