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## Nonmanifold Modeling: An Approach Based on Spatial Subdivision

### Citations

533 | Primitives for the Manipulation of General Subdivisions and the Computation of Voronoi Diagrams - Guibas, Stolfi - 1985 |

348 |
An introduction to solid modeling.
- Mantyla
- 1988
(Show Context)
Citation Context ...tionally proposed to model solid objects. In the first strategy, one aims to represent a solid through an explicit description of its boundary. These are the so-called boundary representations (BRep) =-=[1]-=-, which are based on data-structures that describe the adjacency relationships of the vertices, edges and faces of the solid. The other possibility is the CSG approach [2], which consists in represent... |

192 |
Geometric and Solid Modeling: An Introduction.
- Hoffmann
- 1989
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Citation Context ... in a uniform and coherent way. The study of representation and modeling methods based on arbitrary spatial subdivisions [8–12] generalizes and unifies 2 the so called nonmanifold modeling techniques =-=[13,14]-=- (i.e., the techniques used to model objects that are not necessarily two-manifolds embedded in three dimensional space). The proposed methodology is based on the creation and maintenance of threedime... |

108 |
The Radial Edge Structure: A Topological Representation for Non-Manifold Geometric Boundary Modeling,” Geometric Modeling
- Weiler
- 1988
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Citation Context ...1] represent, in a general way, the adjacency relationships of three dimensional objects not necessarily homogeneous in dimension. Here, we use the Radial Edge (RED) data structure proposed by Weiler =-=[18]-=-. RED explicitly stores the two uses (sides) of a face by the two regions (not necessarily distinct) that share that face. Each face use is bounded by one or more loop uses, which in turn are composed... |

94 | Primitives for the Manipulation of Three-Dimensional Subdivisions,’’ - Dobkin, Laszlo - 1987 |

91 |
Topological Structures for Geometric Modeling.
- WEILER
- 1986
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Citation Context ... data structure consistency when including a new face if that originates a new region. Topological data structures are too complex to be manipulated directly. Weiler has introduced a set of operators =-=[19]-=- that provide a high level method to access RED 1 . These operators are divided in two groups. The first group has operators that act on faces of a CGC and are analogous to Euler operators [1]. The se... |

82 |
Boolean Operations in Solid Modeling: Boundary Evaluation and Merging Algorithms,”
- Requicha, Voelcker
- 1985
(Show Context)
Citation Context ...rsection of a finite set of half-spaces determined by certain surfaces. BRep and CSG have complementary advantages and disadvantages [3], and much work has been done about converting from CSG to BRep =-=[4]-=- and, more recently, from BRep to CSG [5–7]. Both types of conversion use the fact that the surfaces describing the faces are present in both representations, either explicitly represented (BRep) or a... |

79 |
SGC: A dimensionindependent model for pointsets with internal structures and incomplete boundaries.
- ROSSIGNAC, O’CONNOR
- 1990
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Citation Context ...eneous in dimension and satisfying the condition that the intersection of the boundaries of any two cells is necessarily equal to the union of other cells of the decomposition. Rossignac and O’Connor =-=[17]-=- have proposed the concept of a Geometric Complex to formalize appropriately this idea. 3 Complete Geometric Complex Geometrical complexes are not required to cover the entire space. For our purposes,... |

39 | Separation for Boundary to CSG Conversion, - Shapiro, Vossler - 1993 |

34 |
Point in Polygon Strategies
- Haines
- 1994
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Citation Context ...ry vertex of the shell is in R′. If so, move the shell to R′. The problem of point-in-region testing can be solved using techniques similar to those used in the two dimensional version of the problem =-=[21]-=-. It is possible to use an algorithm that counts the number of intersections of a ray, starting at point p, against the faces of region R′ (care should be taken in treating the difficulties introduced... |

32 |
REQUICHA A.: Constructive nonregularized geometry.
- ROSSIGNAC
- 1991
(Show Context)
Citation Context ... CSG-like operations to define solids, while retaining the full boundary representation. An analogous methodology is used here. We discuss how to implement a set of non-regular construction operators =-=[15]-=- in order to supply the user with a modeling process for complex, heterogeneous objects analogous to CSG. The material is organized in six sections. In Section 2, we define spatial subdivisions, and d... |

31 |
The finite element method. Volume 1. Basic formulation and linear problems
- Zienkiewicz, Taylor
- 1989
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Citation Context ...nt Method is a powerful numerical simulation tool which can handle problems of arbitrary geometry and shape. From the modeling perspective, the method is simpler to use than the Finite Element Method =-=[25]-=- because discrete elements have no pre-specified topology, as required by finite elements. However, discrete element modeling, like finite element modeling, is still an open issue: model creation and ... |

25 |
Constructive solid geometry
- gequicha, Voelcker
- 1977
(Show Context)
Citation Context ...g. Most BRep based representation systems provide modeling tools to release the user from the task of directly specifying each bounding surface. The CSG (Constructive Solid Geometry) modeling process =-=[2]-=- is widely used in solid modeling because it provides sculpting refining mechanisms which are familiar to most people. Through regularized boolean operations, certain basic solids are combined to yiel... |

22 | Construction and optimization of csg representations - Shapiro, Vossler - 1991 |

14 |
An editable nonmanifold boundary representation
- Crocker, Reinke
- 1991
(Show Context)
Citation Context ... in a uniform and coherent way. The study of representation and modeling methods based on arbitrary spatial subdivisions [8–12] generalizes and unifies 2 the so called nonmanifold modeling techniques =-=[13,14]-=- (i.e., the techniques used to model objects that are not necessarily two-manifolds embedded in three dimensional space). The proposed methodology is based on the creation and maintenance of threedime... |

13 | E@c:znt CSG Representations of Two-Dimensional Solids, - Shapiro, Vossler - 1991 |

8 | Representation of d-Dimensional Geometric Objects - Brisson - 1990 |

8 |
Topological and Geometrical Modeling Approach to Numerical Discretization and Arbitrary Fracture Simulation in Three Dimensions
- Martha
- 1989
(Show Context)
Citation Context ...ame topological representation adopted in this work has been successfully used in conjunction with meshing algorithms in engineering applications, such as for simulation of fracture propagation in 3D =-=[27]-=- and of 3D reinforced concrete subassemblages [28]. 5 Construction of Heterogeneous Objects As mentioned before, we have chosen CGC as the mathematical model to describe a spatial subdivision. This ap... |

7 |
Architectural issues in solid modelers
- Miller
- 1989
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Citation Context ...imitive solids. These, in turn, are usually represented as the intersection of a finite set of half-spaces determined by certain surfaces. BRep and CSG have complementary advantages and disadvantages =-=[3]-=-, and much work has been done about converting from CSG to BRep [4] and, more recently, from BRep to CSG [5–7]. Both types of conversion use the fact that the surfaces describing the faces are present... |

7 | Extension of the notion of map and subdivisions of a threedimensional space - Lienhardt - 1988 |

4 | A Data Structure for Manipulating Three-dimensional Subdivisions - Laszlo - 1987 |

4 |
A software tool which allows interactive creation of planar subdivisions, and applications to educational programs
- Carvalho, Gattass, et al.
- 1990
(Show Context)
Citation Context ...ng them. In Section 3 we present the chosen representation and the operators to manipulate it. Although it is simple (and convenient) to create planar subdivisions by adding a curve segment at a time =-=[16]-=-, the task of creating a spatial subdivision is much more complex. Thus, in Section 4, we discuss the problems arising when creating a spatial subdivision by inserting a surface patch at a time. In mo... |

4 |
Rational design of tunnel supports: A computer model for rock mass be- havior using interactive graphics for the input and output of geometrical data
- Cundall
- 1974
(Show Context)
Citation Context ...ment Modeling The Discrete Element Method is a numerical method that geotechnical engineers use to analyze the interaction and movement of rock blocks originated from natural fractures in a rock mass =-=[24]-=-. The basic idea of this method is to determine the equilibrium of each block, taking into account distributed body forces, such as its own weight, and contact forces with adjacent blocks along the fr... |

3 |
Non-manifold geometric modeling for set operations and surface operations
- Murabata, Higashi
- 1990
(Show Context)
Citation Context ...lls which are joined in consequence of the addition of the new face. We allow loops with dangling edges. 1 Although some work has been done in presenting nonmanifold operators in a more rigorous form =-=[20]-=-, there is not yet a definitive work about the subject. 6 RRext wireframe shell simple patch set of faces weakly linked R ’ Fig. 3. Creation of a new region. 4 Incremental CGC Creation In this section... |

3 |
Creation and Management of Space Subdivisions
- Cavalcanti
- 1992
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Citation Context ...g. 6, which is an edge to be created on A). There are other criteria to determine which intersection points (on L) generate vertices on a face. A detailed description of the algorithm can be found in =-=[23]-=-. The algorithm above assumes that the two intersecting faces are not coplanar. When this is not the case, the intersection of the faces is no longer contained 10 X 1s2s3s4s5s6s7s8s9 0s1s2s3s4s5s6s7s8... |

2 |
Visualization of 3d geological formations represented by spatial subdivisions
- Castier
- 1995
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Citation Context ...n input data file suitable for analysis is extracted from the radial-edge description to feed a discrete element program. The proposed data representation is also very helpful for model visualization =-=[26]-=-. In Fig. 9, some of the blocks were “turned off,” i.e., made invisible. This effect is accomplished simply by not displaying the faces on the boundaries 14 Fig. 7. Patches of joints in three dimensio... |

2 |
An interactive environment for the simulation of 3d reinforced concrete subassemblages
- Potyondy, Abel, et al.
- 1990
(Show Context)
Citation Context ...k has been successfully used in conjunction with meshing algorithms in engineering applications, such as for simulation of fracture propagation in 3D [27] and of 3D reinforced concrete subassemblages =-=[28]-=-. 5 Construction of Heterogeneous Objects As mentioned before, we have chosen CGC as the mathematical model to describe a spatial subdivision. This approach provides a basis for representing complex o... |

2 |
Genesys - hybrid system for solid modeling
- Fischer
- 1991
(Show Context)
Citation Context ...NRG operators can be described as a disjoint union of distinct two-manifold solids, which can be returned to the BRep modeling system. Such an extension was added by us to the GeneSys modeling system =-=[29]-=-. The model in Fig. 11, for instance, can be produced by GeneSys. First, the two-manifold solids corresponding to each bar are created in GeneSys. Then, SCGCs A e B are created from the descriptions o... |