An Integrated Introduction to Computer Graphics and Geometric Modeling

Processing of Terrestrial Laser Scanning Point Cloud Data for Computational Modelling of Building Facades

“…These basic objects including a sphere and cylinder were subsequently combined by a series of Boolean expressions (rotation and union) to achieve the final object in Fig. (3b) [19]. Advantages of this process are that the solid model produced is continuous and watertight, containing no openings, which reduces the problem of discontinuities in mesh convergence.…”

“…In the 1970s, significant research was undertaken in solid model architecture. Two dominant methods that emerged were (i) Constructive Solid Geometry (CSG), which construct objects by Boolean operations, store CSG tree, and compute boundary representation; and (ii) Boundary Representation (BRep), which stores objects boundaries regardless of construction method or spatial subdivision, and decomposes a solid into a cell with a simple topological and geometric structure, such as the octree [17,18,19]. Brief applications of these are discussed in the following sub-sections.…”

“…Consequently, comparing two identical solid objects is a difficult task due to the large amount of possible trees that could represent that object. Goldman [19] provides an extensive description of these techniques, along with their relative advantages and disadvantages. …”

“…In Boundary Representation (BRep), the solid surface is described as a blanket of faces, edges, and vertices (Hoffman and Rossignac, 1996) [17,19]. In this approach, relationships between entities in terms of topology are recorded.…”

“…algebraic expressions such as union, intersection, and difference). Both the surface and the interior are implicitly defined [17,19]. A special data construction is called a CSG-tree, where the basic solid shapes are leaves and Boolean operations or non-singular transformations are stored as interior nodes.…”