Figure 1.5: The cube is a two manifold object 1.3 Basic classification of solid modeling methods Current computer-aided design and manufacturing(CAD/CAM) systems used for solid object representation are generally based on three different types of modeling methods 1. Decomposition models that represent solids in terms of a subdivision of space. -p7 2. Constructive models that represent solids by boolean(set) operations on primitive solids ch as rectangular boxes, cylinders, spheres, cones, torii (appropriately sized, posi and oriented 3. Boundary models that represent solids in terms of their bounding faces, which are them selves bounded by edges and the edges by vertices. - p16 A more detailed description of these models follows 1.3.1 Decomposition models Exhaustive enumeration Exhaustive enumeration is a representation by means of cubes of uniform size, orientation, and Thich are nonoverlapping, see Figure 1. 12. An object is represented by a three dimensional Boolean array. Each cell represents a cubic volume of space. If a cell intersects with the region of interest it has a true value. Otherwise, the value is false. This can be pictured as a box divided into 3D cubical pixels, with 0 assigned if empty and 1 assigned if full. This representation involves Regular subdivision of space It stores just one corner of each cube For fixed space of interest we need just a 3-D array, Ciik of binary data, and overall box/space coordinates if the cube i, 3, k intersects the solid 0 if the cube i,, k is empty
� P2 P1 Figure 1.5: The cube is a two manifold object. 1.3 Basic classification of solid modeling methods Current computer-aided design and manufacturing (CAD/CAM) systems used for solid object representation are generally based on three different types of modeling methods: 1. Decomposition models that represent solids in terms of a subdivision of space. - p.7 2. Constructive models that represent solids by Boolean (set) operations on primitive solids such as rectangular boxes, cylinders, spheres, cones, torii (appropriately sized, positioned and oriented). - p.14 3. Boundary models that represent solids in terms of their bounding faces, which are themselves bounded by edges and the edges by vertices. - p.16 A more detailed description of these models follows. 1.3.1 Decomposition models Exhaustive enumeration Exhaustive enumeration is a representation by means of cubes of uniform size, orientation, and which are nonoverlapping, see Figure 1.12. An object is represented by a three dimensional Boolean array. Each cell represents a cubic volume of space. If a cell intersects with the region of interest it has a true value. Otherwise, the value is false. This can be pictured as a box divided into 3D cubical pixels, with 0 assigned if empty and 1 assigned if full. This representation involves: • Regular subdivision of space. • It stores just one corner of each cube. • For fixed space of interest we need just a 3-D array, Cijk of binary data, and overall box/space coordinates: 1 if the cube i, j, k intersects the solid Cijk = 0 if the cube i, j, k is empty (1.1)
■■■■■■■■■■■ Figure 1.6: Examples of non-two manifold models
common edge face Figure 1.6: Examples of non-two manifold models