Explain the solid modelling principles of CSG approach ,boundary representation ,decomposition methods and parametric feature based modellingConstructive Solid Geometry (CSG) Constructive Solid Geometry (CSG) uses primitive shapes as building blocks and Boolean set operators (union, difference, and intersection) to construct an object. Primitives are usually translated and/or rotated to position and orient them properly applying Boolean operations. In this method more than one procedure (and hence database) can be used to arrive at the same geometry. Data structure does not define model shape explicitly but rather implies the geometric shape through a procedural description.

Fig: Boolean operation applied in primitivesBoundary Representation (B-rep)In Boundary Representation method object is represented by its bounding faces. Each face is bounded by edges and each edge is bounded by vertices. These faces are regions or subsets of closed and orientable surfaces. B-Rep graph stores faces, edges and vertices as nodes, with pointers, or branches between the nodes to indicate connectivity. A general data structure for a boundary model should have both topological and geometrical information.B-Rep has to fulfil certain conditions to disallow self-intersecting and open objects. These conditions include: Each edge should adjoin exactly two faces and have a vertex at each end. Vertices are geometrically described by point coordinates At least three edges must meet at each vertex Faces are described by surface equations Faces must only intersect at common edges or vertices The boundaries of faces do not intersect themselves

Fig : Data structure in Boundary Representation

Decomposition methodsThese are based on spatial partitioning of object into cubes or primitives, either uniform or adaptive. In this method an object is represented by a three dimensional Boolean array. Each cell represents a cubic volume of space called voxel. If a cell intersects with the region of interest it has a true value (1) otherwise, the value is false (0). There is no concept of partial occupancy. Thus, many solids can be only approximated. Fig: Solid structure represented by VoxelsFeature-based Parametric ModellingThis method eliminates the direct use of common geometric primitives such as cone, cylinder, sphere, etc since these primitives only represent low-level geometric entities. A 2D sketch needs to be generated in the Sketcher mode. The system will automatically assign a dimension value of the sketched feature. The dimensions of sketched feature can be changed at any time by simply entering the desired value, or kept as a variable, allowing even more convenient change of its value. Sweep and extrude are example for this type of operation

Fig : Translational sweep and rotational sweep