Some Material on Swept Solids and Surfaces of Revolution From Chapter 10 of Mortenson Sections 10.5 – 10.6 Geometric Modeling

Scaling Transformations affect geometry but not topology of object primitive shapes Source: Mortenson, Ch 10

Differential Scaling Transformations (continued) restrictions Source: Mortenson, Ch 10

Differential Scaling Transformations (continued) Sample restrictions: Source: Mortenson, Ch 10

Parameterized Shape of Variable Topology Source: Mortenson, Ch 10

Sweep Solids Moving an object along a path. –Generator = sweeping object: curve, surface, or solid –Director = path Common for modeling constant cross-section mechanical parts. Translational sweep (extrusion): moving a planar curve or planar shape along a straight line normal to plane of curve. –More generally, sweep one curve along another. Rotational sweep: rotating a planar curve or shape (with finite area) about an axis. Source: Mortenson, Ch 10

Sweep Solids (continued) Source: Mortenson, Ch 10 some problematic situations

Loss and Eshleman (1974) Position and Direction Specification for Swept Solids Source: Mortenson, Ch 10 trimming

Loss and Eshleman (1974) Position and Direction Specification for Swept Solids (continued) Source: Mortenson, Ch 10

Surfaces of Revolution Source: Mortenson, Ch 10 Example: z-axis of rotation

Surfaces of Revolution (continued) Source: Mortenson, Ch 10 More general example using cubic Hermite curve: goal is to find a Hermite patch describing the surface. axis of rotation Hermite curve angle of rotation