Some Material on Swept Solids and Surfaces of Revolution
From Chapter 10 of Mortenson
Sections 10.5 – 10.6
Geometric Modeling91.580.201
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: thtaabtlhba 4,2,,0,,,,
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
)(sin)(cos)(),( uuuu zxxp
Source: Mortenson, Ch 10
)()()( uuu zxp
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
