Some Material on Swept Solids and Surfaces of Revolution

1
Some Material on Swept Solids and Surfaces of
Revolution
Geometric Modeling91.580.201

• From Chapter 10 of Mortenson
• Sections 10.5 10.6

2
Scaling Transformations
primitive shapes
affect geometry but not topology of object
Source Mortenson, Ch 10
3
Differential Scaling Transformations (continued)
restrictions
Source Mortenson, Ch 10
4
Differential Scaling Transformations (continued)
Sample restrictions
Source Mortenson, Ch 10
5
Parameterized Shape of Variable Topology
Source Mortenson, Ch 10
6
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
7
Sweep Solids (continued)
some problematic situations
Source Mortenson, Ch 10
8
Loss and Eshleman (1974) Position and Direction
Specification for Swept Solids
trimming
Source Mortenson, Ch 10
9
Loss and Eshleman (1974) Position and Direction
Specification for Swept Solids (continued)
Source Mortenson, Ch 10
10
Surfaces of Revolution
Example z-axis of rotation
Source Mortenson, Ch 10
11
Surfaces of Revolution (continued)
axis of rotation
angle of rotation
More general example using cubic Hermite curve
goal is to find a Hermite patch describing the
surface.
Hermite curve
Source Mortenson, Ch 10