Some Material on Swept Solids and Surfaces of Revolution From Chapter 10 of Mortenson Sections 10.5...
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Transcript of Some Material on Swept Solids and Surfaces of Revolution From Chapter 10 of Mortenson Sections 10.5...
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