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PARAMETRIC SURFACES. Surfaces of Known Form Plane surface Cylindrical surface Conical surface Spherical Surface Toroidal Surface . w. u. Cloud Gate at Chicago. Cloud Gate at Chicago. Cloud Gate at Chicago. Machining of Curved Geometries. Pelton cup. Impeller. - PowerPoint PPT Presentation
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PARAMETRIC SURFACES
Surfaces of Known Form
• Plane surface• Cylindrical surface• Conical surface• Spherical Surface• Toroidal Surface
u
w
Cloud Gate at Chicago
Cloud Gate at Chicago
Cloud Gate at Chicago
Machining of Curved Geometries
• Pinion• Forging die for Blade• Intake manifold
• Pelton cup• Knee joint prothesis • Impeller
Three Special Surfaces
RULED SURFACE
Input
Two curves p(u, 0), p(u, 1)
p(u, w) = (1-w) p(u, 0) + w p(u, 1)
Alternate
Line and directrix curve
RULED SURFACE
p(u, 0)
p(u, 1)
BILINEAR SURFACE
(HYPERBOLIC PARABOLOID)
Four Corner Points
p(0, 0), p(1, 0), p(0, 1), p(1, 1)
p(u, w) = (1-u) (1-w) p(0, 0) + u (1-w) p(1, 0) +
(1-u) w p(0, 1) + u w p(1, 1)
BILINEAR SURFACE
p(0, 0)
p(0, 1)
p(1, 0)
p(1, 1)
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