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)