Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

Elementary Surfaces

Ellipsoid, sphere, hyperboloid, cone and more.

The simplest of surfaces are the unbound planes. The next complexity are the second degree or quadric surfaces.

Non-degenerate Quadrics

Ellipsoid

x2 / a2 + y2 / b2 + z2 / c2 = 1                       (1)

where

a, b, c = intrinsic parameters

Sphere

Sphere, a special ellipsoid, can be expressed as

x2 + y2 + z2 = a2                            (2)

where

a = radius

Hyperboloid of one sheet

x2 / a2 + y2 / b2 - z2 / c2 = 1                            (3)

where

a, b, c = intrinsic parameters

Hyperboloid of two sheets

x2 / a2 + y2 / b2 - z2 / c2 = -1                            (4)

where

a, b, c = intrinsic parameters

Quadric Cone

x2 / a2 + y2 / b2 - z2 / c2 = 0                             (5)

where

a, b, c = intrinsic parameters

Elliptic Paraboloid

x2 / a2 + y2 / b2 - 2 z = 0                                (6)

where

a, b = intrinsic parameters

Elliptic Cylinder

x2 / a2 + y2 / b2 = 1                                (7)

where

a, b = intrinsic parameters

Cylinder

x2 + y2 = a2                                (8)

where

a, b = intrinsic parameters

Hyperbolic Cylinder

x2 / a2 - y2 / b2 = 1                                 (9)

where

a, b = intrinsic parameters

Parabolic Cylinder

y2- 2 l x = 0                             (10)

where

l = intrinsic parameters

Degenerate Quadrics

Parallel Planes

x2 - a2 = 0                             (11)

where

a = half the distance between the parallel planes

Intersecting Planes

x2 / a2 - y2 / b2 = 0                          (12)

where

tan-1 (b / a) = half the angle between the intersecting planes

Coincident Planes

x2 = 0                            (13)

3D Engineering ToolBox - draw and model technical applications! 2D Engineering ToolBox - create and share online diagram drawing templates! Engineering ToolBox Apps - mobile online and offline engineering applications!

Unit Converter


















































6.6.11

.