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

Elementary Surfaces

Ellipsoid, sphere, hyperboloid, cone and more

Sponsored Links

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)

Sponsored Links

Related Topics

Related Documents

Tag Search

  • en: elementary surfaces ellipsoid sphere hyperboloid cone elliptic cylinder
Sponsored Links

Search the Engineering ToolBox

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

3D Engineering ToolBox Extension to SketchUp - add parametric components to your SketchUp model

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro .Add the Engineering ToolBox extension to your SketchUp from the SketchUp Pro Sketchup Extension Warehouse!

Translate this page to
About the Engineering ToolBox!

Citation

This page can be cited as

  • Engineering ToolBox, (2009). Elementary Surfaces. [online] Available at: https://www.engineeringtoolbox.com/elementary-surfaces-d_1473.html [Accessed Day Mo. Year].

Modify access date.

Customize Ads in the ToolBox

Make ads more useful in Google Ad Settings .

. .

close

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!

Scientific Online Calculator

Scientific Calculator

6 22

Sponsored Links
.