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.

#### 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

#### 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

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

#### 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)

## Related Topics

• Mathematics - Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more

## Tag Search

• en: elementary surfaces ellipsoid sphere hyperboloid cone elliptic cylinder

## Engineering ToolBox - SketchUp Extension - Online 3D modeling!

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!

## Privacy

We don't collect information from our users. Only emails and answers are saved in our archive. Cookies are only used in the browser to improve user experience.

Some of our calculators and applications let you save application data to your local computer. These applications will - due to browser restrictions - send data between your browser and our server. We don't save this data.

## Citation

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

Modify access date.

. .

#### Scientific Online Calculator 1 24