- published: 01 Aug 2012
- views: 245893
Flattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution (spheroid) respectively. Other terms used are ellipticity, or oblateness. The usual notation for flattening is f and its definition in terms of the semi-axes of the resulting ellipse or ellipsoid is
The compression factor is b/a in each case. For the ellipse, this factor is also the aspect ratio of the ellipse.
There are two other variants of flattening (see below) and when it is necessary to avoid confusion the above flattening is called the first flattening. The following definitions may be found in standard texts and online web texts
In the following, a is the larger dimension (e.g. semimajor axis), whereas b is the smaller (semiminor axis). All flattenings are zero for a circle (a=b).
The flattenings are related to other parameters of the ellipse. For example:
where is the eccentricity.
Death - Flattening of Emotions (Remastered - HQ)
Wood slab flattening: Using a handheld router
Flattening Boards with a Router Sled
174 - Flattening Workbenches and Wide Boards With A Router
5 Best Exercises to Flatten your Lower Belly
Flattening Water Stones
Flattening Whetstones, Oil or Water Sharpening Stones
Tech Tip: SOLIDWORKS 2015 Tutorial - Flattening Surfaces
The Difference Between Merging And Flattening Layers in Photoshop Elements
Flattening Sharpening Stones- Japanese Knife Imports