oblateSpheroid

Oblate ellipsoid of revolution

Description

An oblateSpheroid object encapsulates the interrelated intrinsic properties of an oblate ellipsoid of revolution. An oblate spheroid is symmetric about its polar axis and flattened at the poles, and includes the perfect sphere as a special case.

Creation

You can create an oblateSpheroid object, s, by entering:

s = oblateSpheroid;

on the command line.

Properties

SemimajorAxis — Equatorial radius of spheroid

1 (default) | positive, finite scalar

Equatorial radius of spheroid, specified as a positive, finite scalar. The value of SemimajorAxis is expressed in meters.

When the SemimajorAxis property is changed, the SemiminorAxis property scales as needed to preserve the shape of the spheroid and the values of shape-related properties including InverseFlattening and Eccentricity. The only way to change the SemimajorAxis property is to set it directly, using dot notation.

Example: 6378137

Data Types: double

SemiminorAxis — Distance from center of spheroid to pole

1 (default) | nonnegative, finite scalar

Distance from center of spheroid to pole, specified as a nonnegative, finite scalar. The value of SemiminorAxis is always less than or equal to SemimajorAxis, and is expressed in meters.

When the SemiminorAxis property is changed, the SemimajorAxis property remains unchanged, but the shape of the spheroid changes, which is reflected in changes in the values of InverseFlattening, Eccentricity, and other shape-related properties.

Example: 6356752

Data Types: double

InverseFlattening — Reciprocal of flattening

Inf (default) | positive scalar in the range [1, Inf]

Reciprocal of flattening, specified as positive scalar in the range [1, Inf].

The value of inverse flattening, 1/f, is calculated using SemimajorAxis value a and SemiminorAxis value b according to 1/f = a/(a-b). A value 1/f of Inf designates a perfect sphere. As 1/f approaches 1, the reference spheroid approaches a flattened disk.

When the InverseFlattening property is changed, other shape-related properties update, including Eccentricity. The SemimajorAxis property remains unchanged, but the value of SemiminorAxis adjusts to reflect the new shape.

Example: 300

Data Types: double

Eccentricity — First eccentricity of spheroid

0 (default) | nonnegative scalar in the range [0, 1]

First eccentricity of the spheroid, specified as nonnegative scalar in the range [0, 1].

The value of eccentricity, ecc, is calculated using SemimajorAxis value a and SemiminorAxis value b according to ecc = sqrt(a² - b²)/a. A value ecc of 0 designates a perfect sphere.

When the Eccentricity property is changed, other shape-related properties update, including InverseFlattening. The SemimajorAxis property remains unchanged, but the value of SemiminorAxis adjusts to reflect the new shape.

Example: 0.08

Data Types: double

Flattening — Flattening of spheroid

nonnegative scalar in the range [0, 1]

This property is read-only.

Flattening of the spheroid, specified as nonnegative scalar in the range [0, 1].

The value of flattening, f, is calculated using SemimajorAxis value a and SemiminorAxis value b according to f = (a-b)/a.

Data Types: double

ThirdFlattening — Third flattening of spheroid

nonnegative scalar in the range [0, 1]

This property is read-only.

Third flattening of the spheroid, specified as nonnegative scalar in the range [0, 1].

The value of the third flattening, n, is calculated using SemimajorAxis value a and SemiminorAxis value b according to n = (a-b)/(a+b).

Data Types: double

MeanRadius — Mean radius of the spheroid

positive, finite scalar

This property is read-only.

Mean radius of the spheroid, specified as positive, finite scalar. The MeanRadius property is expressed in meters.

The mean radius of the spheroid, r, is calculated using SemimajorAxis value a and SemiminorAxis value b according to r = (2a+b)/3.

Data Types: double

SurfaceArea — Surface area of the spheroid

positive, finite scalar

This property is read-only.

Surface area of the spheroid, specified as positive, finite scalar. The SurfaceArea property is expressed in square meters.

Data Types: double

Volume — Volume of the spheroid

positive, finite scalar

This property is read-only.

Volume of the spheroid, specified as positive, finite scalar. The Volume property is expressed in cubic meters.

Data Types: double

Examples

Create GRS 80 Ellipsoid

Create a GRS 80 ellipsoid using the oblateSpheroid class.

Start with a unit sphere by default.

s = oblateSpheroid

s = 

oblateSpheroid with defining properties:

        SemimajorAxis: 1
        SemiminorAxis: 1
    InverseFlattening: Inf
         Eccentricity: 0

  and additional properties:

    Flattening
    ThirdFlattening
    MeanRadius
    SurfaceArea
    Volume

Reset the semimajor axis to match the equatorial radius of the GRS 80 reference ellipsoid.

s.SemimajorAxis = 6378137

s = 

oblateSpheroid with defining properties:

        SemimajorAxis: 6378137
        SemiminorAxis: 6378137
    InverseFlattening: Inf
         Eccentricity: 0

  and additional properties:

    Flattening
    ThirdFlattening
    MeanRadius
    SurfaceArea
    Volume

The result is a sphere with radius 6,378,137 meters.

Reset the inverse flattening to the standard value for GRS 80, resulting in an oblate spheroid with a semiminor axis consistent with the value, 6,356,752.3141, tabulated in DMA Technical Memorandum 8358.1, "Datums, Ellipsoids, Grids, and Grid Reference Systems."

s.InverseFlattening = 298.257222101

s = 

oblateSpheroid with defining properties:

        SemimajorAxis: 6378137
        SemiminorAxis: 6356752.31414036
    InverseFlattening: 298.257222101
         Eccentricity: 0.0818191910428158

  and additional properties:

    Flattening
    ThirdFlattening
    MeanRadius
    SurfaceArea
    Volume

Tips

• When you define a spheroid in terms of semimajor and semiminor axes (rather than semimajor axis and inverse flattening, or semimajor axis and eccentricity), a small loss of precision in the last few digits of Flattening, Eccentricity, and ThirdFlattening may occur. This is unavoidable, but does not affect the results of practical computation.