Spherical
Extension
ExtensionDescription
Represents spherical coordinates.
Part of MathLib, a diverse library of mathematical functions.
Class Methods
.new
Create a new spherical coordinate with the given radius, rho, and angles in radians, theta and phi.
Arguments:
| rho |
radius |
| theta |
azimuth angle |
| phi |
elevation angle |
Instance Methods
Accessing
.rho
Get or set the rho coordinate value.
.theta
Get or set the theta coordinate value.
.phi
Get or set the phi coordinate value.
Testing
==
Answers a Boolean whether the receiver equals the argument.
.hash
Returns a hash value for the receiver.
Math
+
-
*
/
The math operations of addition, subtraction, multiplication and division are accomplished by first converting to cartesian coordinates, then answering to spherical coordinates.
.scale
Scale the radius by some value.
.rotate
Rotation about the origin in the XY plane by the angle given in radians.
Discussion:
Positive values rotate from +X towards +Y
.tilt
Rotation about the origin in the YZ plane by the angle given in radians.
Discussion:
Positive values rotate from +Y towards +Z
.tumble
Rotation about the origin in the XZ plane by the angle given in radians.
Discussion:
Positive values rotate from +X towards +Z
.rotateXY
Rotation about the origin in the XY plane by the angle given in radians.
Discussion:
A synonym for rotate.
.rotateYZ
Rotation about the origin in the YZ plane by the angle given in radians.
Discussion:
A synonym for tilt.
.rotateXZ
Rotation about the origin in the XZ plane by the angle given in radians.
Discussion:
A synonym for tumble.
.mirrorX
Mirror x, reflecting across the YZ plane.
.mirrorY
Mirror y, reflecting across the XZ plane.
.mirrorZ
Mirror z, reflecting across the XY plane.
.mirrorO
Mirror across the origin.
.neg
Rotate theta by pi and negate phi.
Discussion:
This operation is equivalent to negating rho, and is a synonym for mirrorO.
Conversion
.magnitude
Answer the radius.
.angle
Answer the azimuth angle, theta, in radians.
.phase
Answer the azimuth angle, theta, in radians.
.angles
Answer the azimuth and elevation angles, theta and phi, in radians.
Returns:
[ theta, phi ]
.phases
Answer the azimuth and elevation angles, theta and phi, in radians.
Returns:
[ theta, phi ]
.x
Answer the cartesian coordinate x of the receiver.
.y
Answer the cartesian coordinate y of the receiver.
.z
Answer the cartesian coordinate z of the receiver.
.real
Answer the cartesian coordinate x of the receiver.
.imag
Answer the cartesian coordinate y of the receiver.
.asSpherical
Returns the receiver.
.asPolar
Convert to Polar, discarding z.
.asComplex
Answers a Complex with x as the real part and y as the imaginary part, discarding z.
.asPoint
Convert to Point, discarding z.
.asCartesian
Convert to Cartesian.
Authors
Joseph Anderson, 2011.