Cartesian
Extension
ExtensionDescription
Defines a point in 3D Cartesian space.
Part of MathLib, a diverse library of mathematical functions.
Class Methods
.new
Defines a new Cartesian point.
Instance Methods
Accessing
.x
Get or set the x coordinate value.
.y
Get or set the y coordinate value.
.z
Get or set the z coordinate value.
.set
Sets the Cartesian point x, y and z values.
Testing
==
Answers a Boolean whether the receiver equals the argument.
.hash
Returns a hash value for the receiver.
Math
+
-
*
Multiplication.
Arguments:
| scale |
Returns:
Cartesian.new(this.x * scale.x, this.y * scale.y, this.z * scale.z)
Discussion:
Note that the result of * for a 3D Cartesian point does not match that of Point, where the result is interpreted as the multiplication of complex numbers.
/
Division.
Arguments:
| scale |
Returns:
Cartesian.new(this.x / scale.x, this.y / scale.y, this.z / scale.z)
Discussion:
Note that the result of / for a 3D Cartesian point does not match that of Point, where the result is interpreted as the division of complex numbers.
.translate
Addition by a Cartesian point.
.scale
Multiplication by a Cartesian point.
.div
Division by a Cartesian point.
.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.
.abs
Absolute value of the point.
.rho
Return the spherical coordinate radius of the receiver.
.theta
Return the spherical coordinate azimuth angle of the receiver.
.phi
Return the spherical coordinate elevation angle of the receiver.
.angle
Return the spherical coordinate azimuth angle of the receiver.
.angles
Return the spherical coordinate azimuth and elevation angles of the receiver.
Returns:
[ theta, phi]
.dist
Return the distance from the receiver to aCart.
.transpose
Return a Cartesian point whose x and y coordinates are swapped.
Discussion:
Matches the return value for Point: -transpose.
.transposeXY
Return a Cartesian point whose x and y coordinates are swapped.
Discussion:
A synonym for transpose.
.transposeYZ
Return a Cartesian point whose y and z coordinates are swapped.
.transposeXZ
Return a Cartesian point whose x and z coordinates are swapped.
.round
Round the coordinate values to a multiple of quantum.
.trunc
Truncate the coordinate values to a multiple of quantum.
Conversion
.asCartesian
Returns the receiver.
.asPoint
Returns a Point, discarding z.
.asComplex
Returns a Complex with x as the real part and y as the imaginary part, discarding z.
.asPolar
Returns a Polar, discarding z.
.asSpherical
Returns a Spherical.
.asArray
Authors
Joseph Anderson, 2011.