Class Eymiha::Point3c
In: lib/eymiha/math3/point3c.rb
Parent: Object

Point3c represents a 3D point in cylindrical coordinates:

  • c_radius is the distance from the cylindrical axis.
  • theta is the angular distance around the cylindrical axis.
  • z is the distance from the cylindrical base-plane.

The cylindrical theta coordinate is equal to the spherical theta. The cylindrical z coordinate is equal to the cartesian z coordinate.

From a cartesian reference, the cylindrical axis is the z axis, theta is measured using the right hand rule with the positive x axis representing 0, and the cylindrical plane is the plane z=0.

Point3c instances may be converted to Point3 and Point3s instances, but information at the "boundaries" may be lost. Besides responding as a Point3c, an instance will also respond like a Point3 and Point3s as it has a full complement of readers for the different coordinate systems.

Methods

==   =~   approximately_equals?   new   phi   point3   point3c   point3s   s_radius   set   theta=   to_s   x   y  

Included Modules

ThreeDimensions

Attributes

c_radius  [RW]  cylindrical radius coordinate reader and writer.
theta  [R]  cylindrical theta reader.
z  [RW]  cylindrical z coordinate reader and writer.

Public Class methods

new(c_radius=0, theta=0, z=0)

Creates and returns a Point3c instance. Sets the coordinates values using the set method.

Public Instance methods

==(point3c)

Returns true if the coordinates of the instance are effectively equal to the coordinates of the given point.

=~(point3c,epsilon=Numeric.epsilon)

Alias for approximately_equals?

approximately_equals?(point3c,epsilon=Numeric.epsilon)

Returns true if the coordinates of the instance are approximately effectively equal to the coordinates of the given point, each coordinate less than a distance epsilon from the target.

phi()

Returns the spherical phi coordinate of the instance.

point3(point3=nil,point3c=self)

Returns a 3D point in cartesian coordinates, filling point3 if given, and copied from point3c.

point3c(c_radius=self.c_radius,theta=self.theta,z=self.z)

Returns a copy of point3c with the given cylindrical coordinates:

  • c_radius is Numeric, the arguments are copied as the coordinates.
  • c_radius responds like a Point3c, its coordinates are copied.
  • otherwise a TypeError is raised.
point3s(point3s=nil,point3c=self)

Returns a 3D point in spherical coordinates, filling point3s if given, and copied from point3c.

s_radius()

Returns the spherical radius coordinate of the instance.

set(c_radius=0, theta=0, z=0)

Sets the coordinate values of the instance. When

  • c_radius is Numeric, the arguments are interpretted as coordinates.
  • c_radius responds like a Point3c, its cylindrical coordinates are assigned.
  • otherwise a TypeError is raised.

The modified instance is returned.

theta=(theta)

cylindrical theta coordinate writer, rectifying theta to a value in [0, 2*pi).

to_s()

Returns a string representation of the instance.

x()

Returns the cartesian x coordinate of the instance.

y()

Returns the cartesian y coordinate of the instance.

[Validate]