Vector geometry

Author: Andrew Berkeley (andrew.berkeley.is@googlemail.com)

Introduction

This library provides an interface for handling vector geometry in 2- and 3-dimensional space.

The following classes are defined

Geometry::Vector	Basic 2- or 3D vector and operations
Geometry::GeoVector	Subclass of Vector providing additional geometric operations relating to the surface of a spheroid
Geometry::EarthVector	Subclass of GeoVector relating specifically to Earth
Geometry::Spheroid::Base	Create a representation of an arbitrary spheriod for associating with a given instance of GeoVector

Vector

Basic vector operations can be performed as follows.

Initialize a vector.

  # 2D - pass x, y
  vector = Geometry::Vector.new(15,20)

  # 3D - pass x, y, z
  vector = Geometry::Vector.new(15,20,4)

  # 2D - pass magnitude and angle 
  vector = Geometry::Vector.from_polar(25, Math::PI)

Vector attributes.

  vector = Geometry::Vector.new(15,20,4)

  vector.x                  #=> 15
  vector.y                  #=> 20
  vector.z                  #=> 4

Vector operations.

  vector = Geometry::Vector.new(3,4,5)

  # Magnitude
  vector.magnitude                      #=> 7.0710678118654755

  # Normalize
  vector.normalize                      #=> <Vector [0.4242640687119285, 0.565685424949238, 0.7071067811865475]>

  vector_1 = Geometry::Vector.new(2,2,1)
  vector_2 = Geometry::Vector.new(2,3,10)

  # Addition
  vector_1 + vector_2                   #=> <Vector [4.0, 5.0, 11.0]>

  # Subtraction
  vector_1 - vector_2                   #=> <Vector [0.0, -1.0, -9.0]>

  # Multiply by scalar value
  vector_1 * 4                          #=> <Vector [8.0, 8.0, 4.0]>

  # Divide by scalar value
  vector * 4                            #=> <Vector [0.5, 0.5, 0.25]>

  # Calculate dot product of 2 vectors
  vector_1.dot(vector_2)                #=> 20.0

  # Calculate cross product of 2 vectors
  vector_1.cross(vector_2)              #=> <Vector [17.0, -18.0, 2.0]>

  # Calculate angle between 2 vectors (in radians)
  vector_1.angle(vector_2)              #=> 0.8929110789963546

Compare vectors.

  
  # Are two vectors parallel or orthogonal?
  vector_1 = Geometry::Vector.new(10,0,0)
  vector_2 = Geometry::Vector.new(20,0,0)
  vector_3 = Geometry::Vector.new(0,10,0)

  vector_1.parallel?(vector_2)          #=> true
  vector_1.parallel?(vector_3)          #=> false

  vector_1.orthogonal?(vector_2)        #=> false
  vector_1.orthogonal?(vector_3)        #=> true

  # Are two vectors equal
  vector_1 == vector_2                  #=> false

GeoVector

The GeoVector class inherits the Vector class but and some functionality for describing geometries on the surface of a spheroid, that is, a flatted sphere, such as plantary bodies. GeoVectors can be instantiated using 3D vector coordinates (with the spheroids centre as the origin), or using geodetic or geocentric angular coordinates (e.g. latitude/longitude, degrees or radians).

Calculate the distance between two points on the Earth's surface

  # Instantiate using geographic coordinates.
  vector_1 = Geometry::EarthVector.from_geographic(80.0,0.0)  #=> <EarthVector [1111.1648732245053, 0.0, 6259.542946575613]>
  vector_2 = Geometry::EarthVector.from_geographic(80.0,1.0)  #=> <EarthVector [1110.9956374322653, 19.392500986346672, 6259.542946575613]>

  # Distance across 1 degree longitude at latitude of 80 degrees (km)
  vector_1.great_circle_distance(vector_2)     #=> 19.43475314292549

Or the distance of point from a line described by two points

  vector_3 = Geometry::EarthVector.from_geographic(75.0,5.0)  #=> <EarthVector [1649.6615168294907, 144.3266813775607, 6138.7656676742445]>
  
  vector_3.great_circle_distance_from_arc(vector_1,vector_2)  #=> 567.3634356328112

Contributing

If you find a bug or think that you improve on the code, feel free to contribute.

You can:

Send the author a message ("andrew.berkeley.is@googlemail.com":mailto:andrew.berkeley.is@googlemail.com)
Create an issue
Fork the project and submit a pull request.

License

Licensed under the MIT license (See COPYING file for details)