Class: EpiMath::Vector

Inherits:
Object
  • Object
show all
Defined in:
lib/epimath100/vector.class.rb

Instance Attribute Summary collapse

Class Method Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(par1, par2 = nil, par3 = nil, verbose = true) ⇒ Vector

Parameters:

par1

The first parameter may be a point coordonate x, or a other Vector. If it’s a Vector, it will be copied. Else if it is anything else, it will be converted as Float and stored as a abcissa.

par2,par3

Theses optionals parameters are used if the first parameter is not a Vector. If it occure, par2 is mandatory (but not par3). They will be stored in @y and @z.

verbose

verbose turn on/off the messages with translate, rotate, …

Returns:

himself

Errors::

If a parameter is invalid, it may be crash the programm with an ERR_HIGH



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# File 'lib/epimath100/vector.class.rb', line 26

def initialize par1, par2=nil, par3=nil, verbose=true
  if par1.is_a?Vector #and par2 == nil and par3 == nil
    @x = par1.x
    @y = par1.y
    @z = par1.z

  elsif par1 != nil and par2 != nil
    if par3 == nil
      par3 = 1.0
    end

    if !Error.isnum?par1 or !Error.isnum?par2 or !Error.isnum?par3
      Error.call "Vector::new : a passed argument is not a valid number"
    end

    @x = par1.to_f
    @y = par2.to_f
    @z = par3.to_f
  else
    Error.call "Vector::new : The vector couldn't be initialisze with theses parameters : :par1 => '#{par1}', :par2 => '#{par2}'"
  end

  @verbose = verbose
  @matrix_op = init_matrix_op
  return self
end

Instance Attribute Details

#matrix_op ⇒ Object (readonly)

Returns the value of attribute matrix_op.



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# File 'lib/epimath100/vector.class.rb', line 9

def matrix_op
  @matrix_op
end

#verbose ⇒ Object

Returns the value of attribute verbose.



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# File 'lib/epimath100/vector.class.rb', line 8

def verbose
  @verbose
end

#x ⇒ Object

Returns the value of attribute x.



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# File 'lib/epimath100/vector.class.rb', line 8

def x
  @x
end

#y ⇒ Object

Returns the value of attribute y.



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# File 'lib/epimath100/vector.class.rb', line 8

def y
  @y
end

#z ⇒ Object

Returns the value of attribute z.



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# File 'lib/epimath100/vector.class.rb', line 8

def z
  @z
end

Class Method Details

.collinear?(u, v) ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/epimath100/vector.class.rb', line 359

def self.collinear? u, v
  Error.call "Vector::col : invalid parameters" if !u.is_a?Vector or !v.is_a?Vector
  Error.call "Vector::col : vector v1 null", Error::ERR_LOW if u.nil?
  Error.call "Vector::col : vector v2 null", Error::ERR_LOW if v.nil?

  x = u.y * v.z - u.z * v.y
  y = u.z * v.x - u.x * v.z
  z = u.x * v.y - u.y * v.x

  if x == 0 and y == 0 and z == 0
    true
  else
    false
  end
end

Instance Method Details

#*(par1) ⇒ Object

Parameters:

par1:

This parameter may be a Vector or a number. If it's a Number, it will multiply all coponents of the Vector.
If it's an other vector, we will multiplie their components 2by2

Returns:

Vector



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# File 'lib/epimath100/vector.class.rb', line 113

def *(par1)
  out = Vector.new(self)
  if par1.is_a?Numeric
    out.x *= par1
    out.y *= par1
    if out.z != nil
      out.z *= par1
    end
  elsif par1.is_a?Matrix
    return (self.to_matrix * par1).to_vector
  elsif par1.is_a?Vector
    ary1 = [self.x, self.y]
    if out.z != nil
      ary1 << out.z
    end

    ary2 = [par1.x, par1.y]
    if out.z != nil
      ary2 << par1.z
    end

    aryr = Matrix.mult_array(ary1, ary2)
    out.x = aryr[0]
    out.y = aryr[1]
    if aryr[2] != nil
      out.z = aryr[2]
    end
  else
    Error.call "Unable to add '#{par1} to this vector", Error::ERR_HIGH
  end
  return out
end

#+(par1) ⇒ Object

Parameters:

par1

It may be a point coordonate x, or a other Vector. If it’s a Vector, it will be used as a couple of coordonates. Else if it is anything else, it will be converted as Float added to @x

Returns:

nothing

Errors::

If a parameter is invalid, it may be crash the programm with an ERR_HIGH If the vectors do not have the same dimensions, it will display a warning



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# File 'lib/epimath100/vector.class.rb', line 75

def +(par1)
  out = Vector.new(self)

  if par1 != nil and par1.is_a?Vector #and par2 == nil and par3 == nil
    out.x += par1.x
    out.y += par1.y

  elsif par1 != nil
    par1 = par1.to_f
    out.x += par1
    out.y += par1

    if out.z != nil and par1 == nil
      Error.call "The vector #{Vector.new(par1, par1, par1).to_s} do not have the same dimensions than #{out.to_s}", Error::ERR_HIGH
    elsif out.z != nil
      out.z += par1
    end
  else
    Error.call "The vector couldn't be added with this parameters : #{par1}", Error::ERR_HIGH
  end
  return out
end

#-(par1) ⇒ Object

Usage:

It is simply like + buf multiply by -1 par1



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# File 'lib/epimath100/vector.class.rb', line 100

def -(par1)
  if par1 == nil
    Error.call "Can't sub nil from vector"
  end
  return (self.+(par1 * -1))
end

#collinear?(v) ⇒ Boolean

Parameters

type

Verify if two vectors are collinear

Return:

True if vector u and v are collinear else false

Returns:

  • (Boolean) 


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# File 'lib/epimath100/vector.class.rb', line 355

def collinear? v
  Vector::colineaire? @self, v
end

#homothétie(c1, c2, c3 = 1.0) ⇒ Object

Parameters:

c1,c2,c3

c1 and c2 are the coeficiens of the homothetie. c3 is optional



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# File 'lib/epimath100/vector.class.rb', line 170

def homothétie c1, c2, c3=1.0
  if c1 == nil or c2 == nil
    Error.call "Coefficients are invalids"
  end

  s = Matrix.new [[c1.to_f, 0, 0], [0, c2.to_f, 0], [0, 0, c3.to_f]]
  @matrix_op = s
  cpy = self
  cpy.z = 1.0

  puts "homothétie de rapports #{c1.to_f}, #{c2.to_f}" if @verbose

  return (s * cpy.to_matrix).to_vector
end

#init_matrix_op ⇒ Object

Returns:

Matrix.new [[1, 0, 0],[0, 1, 0], [0, 0, 1]]



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# File 'lib/epimath100/vector.class.rb', line 60

def init_matrix_op
  @matrix_op = Matrix.new [[1, 0, 0],[0, 1, 0], [0, 0, 1]]
end

#nil? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/epimath100/vector.class.rb', line 342

def nil?
  if @x == 0 and @y == 0 and @z == 0
    true
  else
    false
  end
end

#norm ⇒ Object

Return to the norm of the currenet vector



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# File 'lib/epimath100/vector.class.rb', line 54

def norm
  Math.sqrt(@x**2 + @y**2 + @z**2)
end

#proj_axe(axe = "x") ⇒ Object

Params:

axe

it must be “x” or “y” (case doesn’t checked)

Return:

The vector after the projection



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# File 'lib/epimath100/vector.class.rb', line 232

def proj_axe axe="x"
  if !axe.match(/[xy]/i)
    Error.call "Vector::proj_axe '#{axe} is not a valid axe", Error::ERR_HIGH
  end

  s = nil
  if axe.match(/x/i)
    s = Matrix.new [[1, 0, 0], [0, 0, 0], [0, 0, 1]]
  else
    s = Matrix.new [[0, 0, 0], [0, 1, 0], [0, 0, 1]]
  end

  @matrix_op = s
  cpy = self.to_matrix

  puts "projection sur un axe #{axe}." if @verbose

  return (s * cpy).to_vector
end

#rotate(a) ⇒ Object

Parameters:

a

The angle in degree

Return value:

It returns the vector after the translation.



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# File 'lib/epimath100/vector.class.rb', line 191

def rotate a
  if a == nil
    Error.call "Angle is invalid"
  end

  rad = Math::PI * a.to_f / 180.0
  cpy = self # copy to have the same value in z
  cpy.z = 0.0
  s = Matrix.new [[ Math.cos(rad), -Math.sin(rad), 0], [Math.sin(rad), Math.cos(rad), 0], [0, 0, 1]]
  @matrix_op = s

  puts "rotation d'angle #{a.to_f}" if @verbose

  return (s * cpy.to_matrix).to_vector
end

#symetric(angle) ⇒ Object

Parameters :

angle

It is the incline of the line.

Return value:

It returns the vector after the translation.



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# File 'lib/epimath100/vector.class.rb', line 213

def symetric angle
  Error.call "Variable angle is not a number (#{angle})", Error::ERR_HIGH if !Error.isnum? angle.to_s

  rad = Math::PI * angle.to_f / 180.0
  s = Matrix.new [[Math.cos(2 * rad), Math.sin(2 * rad), 0], [Math.sin(2 * rad), -Math.cos(2 * rad), 0], [0, 0, 1]]
  @matrix_op = s
  cpy = self.to_matrix

  puts "symétrie par rapport à un axe incliné de #{angle.to_f} degrés" if @verbose

  return (s * cpy).to_vector
end

#symetric_pointo ⇒ Object

Params:

nothing

Return:

The vector after the translation



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# File 'lib/epimath100/vector.class.rb', line 256

def symetric_pointo
  return homothétie(-1, -1)
end

#to_a(type = String) ⇒ Object

Parameters:

type

It specify the return. It may be String or Array.

Returns:

String, Array, nil (see type::)

Errors:

nil return occures only if the parameter types

is not supported.



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# File 'lib/epimath100/vector.class.rb', line 330

def to_a type=String
  if type == String
    return self.to_s
  elsif type == Array
    return self.to_ary
  elsif type == Matrix
    return self.to_matrix
  else
    return nil
  end
end

#to_ary(type = 0) ⇒ Object

Parameters:

type

Optionnal. It specify the format of the array returned. It may be “h” (1) or “w” (0).

  • If it’s “w” or 0, the Array will be [x,y]

  • If it’s “h” or 1, the Array returned will be [[x],]

Returns:

Array or an Array of Array



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# File 'lib/epimath100/vector.class.rb', line 296

def to_ary type=0
  array = []
  if type == 0 or type == "w" # everytime true... for the moment
    array << @x << @y
    if @z != nil
      array << @z
    end
  else
    array << [@x] << [@y]
    if @z != nil
      array << [@z]
    end
  end
  return array
end

#to_matrix ⇒ Object

Parameters::

Nothing

Returns:

Matrix



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# File 'lib/epimath100/vector.class.rb', line 317

def to_matrix
  return Matrix.new self.to_ary(1)
end

#to_s(dim = 3, type = String) ⇒ Object

Parameters:

dim

Option option to choose the desired number of dimension of the vector (if is it in 3d, it will be flattened)

type

Optional and not used yet. It specify the format of the string. It may only be String yet.

Returns:

String



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# File 'lib/epimath100/vector.class.rb', line 268

def to_s dim=3, type=String
  string = ""
  if type == String
    if @y == nil or dim == 1
      string = "(#{@x.to_f.round(3)})"
    elsif @z == nil or dim == 2
      string = "(#{@x.to_f.round(3)}; #{@y.to_f.round(3)})"
    elsif dim == 3
      string = "(#{@x.to_f.round(3)}; #{@y.to_f.round(3)}; #{@z.to_f.round(3)})"
    else
      Error.call "Vector::to_s : Invalid number of dimension specified"
    end

  else
    Error.call "Vector::to_s : Invalid type conversion", ERR_HIGH
  end

  return string
end

#translate(par1, par2, par3 = 0.0) ⇒ Object

Parameters:

par1, par2

They are the components of the vector to translate.

par3

Optional component (z)

see + 


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# File 'lib/epimath100/vector.class.rb', line 152

def translate par1, par2, par3=0.0
  if !Error.isnum? par1 or !Error.isnum? par2 or !Error.isnum? par3
    Error.call "A parameter to the translation is not a valid number", Error::ERR_HIGH
  end

  s = Matrix.new [[1.0, 0.0, par1.to_f], [0.0, 1.0, par2.to_f], [0.0, 0.0, 1.0]]
  @matrix_op = s
  cpy = self
  cpy.z = 1.0

  puts "translation de vecteur #{Vector.new(par1,par2,par3).to_s}" if @verbose

  return (s * cpy.to_matrix).to_vector
end