Class: Cartesius::Parabola

Inherits:
Object
  • Object
show all
Includes:
Numerificator
Defined in:
lib/cartesius/parabola.rb

Class Method Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(x2:, x:, k:) ⇒ Parabola

Conic Conic equation type: ax^2 + dx - y + f = 0



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# File 'lib/cartesius/parabola.rb', line 13

def initialize(x2:, x:, k:)
  @x2_coeff, @x_coeff, @y_coeff, @k_coeff = x2.to_r, x.to_r, -1, k.to_r
  validation
end

Class Method Details

.by_definition(directrix:, focus:) ⇒ Object 



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# File 'lib/cartesius/parabola.rb', line 18

def self.by_definition(directrix:, focus:)
  if directrix.include?(focus)
    raise ArgumentError.new('Focus belongs to directrix!')
  end

  unless directrix.horizontal?
    raise ArgumentError.new('Directrix is not parallel to x-axis!')
  end

  a = Rational(1, 2 * (focus.y - directrix.y_intercept))
  b = -2 * a * focus.x
  c = a * (focus.x ** 2) + focus.y - Rational(1, 4 * a)

  new(x2: a, x: b, k: c)
end

.by_points(point1:, point2:, point3:) ⇒ Object 



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# File 'lib/cartesius/parabola.rb', line 34

def self.by_points(point1:, point2:, point3:)
  a, b, c = Cramer.solution3(
      [point1.x ** 2, point1.x, 1],
      [point2.x ** 2, point2.x, 1],
      [point3.x ** 2, point3.x, 1],
      [point1.y, point2.y, point3.y]
  )

  new(x2: a, x: b, k: c)
rescue
  raise ArgumentError.new('Invalid points!')
end

Instance Method Details

#==(parabola) ⇒ Object 



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# File 'lib/cartesius/parabola.rb', line 78

def == (parabola)
  parabola.instance_of?(self.class) &&
      parabola.focus == focus && parabola.directrix == directrix
end

#congruent?(parabola) ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/cartesius/parabola.rb', line 73

def congruent?(parabola)
  parabola.instance_of?(self.class) &&
      parabola.eccentricity == eccentricity
end

#directrix ⇒ Object 



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# File 'lib/cartesius/parabola.rb', line 47

def directrix
  Line.horizontal(known_term: Rational(-delta - 1, 4 * @x2_coeff))
end

#eccentricity ⇒ Object 



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# File 'lib/cartesius/parabola.rb', line 63

def eccentricity
  @x2_coeff.abs
end

#focus ⇒ Object 



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# File 'lib/cartesius/parabola.rb', line 51

def focus
  Point.new(x: Rational(-@x_coeff, 2 * @x2_coeff), y: Rational(1 - delta, 4 * @x2_coeff))
end

#symmetry_axis ⇒ Object 



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# File 'lib/cartesius/parabola.rb', line 59

def symmetry_axis
  Line.vertical(known_term: Rational(-@x_coeff, 2* @x2_coeff))
end

#to_equation ⇒ Object 



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# File 'lib/cartesius/parabola.rb', line 67

def to_equation
  equationfy(
      'x^2' => @x2_coeff, 'x' => @x_coeff, 'y' => -1, '1' => @k_coeff
  )
end

#vertex ⇒ Object 



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# File 'lib/cartesius/parabola.rb', line 55

def vertex
  Point.new(x: Rational(-@x_coeff, 2 * @x2_coeff), y: Rational(-delta, 4 * @x2_coeff))
end