Class: Cartesius::Hyperbola

Inherits:
Object
  • Object
show all
Includes:
Determinator, Numerificator
Defined in:
lib/cartesius/hyperbola.rb

Class Method Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(x2:, y2:, x:, y:, k:) ⇒ Hyperbola

Conic equation type: ax^2 + by^2 + dx + ey + f = 0



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

def initialize(x2:, y2:, x:, y:, k:)
  @x2_coeff, @y2_coeff, @x_coeff, @y_coeff, @k_coeff = normalize(x2, y2, x, y, k)
  validation
end

Class Method Details

.by_axes(transverse_axis:, not_transverse_axis:) ⇒ Object 



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# File 'lib/cartesius/hyperbola.rb', line 53

def self.by_axes(transverse_axis:, not_transverse_axis:)
  if transverse_axis == not_transverse_axis
    raise ArgumentError.new('Axes must be different!')
  end

  if transverse_axis.inclined? or not_transverse_axis.inclined?
    raise ArgumentError.new('Axes must not be inclined!')
  end

  if transverse_axis.horizontal? and not_transverse_axis.horizontal?
    raise ArgumentError.new('Axes can not be both horizontal!')
  end

  if transverse_axis.vertical? and not_transverse_axis.vertical?
    raise ArgumentError.new('Axes can not be both vertical!')
  end

  if transverse_axis.mid != not_transverse_axis.mid
    raise ArgumentError.new('Axes must be the same mid point!')
  end

  if transverse_axis.horizontal?
    a2 = Rational(transverse_axis.length, 2)**2
    b2 = Rational(not_transverse_axis.length, 2)**2
    position = RIGHT_POSITION
  else
    a2 = Rational(not_transverse_axis.length, 2)**2
    b2 = Rational(transverse_axis.length, 2)**2
    position = UP_POSITION
  end

  center = transverse_axis.mid

  build_by(a2, b2, center, position)
end

.by_definition(focus1:, focus2:, distance:) ⇒ Object 



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# File 'lib/cartesius/hyperbola.rb', line 23

def self.by_definition(focus1:, focus2:, distance:)
  if focus1 == focus2
    raise ArgumentError.new('Focus points must be different!')
  end

  focal_axis = Segment.new(extreme1: focus1, extreme2: focus2)
  if focal_axis.inclined?
    raise ArgumentError.new('Focal axis must not be inclined!')
  end

  if distance >= focal_axis.length
    raise ArgumentError.new('Difference between distances must be less than focal distance!')
  end

  c2 = Rational(focal_axis.length, 2)**2
  if focal_axis.horizontal?
    a2 = Rational(distance, 2)**2
    b2 = c2 - a2
    position = RIGHT_POSITION
  else
    b2 = Rational(distance, 2)**2
    a2 = c2 - b2
    position = UP_POSITION
  end

  center = focal_axis.mid

  build_by(a2, b2, center, position)
end

.by_points(center:, vertex:, point:) ⇒ Object 



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# File 'lib/cartesius/hyperbola.rb', line 89

def self.by_points(center:, vertex:, point:)
  if center == vertex or center == point or vertex == point
    raise ArgumentError.new('Points must be different!')
  end

  semi_axis = Segment.new(extreme1: center, extreme2: vertex)
  if semi_axis.inclined?
    raise ArgumentError.new('Vertex must be aligned with center!')
  end

  if semi_axis.horizontal?
    position = RIGHT_POSITION
  else
    position = UP_POSITION
  end

  shifted1 = Point.new(x: vertex.x - center.x, y: vertex.y - center.y)
  shifted2 = Point.new(x: point.x - center.x, y: point.y - center.y)

  begin
    alfa, beta = Cramer.solution2(
        [shifted1.x**2, -shifted1.y**2],
        [shifted2.x**2, -shifted2.y**2],
        [position, position]
    )
  rescue
    raise ArgumentError.new('Center, vertex and point are not valid!')
  end

  a2 = Rational(1, alfa)
  b2 = Rational(1, beta)

  build_by(a2, b2, center, position)
end

Instance Method Details

#==(hyperbola) ⇒ Object 



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# File 'lib/cartesius/hyperbola.rb', line 188

def == (hyperbola)
  hyperbola.instance_of?(self.class) and
      hyperbola.focus1 == focus1 and hyperbola.focus2 == focus2 and hyperbola.distance == distance
end

#ascending_asymptote ⇒ Object 



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# File 'lib/cartesius/hyperbola.rb', line 171

def ascending_asymptote
  Line.create(slope: Rational(b, a), known_term: center.y - center.x * Rational(b, a))
end

#congruent?(hyperbola) ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/cartesius/hyperbola.rb', line 183

def congruent?(hyperbola)
  hyperbola.instance_of?(self.class) and
      hyperbola.eccentricity == eccentricity
end

#descending_asymptote ⇒ Object 



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# File 'lib/cartesius/hyperbola.rb', line 175

def descending_asymptote
  Line.create(slope: -Rational(b, a), known_term: center.y + center.x * Rational(b, a))
end

#distance ⇒ Object 



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# File 'lib/cartesius/hyperbola.rb', line 138

def distance
  discriminating(lambda {2 * a}, lambda {2 * b})
end

#eccentricity ⇒ Object 



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# File 'lib/cartesius/hyperbola.rb', line 167

def eccentricity
  Rational(focal_axis.length, transverse_axis.length)
end

#equilateral? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/cartesius/hyperbola.rb', line 179

def equilateral?
  a2 == b2
end

#focal_axis ⇒ Object 



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# File 'lib/cartesius/hyperbola.rb', line 142

def focal_axis
  Segment.new(extreme1: focus1, extreme2: focus2)
end

#focus1 ⇒ Object 



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# File 'lib/cartesius/hyperbola.rb', line 124

def focus1
  discriminating(
      lambda {Point.new(x: center.x + c, y: center.y)},
      lambda {Point.new(x: center.x, y: center.y + c)}
  )
end

#focus2 ⇒ Object 



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# File 'lib/cartesius/hyperbola.rb', line 131

def focus2
  discriminating(
      lambda {Point.new(x: center.x - c, y: center.y)},
      lambda {Point.new(x: center.x, y: center.y - c)}
  )
end

#not_transverse_axis ⇒ Object 



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# File 'lib/cartesius/hyperbola.rb', line 153

def not_transverse_axis
  discriminating(
      lambda {Segment.new(extreme1: Point.new(x: center.x, y: center.y - b), extreme2: Point.new(x: center.x, y: center.y + b))},
      lambda {Segment.new(extreme1: Point.new(x: center.x - a, y: center.y), extreme2: Point.new(x: center.x + a, y: center.y))}
  )
end

#transverse_axis ⇒ Object 



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# File 'lib/cartesius/hyperbola.rb', line 146

def transverse_axis
  discriminating(
      lambda {Segment.new(extreme1: Point.new(x: center.x - a, y: center.y), extreme2: Point.new(x: center.x + a, y: center.y))},
      lambda {Segment.new(extreme1: Point.new(x: center.x, y: center.y - b), extreme2: Point.new(x: center.x, y: center.y + b))},
  )
end

#vertices ⇒ Object 



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# File 'lib/cartesius/hyperbola.rb', line 160

def vertices
  discriminating(
      lambda {[Point.new(x: center.x - a, y: center.y), Point.new(x: center.x + a, y: center.y)]},
      lambda {[Point.new(x: center.x, y: center.y - b), Point.new(x: center.x, y: center.y + b)]}
  )
end