Class: Sevgi::Geometry::Line

Inherits:
LineBase
  • Object
show all
Defined in:
lib/sevgi/geometry/elements/line.rb,
lib/sevgi/geometry/equation.rb

Overview

Finite, directed line between two endpoints.

Direction affects #left?, #right?, and the sign of #shift. Use #equation when the corresponding infinite line is required; #over? deliberately tests only the finite extent between the endpoints.

Examples:

Query sides of a directed line in screen coordinates

line = Sevgi::Geometry::Line.([0, 0], [10, 0])
line.left?([5, -2])  # => true
line.right?([5, 2])  # => true
line.shift(2).starting.deconstruct # => [0.0, -2.0]

Distinguish the finite segment from its infinite equation

line = Sevgi::Geometry::Line.([0, 0], [10, 0])
line.over?([5, 0])  # => true
line.over?([15, 0]) # => false

Instance Attribute Summary collapse

Class Method Summary collapse

Instance Method Summary collapse

Instance Attribute Details

#A ⇒ Sevgi::Geometry::Point (readonly)

Returns starting point.

Returns:



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# File 'lib/sevgi/geometry/elements/line.rb', line 36

class Line < LineBase
  # @overload [](length, angle, position: Origin)
  #   Builds a line from length and angle.
  #   @param length [Numeric] line length
  #   @param angle [Numeric] clockwise angle in degrees
  #   @param position [Sevgi::Geometry::Point, Array<Numeric>] starting point
  #   @return [Sevgi::Geometry::Line]
  #   @raise [Sevgi::Geometry::Error] when length, angle, or position cannot be coerced to finite geometry values
  # @example Mathematical notation and English convenience are equivalent
  #   Sevgi::Geometry::Line[5, 30] == Sevgi::Geometry::Line.from_length_angle(5, 30)
  def self.[](length, angle, position: Origin) = new_by_segments(Segment[length, angle], position:)

  # Builds a line from length and angle.
  # @param length [Numeric] line length
  # @param angle [Numeric] clockwise angle in degrees
  # @param position [Sevgi::Geometry::Point, Array<Numeric>] starting point
  # @return [Sevgi::Geometry::Line]
  # @raise [Sevgi::Geometry::Error] when length, angle, or position cannot be coerced to finite geometry values
  def self.from_length_angle(length, angle, position: Origin) = self[length, angle, position:]

  # @overload from_points(starting, ending)
  #   Builds a line from two endpoints.
  #   @param starting [Sevgi::Geometry::Point, Array<Numeric>] starting point
  #   @param ending [Sevgi::Geometry::Point, Array<Numeric>] ending point
  #   @return [Sevgi::Geometry::Line]
  #   @raise [Sevgi::Geometry::Error] when either point cannot be coerced
  # @example Mathematical notation and English convenience are equivalent
  #   Sevgi::Geometry::Line.([0, 0], [3, 4]) == Sevgi::Geometry::Line.from_points([0, 0], [3, 4])
  def self.from_points(...) = call(...)

  private_class_method :from_segments

  # Returns the clockwise line angle in degrees.
  # @return [Float]
  def angle = head.angle

  # Returns the ending point.
  # @return [Sevgi::Geometry::Point]
  def ending = points.last

  # Reports whether a point is left of the directed line from {#starting} to {#ending} in screen coordinates.
  # Points on the infinite line are on neither side. A zero-length line has no direction and returns false.
  # @param point [Sevgi::Geometry::Point, Array<Numeric>] point to test
  # @return [Boolean]
  # @raise [Sevgi::Geometry::Error] when point cannot be coerced
  def left?(point) = F.lt?(side(point), 0.0)

  # Reports whether a point is right of the directed line from {#starting} to {#ending} in screen coordinates.
  # Points on the infinite line are on neither side. A zero-length line has no direction and returns false.
  # @param point [Sevgi::Geometry::Point, Array<Numeric>] point to test
  # @return [Boolean]
  # @raise [Sevgi::Geometry::Error] when point cannot be coerced
  def right?(point) = F.gt?(side(point), 0.0)

  # Returns the starting point.
  # @return [Sevgi::Geometry::Point]
  def starting = points.first

  # Draws the line into a graphics node.
  # @param node [Object] graphics node receiving the drawing command
  # @return [Object] graphics node command result
  def draw!(node, **) = node.LineTo(x1: position.x, y1: position.y, x2: ending.x, y2: ending.y, **)

  private :draw!

  # Reports whether a point lies on the finite line segment.
  # @param point [Sevgi::Geometry::Point, Array<Numeric>] point to test
  # @return [Boolean]
  # @raise [Sevgi::Geometry::Error] when point cannot be coerced
  def over?(point)
    point = Tuple[Point, point]

    within_range?(point) && equation.on?(point)
  end

  # Returns a parallel line shifted by a signed perpendicular offset.
  # Positive distance moves to the directed line's left in screen coordinates; reversing the endpoints reverses the
  # shift direction.
  # @param distance [Numeric] signed perpendicular offset
  # @return [Sevgi::Geometry::Line]
  # @raise [Sevgi::Geometry::Error] when distance is not a finite real number
  def shift(distance)
    distance = Real[:distance, distance]
    translate(distance * F.sin(angle), -distance * F.cos(angle))
  end

  private

  def cross(ax, ay, bx, by) = (ax * by) - (ay * bx)
  def delta(from, to) = [to.x - from.x, to.y - from.y]

  def side(point)
    point = Tuple[Point, point]
    cross(*delta(starting, ending), *delta(starting, point))
  end

  def within_range?(point)
    point = point.approx
    points = [starting.approx, ending.approx]

    point.between?(points.min, points.max)
  end
end

#AB ⇒ Sevgi::Geometry::Line (readonly)

Returns line from A to B.

Returns:



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# File 'lib/sevgi/geometry/elements/line.rb', line 36

class Line < LineBase
  # @overload [](length, angle, position: Origin)
  #   Builds a line from length and angle.
  #   @param length [Numeric] line length
  #   @param angle [Numeric] clockwise angle in degrees
  #   @param position [Sevgi::Geometry::Point, Array<Numeric>] starting point
  #   @return [Sevgi::Geometry::Line]
  #   @raise [Sevgi::Geometry::Error] when length, angle, or position cannot be coerced to finite geometry values
  # @example Mathematical notation and English convenience are equivalent
  #   Sevgi::Geometry::Line[5, 30] == Sevgi::Geometry::Line.from_length_angle(5, 30)
  def self.[](length, angle, position: Origin) = new_by_segments(Segment[length, angle], position:)

  # Builds a line from length and angle.
  # @param length [Numeric] line length
  # @param angle [Numeric] clockwise angle in degrees
  # @param position [Sevgi::Geometry::Point, Array<Numeric>] starting point
  # @return [Sevgi::Geometry::Line]
  # @raise [Sevgi::Geometry::Error] when length, angle, or position cannot be coerced to finite geometry values
  def self.from_length_angle(length, angle, position: Origin) = self[length, angle, position:]

  # @overload from_points(starting, ending)
  #   Builds a line from two endpoints.
  #   @param starting [Sevgi::Geometry::Point, Array<Numeric>] starting point
  #   @param ending [Sevgi::Geometry::Point, Array<Numeric>] ending point
  #   @return [Sevgi::Geometry::Line]
  #   @raise [Sevgi::Geometry::Error] when either point cannot be coerced
  # @example Mathematical notation and English convenience are equivalent
  #   Sevgi::Geometry::Line.([0, 0], [3, 4]) == Sevgi::Geometry::Line.from_points([0, 0], [3, 4])
  def self.from_points(...) = call(...)

  private_class_method :from_segments

  # Returns the clockwise line angle in degrees.
  # @return [Float]
  def angle = head.angle

  # Returns the ending point.
  # @return [Sevgi::Geometry::Point]
  def ending = points.last

  # Reports whether a point is left of the directed line from {#starting} to {#ending} in screen coordinates.
  # Points on the infinite line are on neither side. A zero-length line has no direction and returns false.
  # @param point [Sevgi::Geometry::Point, Array<Numeric>] point to test
  # @return [Boolean]
  # @raise [Sevgi::Geometry::Error] when point cannot be coerced
  def left?(point) = F.lt?(side(point), 0.0)

  # Reports whether a point is right of the directed line from {#starting} to {#ending} in screen coordinates.
  # Points on the infinite line are on neither side. A zero-length line has no direction and returns false.
  # @param point [Sevgi::Geometry::Point, Array<Numeric>] point to test
  # @return [Boolean]
  # @raise [Sevgi::Geometry::Error] when point cannot be coerced
  def right?(point) = F.gt?(side(point), 0.0)

  # Returns the starting point.
  # @return [Sevgi::Geometry::Point]
  def starting = points.first

  # Draws the line into a graphics node.
  # @param node [Object] graphics node receiving the drawing command
  # @return [Object] graphics node command result
  def draw!(node, **) = node.LineTo(x1: position.x, y1: position.y, x2: ending.x, y2: ending.y, **)

  private :draw!

  # Reports whether a point lies on the finite line segment.
  # @param point [Sevgi::Geometry::Point, Array<Numeric>] point to test
  # @return [Boolean]
  # @raise [Sevgi::Geometry::Error] when point cannot be coerced
  def over?(point)
    point = Tuple[Point, point]

    within_range?(point) && equation.on?(point)
  end

  # Returns a parallel line shifted by a signed perpendicular offset.
  # Positive distance moves to the directed line's left in screen coordinates; reversing the endpoints reverses the
  # shift direction.
  # @param distance [Numeric] signed perpendicular offset
  # @return [Sevgi::Geometry::Line]
  # @raise [Sevgi::Geometry::Error] when distance is not a finite real number
  def shift(distance)
    distance = Real[:distance, distance]
    translate(distance * F.sin(angle), -distance * F.cos(angle))
  end

  private

  def cross(ax, ay, bx, by) = (ax * by) - (ay * bx)
  def delta(from, to) = [to.x - from.x, to.y - from.y]

  def side(point)
    point = Tuple[Point, point]
    cross(*delta(starting, ending), *delta(starting, point))
  end

  def within_range?(point)
    point = point.approx
    points = [starting.approx, ending.approx]

    point.between?(points.min, points.max)
  end
end

#B ⇒ Sevgi::Geometry::Point (readonly)

Returns ending point.

Returns:



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# File 'lib/sevgi/geometry/elements/line.rb', line 36

class Line < LineBase
  # @overload [](length, angle, position: Origin)
  #   Builds a line from length and angle.
  #   @param length [Numeric] line length
  #   @param angle [Numeric] clockwise angle in degrees
  #   @param position [Sevgi::Geometry::Point, Array<Numeric>] starting point
  #   @return [Sevgi::Geometry::Line]
  #   @raise [Sevgi::Geometry::Error] when length, angle, or position cannot be coerced to finite geometry values
  # @example Mathematical notation and English convenience are equivalent
  #   Sevgi::Geometry::Line[5, 30] == Sevgi::Geometry::Line.from_length_angle(5, 30)
  def self.[](length, angle, position: Origin) = new_by_segments(Segment[length, angle], position:)

  # Builds a line from length and angle.
  # @param length [Numeric] line length
  # @param angle [Numeric] clockwise angle in degrees
  # @param position [Sevgi::Geometry::Point, Array<Numeric>] starting point
  # @return [Sevgi::Geometry::Line]
  # @raise [Sevgi::Geometry::Error] when length, angle, or position cannot be coerced to finite geometry values
  def self.from_length_angle(length, angle, position: Origin) = self[length, angle, position:]

  # @overload from_points(starting, ending)
  #   Builds a line from two endpoints.
  #   @param starting [Sevgi::Geometry::Point, Array<Numeric>] starting point
  #   @param ending [Sevgi::Geometry::Point, Array<Numeric>] ending point
  #   @return [Sevgi::Geometry::Line]
  #   @raise [Sevgi::Geometry::Error] when either point cannot be coerced
  # @example Mathematical notation and English convenience are equivalent
  #   Sevgi::Geometry::Line.([0, 0], [3, 4]) == Sevgi::Geometry::Line.from_points([0, 0], [3, 4])
  def self.from_points(...) = call(...)

  private_class_method :from_segments

  # Returns the clockwise line angle in degrees.
  # @return [Float]
  def angle = head.angle

  # Returns the ending point.
  # @return [Sevgi::Geometry::Point]
  def ending = points.last

  # Reports whether a point is left of the directed line from {#starting} to {#ending} in screen coordinates.
  # Points on the infinite line are on neither side. A zero-length line has no direction and returns false.
  # @param point [Sevgi::Geometry::Point, Array<Numeric>] point to test
  # @return [Boolean]
  # @raise [Sevgi::Geometry::Error] when point cannot be coerced
  def left?(point) = F.lt?(side(point), 0.0)

  # Reports whether a point is right of the directed line from {#starting} to {#ending} in screen coordinates.
  # Points on the infinite line are on neither side. A zero-length line has no direction and returns false.
  # @param point [Sevgi::Geometry::Point, Array<Numeric>] point to test
  # @return [Boolean]
  # @raise [Sevgi::Geometry::Error] when point cannot be coerced
  def right?(point) = F.gt?(side(point), 0.0)

  # Returns the starting point.
  # @return [Sevgi::Geometry::Point]
  def starting = points.first

  # Draws the line into a graphics node.
  # @param node [Object] graphics node receiving the drawing command
  # @return [Object] graphics node command result
  def draw!(node, **) = node.LineTo(x1: position.x, y1: position.y, x2: ending.x, y2: ending.y, **)

  private :draw!

  # Reports whether a point lies on the finite line segment.
  # @param point [Sevgi::Geometry::Point, Array<Numeric>] point to test
  # @return [Boolean]
  # @raise [Sevgi::Geometry::Error] when point cannot be coerced
  def over?(point)
    point = Tuple[Point, point]

    within_range?(point) && equation.on?(point)
  end

  # Returns a parallel line shifted by a signed perpendicular offset.
  # Positive distance moves to the directed line's left in screen coordinates; reversing the endpoints reverses the
  # shift direction.
  # @param distance [Numeric] signed perpendicular offset
  # @return [Sevgi::Geometry::Line]
  # @raise [Sevgi::Geometry::Error] when distance is not a finite real number
  def shift(distance)
    distance = Real[:distance, distance]
    translate(distance * F.sin(angle), -distance * F.cos(angle))
  end

  private

  def cross(ax, ay, bx, by) = (ax * by) - (ay * bx)
  def delta(from, to) = [to.x - from.x, to.y - from.y]

  def side(point)
    point = Tuple[Point, point]
    cross(*delta(starting, ending), *delta(starting, point))
  end

  def within_range?(point)
    point = point.approx
    points = [starting.approx, ending.approx]

    point.between?(points.min, points.max)
  end
end

Class Method Details

.[](length, angle, position: Origin) ⇒ Sevgi::Geometry::Line

Examples:

Mathematical notation and English convenience are equivalent

Sevgi::Geometry::Line[5, 30] == Sevgi::Geometry::Line.from_length_angle(5, 30)

Builds a line from length and angle.

Parameters:

  • length (Numeric) —

    line length

  • angle (Numeric) —

    clockwise angle in degrees

  • position (Sevgi::Geometry::Point, Array<Numeric>) (defaults to: Origin) —

    starting point

Returns:

Raises:



46
 
# File 'lib/sevgi/geometry/elements/line.rb', line 46

def self.[](length, angle, position: Origin) = new_by_segments(Segment[length, angle], position:)

.call(starting, ending) ⇒ Sevgi::Geometry::Line

Builds a line from two endpoints.

Parameters:

Returns:

Raises:



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# File 'lib/sevgi/geometry/elements/line.rb', line 36

class Line < LineBase
  # @overload [](length, angle, position: Origin)
  #   Builds a line from length and angle.
  #   @param length [Numeric] line length
  #   @param angle [Numeric] clockwise angle in degrees
  #   @param position [Sevgi::Geometry::Point, Array<Numeric>] starting point
  #   @return [Sevgi::Geometry::Line]
  #   @raise [Sevgi::Geometry::Error] when length, angle, or position cannot be coerced to finite geometry values
  # @example Mathematical notation and English convenience are equivalent
  #   Sevgi::Geometry::Line[5, 30] == Sevgi::Geometry::Line.from_length_angle(5, 30)
  def self.[](length, angle, position: Origin) = new_by_segments(Segment[length, angle], position:)

  # Builds a line from length and angle.
  # @param length [Numeric] line length
  # @param angle [Numeric] clockwise angle in degrees
  # @param position [Sevgi::Geometry::Point, Array<Numeric>] starting point
  # @return [Sevgi::Geometry::Line]
  # @raise [Sevgi::Geometry::Error] when length, angle, or position cannot be coerced to finite geometry values
  def self.from_length_angle(length, angle, position: Origin) = self[length, angle, position:]

  # @overload from_points(starting, ending)
  #   Builds a line from two endpoints.
  #   @param starting [Sevgi::Geometry::Point, Array<Numeric>] starting point
  #   @param ending [Sevgi::Geometry::Point, Array<Numeric>] ending point
  #   @return [Sevgi::Geometry::Line]
  #   @raise [Sevgi::Geometry::Error] when either point cannot be coerced
  # @example Mathematical notation and English convenience are equivalent
  #   Sevgi::Geometry::Line.([0, 0], [3, 4]) == Sevgi::Geometry::Line.from_points([0, 0], [3, 4])
  def self.from_points(...) = call(...)

  private_class_method :from_segments

  # Returns the clockwise line angle in degrees.
  # @return [Float]
  def angle = head.angle

  # Returns the ending point.
  # @return [Sevgi::Geometry::Point]
  def ending = points.last

  # Reports whether a point is left of the directed line from {#starting} to {#ending} in screen coordinates.
  # Points on the infinite line are on neither side. A zero-length line has no direction and returns false.
  # @param point [Sevgi::Geometry::Point, Array<Numeric>] point to test
  # @return [Boolean]
  # @raise [Sevgi::Geometry::Error] when point cannot be coerced
  def left?(point) = F.lt?(side(point), 0.0)

  # Reports whether a point is right of the directed line from {#starting} to {#ending} in screen coordinates.
  # Points on the infinite line are on neither side. A zero-length line has no direction and returns false.
  # @param point [Sevgi::Geometry::Point, Array<Numeric>] point to test
  # @return [Boolean]
  # @raise [Sevgi::Geometry::Error] when point cannot be coerced
  def right?(point) = F.gt?(side(point), 0.0)

  # Returns the starting point.
  # @return [Sevgi::Geometry::Point]
  def starting = points.first

  # Draws the line into a graphics node.
  # @param node [Object] graphics node receiving the drawing command
  # @return [Object] graphics node command result
  def draw!(node, **) = node.LineTo(x1: position.x, y1: position.y, x2: ending.x, y2: ending.y, **)

  private :draw!

  # Reports whether a point lies on the finite line segment.
  # @param point [Sevgi::Geometry::Point, Array<Numeric>] point to test
  # @return [Boolean]
  # @raise [Sevgi::Geometry::Error] when point cannot be coerced
  def over?(point)
    point = Tuple[Point, point]

    within_range?(point) && equation.on?(point)
  end

  # Returns a parallel line shifted by a signed perpendicular offset.
  # Positive distance moves to the directed line's left in screen coordinates; reversing the endpoints reverses the
  # shift direction.
  # @param distance [Numeric] signed perpendicular offset
  # @return [Sevgi::Geometry::Line]
  # @raise [Sevgi::Geometry::Error] when distance is not a finite real number
  def shift(distance)
    distance = Real[:distance, distance]
    translate(distance * F.sin(angle), -distance * F.cos(angle))
  end

  private

  def cross(ax, ay, bx, by) = (ax * by) - (ay * bx)
  def delta(from, to) = [to.x - from.x, to.y - from.y]

  def side(point)
    point = Tuple[Point, point]
    cross(*delta(starting, ending), *delta(starting, point))
  end

  def within_range?(point)
    point = point.approx
    points = [starting.approx, ending.approx]

    point.between?(points.min, points.max)
  end
end

.from_length_angle(length, angle, position: Origin) ⇒ Sevgi::Geometry::Line

Builds a line from length and angle.

Parameters:

  • length (Numeric) —

    line length

  • angle (Numeric) —

    clockwise angle in degrees

  • position (Sevgi::Geometry::Point, Array<Numeric>) (defaults to: Origin) —

    starting point

Returns:

Raises:



54
 
# File 'lib/sevgi/geometry/elements/line.rb', line 54

def self.from_length_angle(length, angle, position: Origin) = self[length, angle, position:]

.from_points(starting, ending) ⇒ Sevgi::Geometry::Line

Examples:

Mathematical notation and English convenience are equivalent

Sevgi::Geometry::Line.([0, 0], [3, 4]) == Sevgi::Geometry::Line.from_points([0, 0], [3, 4])

Builds a line from two endpoints.

Parameters:

Returns:

Raises:



64
 
# File 'lib/sevgi/geometry/elements/line.rb', line 64

def self.from_points(...) = call(...)

Instance Method Details

#angle ⇒ Float

Returns the clockwise line angle in degrees.

Returns:

  • (Float) 


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# File 'lib/sevgi/geometry/elements/line.rb', line 70

def angle = head.angle

#ending ⇒ Sevgi::Geometry::Point

Returns the ending point.

Returns:



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# File 'lib/sevgi/geometry/elements/line.rb', line 74

def ending = points.last

#equation ⇒ Sevgi::Geometry::Equation::Linear

Returns the linear equation containing this line.

Returns:



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# File 'lib/sevgi/geometry/equation.rb', line 131

def equation = position.equation(angle)

#left?(point) ⇒ Boolean

Reports whether a point is left of the directed line from #starting to #ending in screen coordinates. Points on the infinite line are on neither side. A zero-length line has no direction and returns false.

Parameters:

Returns:

  • (Boolean)

Raises:



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# File 'lib/sevgi/geometry/elements/line.rb', line 81

def left?(point) = F.lt?(side(point), 0.0)

#over?(point) ⇒ Boolean

Reports whether a point lies on the finite line segment.

Parameters:

Returns:

  • (Boolean)

Raises:



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# File 'lib/sevgi/geometry/elements/line.rb', line 105

def over?(point)
  point = Tuple[Point, point]

  within_range?(point) && equation.on?(point)
end

#right?(point) ⇒ Boolean

Reports whether a point is right of the directed line from #starting to #ending in screen coordinates. Points on the infinite line are on neither side. A zero-length line has no direction and returns false.

Parameters:

Returns:

  • (Boolean)

Raises:



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# File 'lib/sevgi/geometry/elements/line.rb', line 88

def right?(point) = F.gt?(side(point), 0.0)

#shift(distance) ⇒ Sevgi::Geometry::Line

Returns a parallel line shifted by a signed perpendicular offset. Positive distance moves to the directed line's left in screen coordinates; reversing the endpoints reverses the shift direction.

Parameters:

  • distance (Numeric) —

    signed perpendicular offset

Returns:

Raises:



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# File 'lib/sevgi/geometry/elements/line.rb', line 117

def shift(distance)
  distance = Real[:distance, distance]
  translate(distance * F.sin(angle), -distance * F.cos(angle))
end

#starting ⇒ Sevgi::Geometry::Point

Returns the starting point.

Returns:



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# File 'lib/sevgi/geometry/elements/line.rb', line 92

def starting = points.first