Class: PerfectShape::Arc

Inherits:
Shape
  • Object
show all
Includes:
RectangularShape
Defined in:
lib/perfect_shape/arc.rb

Direct Known Subclasses

Ellipse

Constant Summary collapse

TYPES = 
[:open, :chord, :pie]
DEFAULT_OUTLINE_RADIUS = 
BigDecimal('0.001')

Instance Attribute Summary collapse

Instance Method Summary collapse

Methods included from RectangularShape

#max_x, #max_y

Methods included from PointLocation

#first_point, #min_x, #min_y

Methods inherited from Shape

#==, #bounding_box, #center_point, #max_x, #max_y, #min_x, #min_y

Constructor Details

#initialize(type: :open, x: 0, y: 0, width: 1, height: 1, start: 0, extent: 360, center_x: nil, center_y: nil, radius_x: nil, radius_y: nil) ⇒ Arc

Returns a new instance of Arc.



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# File 'lib/perfect_shape/arc.rb', line 37

def initialize(type: :open, x: 0, y: 0, width: 1, height: 1, start: 0, extent: 360, center_x: nil, center_y: nil, radius_x: nil, radius_y: nil)
  if center_x && center_y && radius_x && radius_y
    self.center_x = center_x
    self.center_y = center_y
    self.radius_x = radius_x
    self.radius_y = radius_y
  else
    super(x: x, y: y, width: width, height: height)
  end
  @type = type
  self.start = start
  self.extent = extent
end

Instance Attribute Details

#extent ⇒ Object

Returns the value of attribute extent.



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# File 'lib/perfect_shape/arc.rb', line 35

def extent
  @extent
end

#start ⇒ Object

Returns the value of attribute start.



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# File 'lib/perfect_shape/arc.rb', line 35

def start
  @start
end

#type ⇒ Object

Returns the value of attribute type.



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# File 'lib/perfect_shape/arc.rb', line 34

def type
  @type
end

Instance Method Details

#btan(increment) ⇒ Object

btan computes the length (k) of the control segments at the beginning and end of a cubic bezier that approximates a segment of an arc with extent less than or equal to 90 degrees. This length (k) will be used to generate the 2 bezier control points for such a segment.

Assumptions:
  a) arc is centered on 0,0 with radius of 1.0
  b) arc extent is less than 90 degrees
  c) control points should preserve tangent
  d) control segments should have equal length

Initial data:
  start angle: ang1
  end angle:   ang2 = ang1 + extent
  start point: P1 = (x1, y1) = (cos(ang1), sin(ang1))
  end point:   P4 = (x4, y4) = (cos(ang2), sin(ang2))

Control points:
  P2 = (x2, y2)
  | x2 = x1 - k * sin(ang1) = cos(ang1) - k * sin(ang1)
  | y2 = y1 + k * cos(ang1) = sin(ang1) + k * cos(ang1)

  P3 = (x3, y3)
  | x3 = x4 + k * sin(ang2) = cos(ang2) + k * sin(ang2)
  | y3 = y4 - k * cos(ang2) = sin(ang2) - k * cos(ang2)

The formula for this length (k) can be found using the following derivations:

Midpoints:
  a) bezier (t = 1/2)
     bPm = P1 * (1-t)^3 +
           3 * P2 * t * (1-t)^2 +
           3 * P3 * t^2 * (1-t) +
           P4 * t^3 =
         = (P1 + 3P2 + 3P3 + P4)/8

  b) arc
     aPm = (cos((ang1 + ang2)/2), sin((ang1 + ang2)/2))

Let angb = (ang2 - ang1)/2; angb is half of the angle
between ang1 and ang2.

Solve the equation bPm == aPm

  a) For xm coord:
     x1 + 3*x2 + 3*x3 + x4 = 8*cos((ang1 + ang2)/2)

     cos(ang1) + 3*cos(ang1) - 3*k*sin(ang1) +
     3*cos(ang2) + 3*k*sin(ang2) + cos(ang2) =
     = 8*cos((ang1 + ang2)/2)

     4*cos(ang1) + 4*cos(ang2) + 3*k*(sin(ang2) - sin(ang1)) =
     = 8*cos((ang1 + ang2)/2)

     8*cos((ang1 + ang2)/2)*cos((ang2 - ang1)/2) +
     6*k*sin((ang2 - ang1)/2)*cos((ang1 + ang2)/2) =
     = 8*cos((ang1 + ang2)/2)

     4*cos(angb) + 3*k*sin(angb) = 4

     k = 4 / 3 * (1 - cos(angb)) / sin(angb)

  b) For ym coord we derive the same formula.

Since this formula can generate “NaN” values for small angles, we will derive a safer form that does not involve dividing by very small values:

(1 - cos(angb)) / sin(angb) =
= (1 - cos(angb))*(1 + cos(angb)) / sin(angb)*(1 + cos(angb)) =
= (1 - cos(angb)^2) / sin(angb)*(1 + cos(angb)) =
= sin(angb)^2 / sin(angb)*(1 + cos(angb)) =
= sin(angb) / (1 + cos(angb))



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# File 'lib/perfect_shape/arc.rb', line 461

def btan(increment)
  return 0 if increment.nan?
  increment /= BigDecimal('2.0')
  BigDecimal('4.0') / BigDecimal('3.0') * Math.sin(increment) / (BigDecimal('1.0') + Math.cos(increment))
end

#center_x ⇒ Object 



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# File 'lib/perfect_shape/arc.rb', line 101

def center_x
  super || @center_x
end

#center_x=(value) ⇒ Object 



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# File 'lib/perfect_shape/arc.rb', line 117

def center_x=(value)
  @center_x = BigDecimal(value.to_s)
  @x = nil
  self.radius_x = radius_x if @width
end

#center_y ⇒ Object 



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# File 'lib/perfect_shape/arc.rb', line 105

def center_y
  super || @center_y
end

#center_y=(value) ⇒ Object 



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# File 'lib/perfect_shape/arc.rb', line 123

def center_y=(value)
  @center_y = BigDecimal(value.to_s)
  @y = nil
  self.radius_y = radius_y if @height
end

#contain?(x_or_point, y = nil, outline: false, distance_tolerance: 0) ⇒ Boolean

Checks if arc contains point (two-number Array or x, y args)

the arc, false if the point lies outside of the arc’s bounds.

Parameters:

  • x —

    The X coordinate of the point to test.

  • y (defaults to: nil) —

    The Y coordinate of the point to test.

Returns:

  • (Boolean) —

    true if the point lies within the bound of



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# File 'lib/perfect_shape/arc.rb', line 147

def contain?(x_or_point, y = nil, outline: false, distance_tolerance: 0)
  x, y = Point.normalize_point(x_or_point, y)
  return unless x && y
  if outline
    if type == :pie && x == center_x && y == center_y
      true
    else
      distance_tolerance = BigDecimal(distance_tolerance.to_s)
      outside_inside_radius_difference = DEFAULT_OUTLINE_RADIUS + distance_tolerance * 2
      outside_radius_difference = inside_radius_difference = outside_inside_radius_difference / 2
      outside_shape = Arc.new(type: type, center_x: center_x, center_y: center_y, radius_x: radius_x + outside_radius_difference, radius_y: radius_y + outside_radius_difference, start: start, extent: extent)
      inside_shape = Arc.new(type: type, center_x: center_x, center_y: center_y, radius_x: radius_x - inside_radius_difference, radius_y: radius_y - inside_radius_difference, start: start, extent: extent)
      outside_shape.contain?(x, y, outline: false) and
        !inside_shape.contain?(x, y, outline: false)
    end
  else
    # Normalize the coordinates compared to the ellipse
    # having a center at 0,0 and a radius of 0.5.
    ellw = width
    return false if (ellw <= 0.0)
    normx = (x - self.x) / ellw - 0.5
    ellh = height
    return false if (ellh <= 0.0)
    normy = (y - self.y) / ellh - 0.5
    dist_sq = (normx * normx) + (normy * normy)
    return false if (dist_sq >= 0.25)
    ang_ext = self.extent.abs
    return true if (ang_ext >= 360.0)
    inarc = contain_angle?(-1*Math.radians_to_degrees(Math.atan2(normy, normx)))
    
    return inarc if type == :pie
    # CHORD and OPEN behave the same way
    if inarc
      return true if ang_ext >= 180.0
      # point must be outside the "pie triangle"
    else
      return false if ang_ext <= 180.0
      # point must be inside the "pie triangle"
    end
    
    # The point is inside the pie triangle iff it is on the same
    # side of the line connecting the ends of the arc as the center.
    angle = Math.degrees_to_radians(-start)
    x1 = Math.cos(angle)
    y1 = Math.sin(angle)
    angle += Math.degrees_to_radians(-extent)
    x2 = Math.cos(angle)
    y2 = Math.sin(angle)
    inside = (Line.relative_counterclockwise(x1, y1, x2, y2, 2*normx, 2*normy) *
                      Line.relative_counterclockwise(x1, y1, x2, y2, 0, 0) >= 0)
    inarc ? !inside : inside
  end
end

#contain_angle?(angle) ⇒ Boolean

Determines whether or not the specified angle is within the angular extents of the arc.

Returns:

  • (Boolean) 


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# File 'lib/perfect_shape/arc.rb', line 203

def contain_angle?(angle)
  ang_ext = self.extent
  backwards = ang_ext < 0.0
  ang_ext = -ang_ext if backwards
  return true if ang_ext >= 360.0

  angle = Math.normalize_degrees(angle) - Math.normalize_degrees(start)
  angle = -angle if backwards
  angle += 360.0 if angle < 0.0

  (angle >= 0.0) && (angle < ang_ext)
end

#end_point ⇒ Object

Returns the ending point of the arc. This point is the intersection of the ray from the center defined by the starting angle plus the angular extent of the arc and the elliptical boundary of the arc.

x,y coordinates of the ending point of the arc.



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# File 'lib/perfect_shape/arc.rb', line 309

def end_point
  angle = Math.degrees_to_radians(-self.start - self.extent)
  x = self.x + (Math.cos(angle) * 0.5 + 0.5) * self.width
  y = self.y + (Math.sin(angle) * 0.5 + 0.5) * self.height
  [x, y]
end

#height ⇒ Object 



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# File 'lib/perfect_shape/arc.rb', line 71

def height
  @radius_y ? @radius_y * BigDecimal('2.0') : super
end

#height=(value) ⇒ Object

Sets height, normalizing to BigDecimal



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# File 'lib/perfect_shape/arc.rb', line 96

def height=(value)
  super
  @radius_y = nil
end

#intersect?(rectangle) ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/perfect_shape/arc.rb', line 216

def intersect?(rectangle)
  x = rectangle.x
  y = rectangle.y
  w = rectangle.width
  h = rectangle.height
  aw = self.width
  ah = self.height

  return false if w <= 0 || h <= 0 || aw <= 0 || ah <= 0
  ext = self.extent
  return false if ext == 0

  ax  = self.x
  ay  = self.y
  axw = ax + aw
  ayh = ay + ah
  xw  = x + w
  yh  = y + h

  # check bbox
  return false if x >= axw || y >= ayh || xw <= ax || yh <= ay

  # extract necessary data
  axc = self.center_x
  ayc = self.center_y
  sx, sy = self.start_point
  ex, ey = self.end_point

  # Try to catch rectangles that intersect arc in areas
  # outside of rectagle with left top corner coordinates
  # (min(center x, start point x, end point x),
  #  min(center y, start point y, end point y))
  # and rigth bottom corner coordinates
  # (max(center x, start point x, end point x),
  #  max(center y, start point y, end point y)).
  # So we'll check axis segments outside of rectangle above.
  if ayc >= y && ayc <= yh # 0 and 180
    return true if (sx < xw && ex < xw && axc < xw &&
         axw > x && contain_angle?(0)) ||
        (sx > x && ex > x && axc > x &&
         ax < xw && contain_angle?(180))
  end
  if axc >= x && axc <= xw # 90 and 270
    return true if (sy > y && ey > y && ayc > y &&
         ay < yh && contain_angle?(90)) ||
        (sy < yh && ey < yh && ayc < yh &&
         ayh > y && contain_angle?(270))
  end

  # For PIE we should check intersection with pie slices
  # also we should do the same for arcs with extent is greater
  # than 180, because we should cover case of rectangle, which
  # situated between center of arc and chord, but does not
  # intersect the chord.
  rect = PerfectShape::Rectangle.new(x: x, y: y, width: w, height: h)
  if type == :pie || ext.abs > 180
    # for PIE: try to find intersections with pie slices
    line1 = PerfectShape::Line.new(points: [[axc, ayc], [sx, sy]])
    line2 = PerfectShape::Line.new(points: [[axc, ayc], [ex, ey]])
    return true if line1.intersect?(rect) || line2.intersect?(rect)
  else
    # for CHORD and OPEN: try to find intersections with chord
    line = PerfectShape::Line.new(points: [[sx, sy], [ex, ey]])
    return true if line.intersect?(rect)
  end

  # finally check the rectangle corners inside the arc
  return true if contain?(x, y) || contain?(x + w, y) ||
                 contain?(x, y + h) || contain?(x + w, y + h)

  false
end

#radius_x ⇒ Object 



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# File 'lib/perfect_shape/arc.rb', line 109

def radius_x
  @width ? @width/BigDecimal('2.0') : @radius_x
end

#radius_x=(value) ⇒ Object 



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# File 'lib/perfect_shape/arc.rb', line 129

def radius_x=(value)
  @radius_x = BigDecimal(value.to_s)
  @width = nil
end

#radius_y ⇒ Object 



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# File 'lib/perfect_shape/arc.rb', line 113

def radius_y
  @height ? @height/BigDecimal('2.0') : @radius_y
end

#radius_y=(value) ⇒ Object 



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# File 'lib/perfect_shape/arc.rb', line 134

def radius_y=(value)
  @radius_y = BigDecimal(value.to_s)
  @height = nil
end

#start_point ⇒ Object

Returns the starting point of the arc. This point is the intersection of the ray from the center defined by the starting angle and the elliptical boundary of the arc.

x,y coordinates of the starting point of the arc.



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# File 'lib/perfect_shape/arc.rb', line 295

def start_point
  angle = Math.degrees_to_radians(-self.start)
  x = self.x + (Math.cos(angle) * 0.5 + 0.5) * self.width
  y = self.y + (Math.sin(angle) * 0.5 + 0.5) * self.height
  [x, y]
end

#to_path_shapes ⇒ Object

Converts Arc into basic Path shapes made up of Points, Lines, and CubicBezierCurves Used by Path when adding an Arc to Path shapes



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# File 'lib/perfect_shape/arc.rb', line 318

def to_path_shapes
  w = BigDecimal(self.width.to_s) / 2
  h = BigDecimal(self.height.to_s) / 2
  x = self.x + w
  y = self.x + h
  ang_st_rad = -Math.degrees_to_radians(self.start)
  ext = -self.extent
  if ext >= 360.0 || ext <= -360
    arc_segs = 4
    increment = Math::PI / 2
    cv = 0.5522847498307933
    if ext < 0
      increment = -increment
      cv = -cv
    end
  else
    arc_segs = (ext.abs / 90.0).ceil
    increment = Math.degrees_to_radians(ext / arc_segs)
    cv = btan(increment)
    arc_segs = 0 if cv == 0
  end
  line_segs = nil
  case self.type
  when :open
    line_segs = 0
  when :chord
    line_segs = 1
  when :pie
    line_segs = 2
  end
  arc_segs = line_segs = -1 if w < 0 || h < 0
  
  first_point_x = first_point_y = nil
  (arc_segs + line_segs + 1).to_i.times.map do |index|
    coords = []
    angle = ang_st_rad
    if index == 0
      first_point_x = coords[0] = x + Math.cos(angle) * w
      first_point_y = coords[1] = y + Math.sin(angle) * h
      Point.new(*coords)
    elsif (index > arc_segs) && (extent - start) != 0 && ((extent - start)%360 == 0)
      nil
    elsif (index > arc_segs) && (index < arc_segs + line_segs) && (extent - start) == 0
      nil
    elsif (index > arc_segs) && (index == arc_segs + line_segs)
      Line.new(points: [[first_point_x, first_point_y]])
    elsif index > arc_segs
      coords[0] = x
      coords[1] = y
      Line.new(points: coords)
    else
      angle += increment * (index - 1)
      relx = Math.cos(angle)
      rely = Math.sin(angle)
      coords[0] = x + (relx - cv * rely) * w
      coords[1] = y + (rely + cv * relx) * h
      angle += increment
      relx = Math.cos(angle)
      rely = Math.sin(angle)
      coords[2] = x + (relx + cv * rely) * w
      coords[3] = y + (rely - cv * relx) * h
      coords[4] = x + relx * w
      coords[5] = y + rely * h
      CubicBezierCurve.new(points: coords)
    end
  end.compact
end

#width ⇒ Object 



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# File 'lib/perfect_shape/arc.rb', line 67

def width
  @radius_x ? @radius_x * BigDecimal('2.0') : super
end

#width=(value) ⇒ Object

Sets width, normalizing to BigDecimal



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# File 'lib/perfect_shape/arc.rb', line 90

def width=(value)
  super
  @radius_x = nil
end

#x ⇒ Object 



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# File 'lib/perfect_shape/arc.rb', line 59

def x
  @center_x && @radius_x ? @center_x - @radius_x : super
end

#x=(value) ⇒ Object

Sets x, normalizing to BigDecimal



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# File 'lib/perfect_shape/arc.rb', line 76

def x=(value)
  super
  @center_x = nil
  self.width = width if @radius_x
end

#y ⇒ Object 



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# File 'lib/perfect_shape/arc.rb', line 63

def y
  @center_y && @radius_y ? @center_y - @radius_y : super
end

#y=(value) ⇒ Object

Sets y, normalizing to BigDecimal



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# File 'lib/perfect_shape/arc.rb', line 83

def y=(value)
  super
  @center_y = nil
  self.height = height if @radius_y
end