Class: PerfectShape::CubicBezierCurve

Inherits:
Shape
  • Object
show all
Includes:
MultiPoint
Defined in:
lib/perfect_shape/cubic_bezier_curve.rb

Overview

Mostly ported from java.awt.geom: https://docs.oracle.com/javase/8/docs/api/java/awt/geom/QuadCurve2D.html

Constant Summary collapse

OUTLINE_MINIMUM_DISTANCE_THRESHOLD = 
BigDecimal('0.001')

Instance Attribute Summary

Attributes included from MultiPoint

#points

Class Method Summary collapse

Instance Method Summary collapse

Methods included from MultiPoint

#initialize, #max_x, #max_y, #min_x, #min_y

Methods inherited from Shape

#==, #bounding_box, #center_x, #center_y, #height, #max_x, #max_y, #min_x, #min_y, #normalize_point, #width

Class Method Details

.point_crossings(x1, y1, xc1, yc1, xc2, yc2, x2, y2, px, py, level = 0) ⇒ Object

Calculates the number of times the cubic bézier curve from (x1,y1) to (x2,y2) crosses the ray extending to the right from (x,y). If the point lies on a part of the curve, then no crossings are counted for that intersection. the level parameter should be 0 at the top-level call and will count up for each recursion level to prevent infinite recursion +1 is added for each crossing where the Y coordinate is increasing -1 is added for each crossing where the Y coordinate is decreasing



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

def point_crossings(x1, y1, xc1, yc1, xc2, yc2, x2, y2, px, py, level = 0)
  return 0 if (py <  y1 && py <  yc1 && py <  yc2 && py <  y2)
  return 0 if (py >= y1 && py >= yc1 && py >= yc2 && py >= y2)
  # Note y1 could equal yc1...
  return 0 if (px >= x1 && px >= xc1 && px >= xc2 && px >= x2)
  if (px <  x1 && px <  xc1 && px <  xc2 && px <  x2)
    if (py >= y1)
      return 1 if (py < y2)
    else
      # py < y1
      return -1 if (py >= y2)
    end
    # py outside of y12 range, and/or y1==yc1
    return 0
  end
  # double precision only has 52 bits of mantissa
  return PerfectShape::Line.point_crossings(x1, y1, x2, y2, px, py) if (level > 52)
  xmid = BigDecimal((xc1 + xc2).to_s) / 2;
  ymid = BigDecimal((yc1 + yc2).to_s) / 2;
  xc1 = BigDecimal((x1 + xc1).to_s) / 2;
  yc1 = BigDecimal((y1 + yc1).to_s) / 2;
  xc2 = BigDecimal((xc2 + x2).to_s) / 2;
  yc2 = BigDecimal((yc2 + y2).to_s) / 2;
  xc1m = BigDecimal((xc1 + xmid).to_s) / 2;
  yc1m = BigDecimal((yc1 + ymid).to_s) / 2;
  xmc1 = BigDecimal((xmid + xc2).to_s) / 2;
  ymc1 = BigDecimal((ymid + yc2).to_s) / 2;
  xmid = BigDecimal((xc1m + xmc1).to_s) / 2;
  ymid = BigDecimal((yc1m + ymc1).to_s) / 2;
  # [xy]mid are NaN if any of [xy]c0m or [xy]mc1 are NaN
  # [xy]c0m or [xy]mc1 are NaN if any of [xy][c][01] are NaN
  # These values are also NaN if opposing infinities are added
  return 0 if (xmid.nan? || ymid.nan?)
  point_crossings(x1, y1, xc1, yc1, xc1m, yc1m, xmid, ymid, px, py, level+1) +
    point_crossings(xmid, ymid, xmc1, ymc1, xc2, yc2, x2, y2, px, py, level+1)
end

Instance Method Details

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

Checks if cubic bézier curve contains point (two-number Array or x, y args)

the cubic bézier curve, false if the point lies outside of the cubic bézier curve'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:

  • (@code true) —

    if the point lies within the bound of



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# File 'lib/perfect_shape/cubic_bezier_curve.rb', line 88

def contain?(x_or_point, y = nil, outline: false, distance_tolerance: 0)
  x, y = normalize_point(x_or_point, y)
  return unless x && y
  
  if outline
    minimum_distance_threshold = OUTLINE_MINIMUM_DISTANCE_THRESHOLD + distance_tolerance
    point_segment_distance(x, y, minimum_distance_threshold: minimum_distance_threshold) < minimum_distance_threshold
  else
    # Either x or y was infinite or NaN.
    # A NaN always produces a negative response to any test
    # and Infinity values cannot be "inside" any path so
    # they should return false as well.
    return false if (!(x * 0.0 + y * 0.0 == 0.0))
    # We count the "Y" crossings to determine if the point is
    # inside the curve bounded by its closing line.
    x1 = points[0][0]
    y1 = points[0][1]
    x2 = points[3][0]
    y2 = points[3][1]
    line = PerfectShape::Line.new(points: [[x1, y1], [x2, y2]])
    crossings = line.point_crossings(x, y) + point_crossings(x, y);
    (crossings & 1) == 1
  end
end

#curve_center_point ⇒ Object

The center point on the outline of the curve



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# File 'lib/perfect_shape/cubic_bezier_curve.rb', line 128

def curve_center_point
  subdivisions.last.points[0]
end

#curve_center_x ⇒ Object

The center point x on the outline of the curve



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# File 'lib/perfect_shape/cubic_bezier_curve.rb', line 133

def curve_center_x
  subdivisions.last.points[0][0]
end

#curve_center_y ⇒ Object

The center point y on the outline of the curve



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# File 'lib/perfect_shape/cubic_bezier_curve.rb', line 138

def curve_center_y
  subdivisions.last.points[0][1]
end

#point_crossings(x_or_point, y = nil, level = 0) ⇒ Object

Calculates the number of times the cubic bézier curve crosses the ray extending to the right from (x,y). If the point lies on a part of the curve, then no crossings are counted for that intersection. the level parameter should be 0 at the top-level call and will count up for each recursion level to prevent infinite recursion +1 is added for each crossing where the Y coordinate is increasing -1 is added for each crossing where the Y coordinate is decreasing



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# File 'lib/perfect_shape/cubic_bezier_curve.rb', line 121

def point_crossings(x_or_point, y = nil, level = 0)
  x, y = normalize_point(x_or_point, y)
  return unless x && y
  CubicBezierCurve.point_crossings(points[0][0], points[0][1], points[1][0], points[1][1], points[2][0], points[2][1], points[3][0], points[3][1], x, y, level)
end

#point_segment_distance(x_or_point, y = nil, minimum_distance_threshold: OUTLINE_MINIMUM_DISTANCE_THRESHOLD) ⇒ Object 



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# File 'lib/perfect_shape/cubic_bezier_curve.rb', line 180

def point_segment_distance(x_or_point, y = nil, minimum_distance_threshold: OUTLINE_MINIMUM_DISTANCE_THRESHOLD)
  x, y = normalize_point(x_or_point, y)
  return unless x && y
  
  point = Point.new(x, y)
  current_curve = self
  minimum_distance = point.point_distance(curve_center_point)
  last_minimum_distance = minimum_distance + 1 # start bigger to ensure going through loop once at least
  while minimum_distance >= minimum_distance_threshold && minimum_distance < last_minimum_distance
    curve1, curve2 = current_curve.subdivisions
    distance1 = point.point_distance(curve1.curve_center_point)
    distance2 = point.point_distance(curve2.curve_center_point)
    last_minimum_distance = minimum_distance
    if distance1 < distance2
      minimum_distance = distance1
      current_curve = curve1
    else
      minimum_distance = distance2
      current_curve = curve2
    end
  end
  if minimum_distance < minimum_distance_threshold
    minimum_distance
  else
    last_minimum_distance
  end
end

#subdivisions(number = 2) ⇒ Object

Subdivides CubicBezierCurve exactly at its curve center returning 2 CubicBezierCurve's as a two-element Array by default number parameter may be specified as an even number in case more subdivisions are needed. If an odd number is given, it is rounded up to the closest even number above it (e.g. 3 becomes 4).



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

def subdivisions(number = 2)
  number = (number.to_i / 2.0).ceil*2
  x1 = points[0][0]
  y1 = points[0][1]
  ctrlx1 = points[1][0]
  ctrly1 = points[1][1]
  ctrlx2 = points[2][0]
  ctrly2 = points[2][1]
  x2 = points[3][0]
  y2 = points[3][1]
  centerx = (ctrlx1 + ctrlx2) / 2.0
  centery = (ctrly1 + ctrly2) / 2.0
  ctrlx1 = (x1 + ctrlx1) / 2.0
  ctrly1 = (y1 + ctrly1) / 2.0
  ctrlx2 = (x2 + ctrlx2) / 2.0
  ctrly2 = (y2 + ctrly2) / 2.0
  ctrlx12 = (ctrlx1 + centerx) / 2.0
  ctrly12 = (ctrly1 + centery) / 2.0
  ctrlx21 = (ctrlx2 + centerx) / 2.0
  ctrly21 = (ctrly2 + centery) / 2.0
  centerx = (ctrlx12 + ctrlx21) / 2.0
  centery = (ctrly12 + ctrly21) / 2.0
  default_subdivisions = [
    CubicBezierCurve.new(points: [x1, y1, ctrlx1, ctrly1, ctrlx12, ctrly12, centerx, centery]),
    CubicBezierCurve.new(points: [centerx, centery, ctrlx21, ctrly21, ctrlx2, ctrly2, x2, y2])
  ]
  if number > 2
    default_subdivisions.map { |curve| curve.subdivisions(number - 2) }.flatten
  else
    default_subdivisions
  end
end