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: docs.oracle.com/javase/8/docs/api/java/awt/geom/QuadCurve2D.html

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) ⇒ @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 86

def contain?(x_or_point, y = nil)
  x, y = normalize_point(x_or_point, y)
  return unless x && y
  
  # 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

#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 114

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