class HexaPDF::Content::GraphicObject::EndpointArc

def compute_arc_values(x1, y1)

See: ARC F.6.5, F.6.6

The argument (x1, y1) is the starting point.

Compute the center parameterization from the endpoint parameterization. 
def compute_arc_values(x1, y1)
  x2 = @x
  y2 = @y
  rx = @a
  ry = @b
  theta = deg_to_rad(@inclination)
  cos_theta = Math.cos(theta)
  sin_theta = Math.sin(theta)
  # F.6.5.1
  x1p = (x1 - x2) / 2.0 * cos_theta + (y1 - y2) / 2.0 * sin_theta
  y1p = (x1 - x2) / 2.0 * -sin_theta + (y1 - y2) / 2.0 * cos_theta
  x1ps = x1p**2
  y1ps = y1p**2
  rxs = rx**2
  rys = ry**2
  # F.6.6.2
  l = x1ps / rxs + y1ps / rys
  if l > 1
    rx *= Math.sqrt(l)
    ry *= Math.sqrt(l)
    rxs = rx**2
    rys = ry**2
  end
  # F.6.5.2
  sqrt = (rxs * rys - rxs * y1ps - rys * x1ps) / (rxs * y1ps + rys * x1ps)
  sqrt = 0 if sqrt.abs < EPSILON
  sqrt = Math.sqrt(sqrt)
  sqrt *= -1 unless @large_arc == @clockwise
  cxp = sqrt * rx * y1p / ry
  cyp = - sqrt * ry * x1p / rx
  # F.6.5.3
  cx = cos_theta * cxp - sin_theta * cyp + (x1 + x2) / 2.0
  cy = sin_theta * cxp + cos_theta * cyp + (y1 + y2) / 2.0
  # F.6.5.5
  start_angle = compute_angle_to_x_axis((x1p - cxp), (y1p - cyp)) % 360
  # F.6.5.6 (modified bc we just need the end angle)
  end_angle = compute_angle_to_x_axis((-x1p - cxp), (-y1p - cyp)) % 360
  {cx: cx, cy: cy, a: rx, b: ry, start_angle: start_angle, end_angle: end_angle,
   inclination: @inclination, clockwise: @clockwise, max_curves: @max_curves}
end