class Prawn::SVG::Elements::Path < Prawn::SVG::Elements::Base
  INSIDE_SPACE_REGEXP = /[ \t\r\n,]*/
  OUTSIDE_SPACE_REGEXP = /[ \t\r\n]*/
  INSIDE_REGEXP = /#{INSIDE_SPACE_REGEXP}([+-]?(?:[0-9]+(?:\.[0-9]*)?|\.[0-9]+)(?:(?<=[0-9])e[+-]?[0-9]+)?)/
  VALUES_REGEXP = /^#{INSIDE_REGEXP}/
  COMMAND_REGEXP = /^#{OUTSIDE_SPACE_REGEXP}([A-Za-z])((?:#{INSIDE_REGEXP})*)#{OUTSIDE_SPACE_REGEXP}/

  FLOAT_ERROR_DELTA = 1e-10

  attr_reader :commands

  def parse
    require_attributes 'd'

    @commands = []

    data = attributes["d"].gsub(/#{OUTSIDE_SPACE_REGEXP}$/, '')

    matched_commands = match_all(data, COMMAND_REGEXP)
    raise SkipElementError, "Invalid/unsupported syntax for SVG path data" if matched_commands.nil?

    matched_commands.each do |matched_command|
      command = matched_command[1]
      matched_values = match_all(matched_command[2], VALUES_REGEXP)
      raise "should be impossible to have invalid inside data, but we ended up here" if matched_values.nil?
      values = matched_values.collect {|value| value[1].to_f}
      run_path_command(command, values)
    end
  end

  def apply
    add_call 'join_style', :bevel

    @commands.collect do |command, args|
      if args && args.length > 0
        point_to = [x(args[0]), y(args[1])]
        if command == 'curve_to'
          opts = {:bounds => [[x(args[2]), y(args[3])], [x(args[4]), y(args[5])]]}
        end
        add_call command, point_to, opts
      else
        add_call command
      end
    end
  end

  def bounding_box
    x1, x2 = @commands.map {|_, args| x(args[0]) if args}.compact.minmax
    y2, y1 = @commands.map {|_, args| y(args[1]) if args}.compact.minmax

    [x1, y1, x2, y2]
  end

  protected

  def run_path_command(command, values)
    upcase_command = command.upcase
    relative = command != upcase_command

    case upcase_command
    when 'M' # moveto
      x = values.shift
      y = values.shift

      if relative && @last_point
        x += @last_point.first
        y += @last_point.last
      end

      @last_point = @subpath_initial_point = [x, y]
      @commands << ["move_to", @last_point]

      return run_path_command(relative ? 'l' : 'L', values) if values.any?

    when 'Z' # closepath
      if @subpath_initial_point
        #@commands << ["line_to", @subpath_initial_point]
        @commands << ["close_path"]
        @last_point = @subpath_initial_point
      end

    when 'L' # lineto
      while values.any?
        x = values.shift
        y = values.shift
        if relative && @last_point
          x += @last_point.first
          y += @last_point.last
        end
        @last_point = [x, y]
        @commands << ["line_to", @last_point]
      end

    when 'H' # horizontal lineto
      while values.any?
        x = values.shift
        x += @last_point.first if relative && @last_point
        @last_point = [x, @last_point.last]
        @commands << ["line_to", @last_point]
      end

    when 'V' # vertical lineto
      while values.any?
        y = values.shift
        y += @last_point.last if relative && @last_point
        @last_point = [@last_point.first, y]
        @commands << ["line_to", @last_point]
      end

    when 'C' # curveto
      while values.any?
        x1, y1, x2, y2, x, y = (1..6).collect {values.shift}
        if relative && @last_point
          x += @last_point.first
          x1 += @last_point.first
          x2 += @last_point.first
          y += @last_point.last
          y1 += @last_point.last
          y2 += @last_point.last
        end

        @last_point = [x, y]
        @previous_control_point = [x2, y2]
        @commands << ["curve_to", [x, y, x1, y1, x2, y2]]
      end

    when 'S' # shorthand/smooth curveto
      while values.any?
        x2, y2, x, y = (1..4).collect {values.shift}
        if relative && @last_point
          x += @last_point.first
          x2 += @last_point.first
          y += @last_point.last
          y2 += @last_point.last
        end

        if @previous_control_point
          x1 = 2 * @last_point.first - @previous_control_point.first
          y1 = 2 * @last_point.last - @previous_control_point.last
        else
          x1, y1 = @last_point
        end

        @last_point = [x, y]
        @previous_control_point = [x2, y2]
        @commands << ["curve_to", [x, y, x1, y1, x2, y2]]
      end

    when 'Q', 'T' # quadratic curveto
      while values.any?
        if shorthand = upcase_command == 'T'
          x, y = (1..2).collect {values.shift}
        else
          x1, y1, x, y = (1..4).collect {values.shift}
        end

        if relative && @last_point
          x += @last_point.first
          x1 += @last_point.first if x1
          y += @last_point.last
          y1 += @last_point.last if y1
        end

        if shorthand
          if @previous_quadratic_control_point
            x1 = 2 * @last_point.first - @previous_quadratic_control_point.first
            y1 = 2 * @last_point.last - @previous_quadratic_control_point.last
          else
            x1, y1 = @last_point
          end
        end

        # convert from quadratic to cubic
        cx1 = @last_point.first + (x1 - @last_point.first) * 2 / 3.0
        cy1 = @last_point.last + (y1 - @last_point.last) * 2 / 3.0
        cx2 = cx1 + (x - @last_point.first) / 3.0
        cy2 = cy1 + (y - @last_point.last) / 3.0

        @last_point = [x, y]
        @previous_quadratic_control_point = [x1, y1]

        @commands << ["curve_to", [x, y, cx1, cy1, cx2, cy2]]
      end

    when 'A'
      return unless @last_point

      while values.any?
        rx, ry, phi, fa, fs, x2, y2 = (1..7).collect {values.shift}
        x1, y1 = @last_point

        return if rx.zero? && ry.zero?

        if relative
          x2 += x1
          y2 += y1
        end

        # Normalise values as per F.6.2
        rx = rx.abs
        ry = ry.abs
        phi = (phi % 360) * 2 * Math::PI / 360.0

        # F.6.2: If the endpoints (x1, y1) and (x2, y2) are identical, then this is equivalent to omitting the elliptical arc segment entirely.
        return if within_float_delta?(x1, x2) && within_float_delta?(y1, y2)

        # F.6.2: If rx = 0 or ry = 0 then this arc is treated as a straight line segment (a "lineto") joining the endpoints.
        if within_float_delta?(rx, 0) || within_float_delta?(ry, 0)
          @last_point = [x2, y2]
          @commands << ["line_to", @last_point]
          return
        end

        # We need to get the center co-ordinates, as well as the angles from the X axis to the start and end
        # points.  To do this, we use the algorithm documented in the SVG specification section F.6.5.

        # F.6.5.1
        xp1 = Math.cos(phi) * ((x1-x2)/2.0) + Math.sin(phi) * ((y1-y2)/2.0)
        yp1 = -Math.sin(phi) * ((x1-x2)/2.0) + Math.cos(phi) * ((y1-y2)/2.0)

        # F.6.6.2
        r2x = rx * rx
        r2y = ry * ry
        hat = xp1 * xp1 / r2x + yp1 * yp1 / r2y
        if hat > 1
          rx *= Math.sqrt(hat)
          ry *= Math.sqrt(hat)
        end

        # F.6.5.2
        r2x = rx * rx
        r2y = ry * ry
        square = (r2x * r2y - r2x * yp1 * yp1 - r2y * xp1 * xp1) / (r2x * yp1 * yp1 + r2y * xp1 * xp1)
        square = 0 if square < 0 && square > -FLOAT_ERROR_DELTA # catch rounding errors
        base = Math.sqrt(square)
        base *= -1 if fa == fs
        cpx = base * rx * yp1 / ry
        cpy = base * -ry * xp1 / rx

        # F.6.5.3
        cx = Math.cos(phi) * cpx + -Math.sin(phi) * cpy + (x1 + x2) / 2
        cy = Math.sin(phi) * cpx + Math.cos(phi) * cpy + (y1 + y2) / 2

        # F.6.5.5
        vx = (xp1 - cpx) / rx
        vy = (yp1 - cpy) / ry
        theta_1 = Math.acos(vx / Math.sqrt(vx * vx + vy * vy))
        theta_1 *= -1 if vy < 0

        # F.6.5.6
        ux = vx
        uy = vy
        vx = (-xp1 - cpx) / rx
        vy = (-yp1 - cpy) / ry

        numerator = ux * vx + uy * vy
        denominator = Math.sqrt(ux * ux + uy * uy) * Math.sqrt(vx * vx + vy * vy)
        division = numerator / denominator
        division = -1 if division < -1 # for rounding errors

        d_theta = Math.acos(division) % (2 * Math::PI)
        d_theta *= -1 if ux * vy - uy * vx < 0

        # Adjust range
        if fs == 0
          d_theta -= 2 * Math::PI if d_theta > 0
        else
          d_theta += 2 * Math::PI if d_theta < 0
        end

        theta_2 = theta_1 + d_theta

        calculate_bezier_curve_points_for_arc(cx, cy, rx, ry, theta_1, theta_2, phi).each do |points|
          @commands << ["curve_to", points[:p2] + points[:q1] + points[:q2]]
          @last_point = points[:p2]
        end
      end
    end

    @previous_control_point = nil unless %w(C S).include?(upcase_command)
    @previous_quadratic_control_point = nil unless %w(Q T).include?(upcase_command)
  end

  def within_float_delta?(a, b)
    (a - b).abs < FLOAT_ERROR_DELTA
  end

  def match_all(string, regexp) # regexp must start with ^
    result = []
    while string != ""
      matches = string.match(regexp)
      result << matches
      return if matches.nil?
      string = matches.post_match
    end
    result
  end

  def calculate_eta_from_lambda(a, b, lambda_1, lambda_2)
    # 2.2.1
    eta1 = Math.atan2(Math.sin(lambda_1) / b, Math.cos(lambda_1) / a)
    eta2 = Math.atan2(Math.sin(lambda_2) / b, Math.cos(lambda_2) / a)

    # ensure eta1 <= eta2 <= eta1 + 2*PI
    eta2 -= 2 * Math::PI * ((eta2 - eta1) / (2 * Math::PI)).floor
    eta2 += 2 * Math::PI if lambda_2 - lambda_1 > Math::PI && eta2 - eta1 < Math::PI

    [eta1, eta2]
  end

  # Convert the elliptical arc to a cubic bézier curve using this algorithm:
  # http://www.spaceroots.org/documents/ellipse/elliptical-arc.pdf
  def calculate_bezier_curve_points_for_arc(cx, cy, a, b, lambda_1, lambda_2, theta)
    e = lambda do |eta|
      [
        cx + a * Math.cos(theta) * Math.cos(eta) - b * Math.sin(theta) * Math.sin(eta),
        cy + a * Math.sin(theta) * Math.cos(eta) + b * Math.cos(theta) * Math.sin(eta)
      ]
    end

    ep = lambda do |eta|
      [
        -a * Math.cos(theta) * Math.sin(eta) - b * Math.sin(theta) * Math.cos(eta),
        -a * Math.sin(theta) * Math.sin(eta) + b * Math.cos(theta) * Math.cos(eta)
      ]
    end

    iterations = 1
    d_lambda = lambda_2 - lambda_1

    while iterations < 1024
      if d_lambda.abs <= Math::PI / 2.0
        # TODO : run error algorithm, see whether it meets threshold or not
        # puts "error = #{calculate_curve_approximation_error(a, b, eta1, eta1 + d_eta)}"
        break
      end
      iterations *= 2
      d_lambda = (lambda_2 - lambda_1) / iterations
    end

    (0...iterations).collect do |iteration|
      eta_a, eta_b = calculate_eta_from_lambda(a, b, lambda_1+iteration*d_lambda, lambda_1+(iteration+1)*d_lambda)
      d_eta = eta_b - eta_a

      alpha = Math.sin(d_eta) * ((Math.sqrt(4 + 3 * Math.tan(d_eta / 2) ** 2) - 1) / 3)

      x1, y1 = e[eta_a]
      x2, y2 = e[eta_b]

      ep_eta1_x, ep_eta1_y = ep[eta_a]
      q1_x = x1 + alpha * ep_eta1_x
      q1_y = y1 + alpha * ep_eta1_y

      ep_eta2_x, ep_eta2_y = ep[eta_b]
      q2_x = x2 - alpha * ep_eta2_x
      q2_y = y2 - alpha * ep_eta2_y

      {:p2 => [x2, y2], :q1 => [q1_x, q1_y], :q2 => [q2_x, q2_y]}
    end
  end

  ERROR_COEFFICIENTS_A = [
    [
      [3.85268, -21.229, -0.330434, 0.0127842],
      [-1.61486, 0.706564, 0.225945, 0.263682],
      [-0.910164, 0.388383, 0.00551445, 0.00671814],
      [-0.630184, 0.192402, 0.0098871, 0.0102527]
    ],
    [
      [-0.162211, 9.94329, 0.13723, 0.0124084],
      [-0.253135, 0.00187735, 0.0230286, 0.01264],
      [-0.0695069, -0.0437594, 0.0120636, 0.0163087],
      [-0.0328856, -0.00926032, -0.00173573, 0.00527385]
    ]
  ]

  ERROR_COEFFICIENTS_B = [
    [
      [0.0899116, -19.2349, -4.11711, 0.183362],
      [0.138148, -1.45804, 1.32044, 1.38474],
      [0.230903, -0.450262, 0.219963, 0.414038],
      [0.0590565, -0.101062, 0.0430592, 0.0204699]
    ],
    [
      [0.0164649, 9.89394, 0.0919496, 0.00760802],
      [0.0191603, -0.0322058, 0.0134667, -0.0825018],
      [0.0156192, -0.017535, 0.00326508, -0.228157],
      [-0.0236752, 0.0405821, -0.0173086, 0.176187]
    ]
  ]

  def calculate_curve_approximation_error(a, b, eta1, eta2)
    b_over_a = b / a
    coefficents = b_over_a < 0.25 ? ERROR_COEFFICIENTS_A : ERROR_COEFFICIENTS_B

    c = lambda do |i|
      (0..3).inject(0) do |accumulator, j|
        coef = coefficents[i][j]
        accumulator + ((coef[0] * b_over_a**2 + coef[1] * b_over_a + coef[2]) / (b_over_a * coef[3])) * Math.cos(j * (eta1 + eta2))
      end
    end

    ((0.001 * b_over_a**2 + 4.98 * b_over_a + 0.207) / (b_over_a * 0.0067)) * a * Math.exp(c[0] + c[1] * (eta2 - eta1))
  end
end