module Prawn module Svg class Parser::Path # Raised if the SVG path cannot be parsed. InvalidError = Class.new(StandardError) 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 # # Parses an SVG path and returns a Prawn-compatible call tree. # def parse(data) @subpath_initial_point = @last_point = nil @previous_control_point = @previous_quadratic_control_point = nil @calls = [] data = data.gsub(/#{OUTSIDE_SPACE_REGEXP}$/, '') matched_commands = match_all(data, COMMAND_REGEXP) raise InvalidError, "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 @calls end private 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] @calls << ["move_to", @last_point] return run_path_command(relative ? 'l' : 'L', values) if values.any? when 'Z' # closepath if @subpath_initial_point #@calls << ["line_to", @subpath_initial_point] @calls << ["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] @calls << ["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] @calls << ["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] @calls << ["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] @calls << ["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] @calls << ["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] @calls << ["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] @calls << ["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| @calls << ["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 end end