Module: Postsvg::Translation::ArcConverter

Defined in:
lib/postsvg/translation/arc_converter.rb

Overview

SVG endpoint-to-center arc parametrization converter. Implements the algorithm documented in the SVG 1.1 implementation notes (appendix F.6.5). Returns the PS-style center parametrization: center x/y, normalized radii, rotation, and start/end angles.

Constant Summary collapse

EPSILON = 
1e-12

Class Method Summary collapse

Class Method Details

.angle_between(ux, uy, vx, vy) ⇒ Object

rubocop:enable Metrics/AbcSize, Metrics/MethodLength, Metrics/ParameterLists



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# File 'lib/postsvg/translation/arc_converter.rb', line 75

def angle_between(ux, uy, vx, vy)
  dot = ux * vx + uy * vy
  len = Math.sqrt((ux * ux + uy * uy) * (vx * vx + vy * vy))
  return 0.0 if len < EPSILON

  cos_val = (dot / len).clamp(-1.0, 1.0)
  sign = (ux * vy - uy * vx).negative? ? -1.0 : 1.0
  sign * Math.acos(cos_val)
end

.endpoint_to_center(x1:, y1:, rx:, ry:, x_axis_rotation:, large_arc:, sweep:, x2:, y2:) ⇒ Object

rubocop:disable Metrics/AbcSize, Metrics/MethodLength, Metrics/ParameterLists



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# File 'lib/postsvg/translation/arc_converter.rb', line 15

def endpoint_to_center(x1:, y1:, rx:, ry:, x_axis_rotation:,
                       large_arc:, sweep:, x2:, y2:)
  rx = rx.abs
  ry = ry.abs
  # If the endpoints coincide, the arc is degenerate.
  return [x1, y1, 0.0, 0.0, 0.0, 0.0, 0.0] if rx < EPSILON || ry < EPSILON

  phi = x_axis_rotation * Math::PI / 180.0
  cos_phi = Math.cos(phi)
  sin_phi = Math.sin(phi)

  # Step 1: rotate and scale (x1,y1) into the unit-circle frame.
  dx = (x1 - x2) / 2.0
  dy = (y1 - y2) / 2.0
  x1p =  cos_phi * dx + sin_phi * dy
  y1p = -sin_phi * dx + cos_phi * dy

  # Ensure radii are large enough; if not, scale them up.
  rx_sq = rx * rx
  ry_sq = ry * ry
  x1p_sq = x1p * x1p
  y1p_sq = y1p * y1p
  lambda = (x1p_sq / rx_sq) + (y1p_sq / ry_sq)
  if lambda > 1.0
    sqrt_lambda = Math.sqrt(lambda)
    rx *= sqrt_lambda
    ry *= sqrt_lambda
    rx_sq = rx * rx
    ry_sq = ry * ry
  end

  # Step 2: compute center (cx', cy') in the rotated frame.
  sign = (large_arc == sweep) ? -1 : 1
  num = rx_sq * ry_sq - rx_sq * y1p_sq - ry_sq * x1p_sq
  den = rx_sq * y1p_sq + ry_sq * x1p_sq
  den = EPSILON if den.abs < EPSILON
  coef = sign * Math.sqrt([num / den, 0.0].max)
  cxp =  coef * (rx * y1p) / ry
  cyp = -coef * (ry * x1p) / rx

  # Step 3: rotate (cx', cy') back into original frame.
  cx = cos_phi * cxp - sin_phi * cyp + (x1 + x2) / 2.0
  cy = sin_phi * cxp + cos_phi * cyp + (y1 + y2) / 2.0

  # Step 4: compute angles.
  ux = (x1p - cxp) / rx
  uy = (y1p - cyp) / ry
  vx = (-x1p - cxp) / rx
  vy = (-y1p - cyp) / ry

  theta1 = angle_between(1.0, 0.0, ux, uy)
  delta_theta = angle_between(ux, uy, vx, vy) % (2 * Math::PI)
  delta_theta -= 2 * Math::PI if !sweep && delta_theta.positive?

  theta2 = theta1 + delta_theta

  [cx, cy, rx, ry, phi, theta1 * 180.0 / Math::PI, theta2 * 180.0 / Math::PI]
end