arc.js

import constant from "./constant.js";
import {abs, acos, asin, atan2, cos, epsilon, halfPi, max, min, pi, sin, sqrt, tau} from "./math.js";
import {withPath} from "./path.js";

function arcInnerRadius(d) {
  return d.innerRadius;
}

function arcOuterRadius(d) {
  return d.outerRadius;
}

function arcStartAngle(d) {
  return d.startAngle;
}

function arcEndAngle(d) {
  return d.endAngle;
}

function arcPadAngle(d) {
  return d && d.padAngle; // Note: optional!
}

function intersect(x0, y0, x1, y1, x2, y2, x3, y3) {
  var x10 = x1 - x0, y10 = y1 - y0,
      x32 = x3 - x2, y32 = y3 - y2,
      t = y32 * x10 - x32 * y10;
  if (t * t < epsilon) return;
  t = (x32 * (y0 - y2) - y32 * (x0 - x2)) / t;
  return [x0 + t * x10, y0 + t * y10];
}

// Compute perpendicular offset line of length rc.
// http://mathworld.wolfram.com/Circle-LineIntersection.html
function cornerTangents(x0, y0, x1, y1, r1, rc, cw) {
  var x01 = x0 - x1,
      y01 = y0 - y1,
      lo = (cw ? rc : -rc) / sqrt(x01 * x01 + y01 * y01),
      ox = lo * y01,
      oy = -lo * x01,
      x11 = x0 + ox,
      y11 = y0 + oy,
      x10 = x1 + ox,
      y10 = y1 + oy,
      x00 = (x11 + x10) / 2,
      y00 = (y11 + y10) / 2,
      dx = x10 - x11,
      dy = y10 - y11,
      d2 = dx * dx + dy * dy,
      r = r1 - rc,
      D = x11 * y10 - x10 * y11,
      d = (dy < 0 ? -1 : 1) * sqrt(max(0, r * r * d2 - D * D)),
      cx0 = (D * dy - dx * d) / d2,
      cy0 = (-D * dx - dy * d) / d2,
      cx1 = (D * dy + dx * d) / d2,
      cy1 = (-D * dx + dy * d) / d2,
      dx0 = cx0 - x00,
      dy0 = cy0 - y00,
      dx1 = cx1 - x00,
      dy1 = cy1 - y00;

  // Pick the closer of the two intersection points.
  // TODO Is there a faster way to determine which intersection to use?
  if (dx0 * dx0 + dy0 * dy0 > dx1 * dx1 + dy1 * dy1) cx0 = cx1, cy0 = cy1;

  return {
    cx: cx0,
    cy: cy0,
    x01: -ox,
    y01: -oy,
    x11: cx0 * (r1 / r - 1),
    y11: cy0 * (r1 / r - 1)
  };
}

export default function() {
  var innerRadius = arcInnerRadius,
      outerRadius = arcOuterRadius,
      cornerRadius = constant(0),
      padRadius = null,
      startAngle = arcStartAngle,
      endAngle = arcEndAngle,
      padAngle = arcPadAngle,
      context = null,
      path = withPath(arc);

  function arc() {
    var buffer,
        r,
        r0 = +innerRadius.apply(this, arguments),
        r1 = +outerRadius.apply(this, arguments),
        a0 = startAngle.apply(this, arguments) - halfPi,
        a1 = endAngle.apply(this, arguments) - halfPi,
        da = abs(a1 - a0),
        cw = a1 > a0;

    if (!context) context = buffer = path();

    // Ensure that the outer radius is always larger than the inner radius.
    if (r1 < r0) r = r1, r1 = r0, r0 = r;

    // Is it a point?
    if (!(r1 > epsilon)) context.moveTo(0, 0);

    // Or is it a circle or annulus?
    else if (da > tau - epsilon) {
      context.moveTo(r1 * cos(a0), r1 * sin(a0));
      context.arc(0, 0, r1, a0, a1, !cw);
      if (r0 > epsilon) {
        context.moveTo(r0 * cos(a1), r0 * sin(a1));
        context.arc(0, 0, r0, a1, a0, cw);
      }
    }

    // Or is it a circular or annular sector?
    else {
      var a01 = a0,
          a11 = a1,
          a00 = a0,
          a10 = a1,
          da0 = da,
          da1 = da,
          ap = padAngle.apply(this, arguments) / 2,
          rp = (ap > epsilon) && (padRadius ? +padRadius.apply(this, arguments) : sqrt(r0 * r0 + r1 * r1)),
          rc = min(abs(r1 - r0) / 2, +cornerRadius.apply(this, arguments)),
          rc0 = rc,
          rc1 = rc,
          t0,
          t1;

      // Apply padding? Note that since r1 ≥ r0, da1 ≥ da0.
      if (rp > epsilon) {
        var p0 = asin(rp / r0 * sin(ap)),
            p1 = asin(rp / r1 * sin(ap));
        if ((da0 -= p0 * 2) > epsilon) p0 *= (cw ? 1 : -1), a00 += p0, a10 -= p0;
        else da0 = 0, a00 = a10 = (a0 + a1) / 2;
        if ((da1 -= p1 * 2) > epsilon) p1 *= (cw ? 1 : -1), a01 += p1, a11 -= p1;
        else da1 = 0, a01 = a11 = (a0 + a1) / 2;
      }

      var x01 = r1 * cos(a01),
          y01 = r1 * sin(a01),
          x10 = r0 * cos(a10),
          y10 = r0 * sin(a10);

      // Apply rounded corners?
      if (rc > epsilon) {
        var x11 = r1 * cos(a11),
            y11 = r1 * sin(a11),
            x00 = r0 * cos(a00),
            y00 = r0 * sin(a00),
            oc;

        // Restrict the corner radius according to the sector angle. If this
        // intersection fails, it’s probably because the arc is too small, so
        // disable the corner radius entirely.
        if (da < pi) {
          if (oc = intersect(x01, y01, x00, y00, x11, y11, x10, y10)) {
            var ax = x01 - oc[0],
                ay = y01 - oc[1],
                bx = x11 - oc[0],
                by = y11 - oc[1],
                kc = 1 / sin(acos((ax * bx + ay * by) / (sqrt(ax * ax + ay * ay) * sqrt(bx * bx + by * by))) / 2),
                lc = sqrt(oc[0] * oc[0] + oc[1] * oc[1]);
            rc0 = min(rc, (r0 - lc) / (kc - 1));
            rc1 = min(rc, (r1 - lc) / (kc + 1));
          } else {
            rc0 = rc1 = 0;
          }
        }
      }

      // Is the sector collapsed to a line?
      if (!(da1 > epsilon)) context.moveTo(x01, y01);

      // Does the sector’s outer ring have rounded corners?
      else if (rc1 > epsilon) {
        t0 = cornerTangents(x00, y00, x01, y01, r1, rc1, cw);
        t1 = cornerTangents(x11, y11, x10, y10, r1, rc1, cw);

        context.moveTo(t0.cx + t0.x01, t0.cy + t0.y01);

        // Have the corners merged?
        if (rc1 < rc) context.arc(t0.cx, t0.cy, rc1, atan2(t0.y01, t0.x01), atan2(t1.y01, t1.x01), !cw);

        // Otherwise, draw the two corners and the ring.
        else {
          context.arc(t0.cx, t0.cy, rc1, atan2(t0.y01, t0.x01), atan2(t0.y11, t0.x11), !cw);
          context.arc(0, 0, r1, atan2(t0.cy + t0.y11, t0.cx + t0.x11), atan2(t1.cy + t1.y11, t1.cx + t1.x11), !cw);
          context.arc(t1.cx, t1.cy, rc1, atan2(t1.y11, t1.x11), atan2(t1.y01, t1.x01), !cw);
        }
      }

      // Or is the outer ring just a circular arc?
      else context.moveTo(x01, y01), context.arc(0, 0, r1, a01, a11, !cw);

      // Is there no inner ring, and it’s a circular sector?
      // Or perhaps it’s an annular sector collapsed due to padding?
      if (!(r0 > epsilon) || !(da0 > epsilon)) context.lineTo(x10, y10);

      // Does the sector’s inner ring (or point) have rounded corners?
      else if (rc0 > epsilon) {
        t0 = cornerTangents(x10, y10, x11, y11, r0, -rc0, cw);
        t1 = cornerTangents(x01, y01, x00, y00, r0, -rc0, cw);

        context.lineTo(t0.cx + t0.x01, t0.cy + t0.y01);

        // Have the corners merged?
        if (rc0 < rc) context.arc(t0.cx, t0.cy, rc0, atan2(t0.y01, t0.x01), atan2(t1.y01, t1.x01), !cw);

        // Otherwise, draw the two corners and the ring.
        else {
          context.arc(t0.cx, t0.cy, rc0, atan2(t0.y01, t0.x01), atan2(t0.y11, t0.x11), !cw);
          context.arc(0, 0, r0, atan2(t0.cy + t0.y11, t0.cx + t0.x11), atan2(t1.cy + t1.y11, t1.cx + t1.x11), cw);
          context.arc(t1.cx, t1.cy, rc0, atan2(t1.y11, t1.x11), atan2(t1.y01, t1.x01), !cw);
        }
      }

      // Or is the inner ring just a circular arc?
      else context.arc(0, 0, r0, a10, a00, cw);
    }

    context.closePath();

    if (buffer) return context = null, buffer + "" || null;
  }

  arc.centroid = function() {
    var r = (+innerRadius.apply(this, arguments) + +outerRadius.apply(this, arguments)) / 2,
        a = (+startAngle.apply(this, arguments) + +endAngle.apply(this, arguments)) / 2 - pi / 2;
    return [cos(a) * r, sin(a) * r];
  };

  arc.innerRadius = function(_) {
    return arguments.length ? (innerRadius = typeof _ === "function" ? _ : constant(+_), arc) : innerRadius;
  };

  arc.outerRadius = function(_) {
    return arguments.length ? (outerRadius = typeof _ === "function" ? _ : constant(+_), arc) : outerRadius;
  };

  arc.cornerRadius = function(_) {
    return arguments.length ? (cornerRadius = typeof _ === "function" ? _ : constant(+_), arc) : cornerRadius;
  };

  arc.padRadius = function(_) {
    return arguments.length ? (padRadius = _ == null ? null : typeof _ === "function" ? _ : constant(+_), arc) : padRadius;
  };

  arc.startAngle = function(_) {
    return arguments.length ? (startAngle = typeof _ === "function" ? _ : constant(+_), arc) : startAngle;
  };

  arc.endAngle = function(_) {
    return arguments.length ? (endAngle = typeof _ === "function" ? _ : constant(+_), arc) : endAngle;
  };

  arc.padAngle = function(_) {
    return arguments.length ? (padAngle = typeof _ === "function" ? _ : constant(+_), arc) : padAngle;
  };

  arc.context = function(_) {
    return arguments.length ? ((context = _ == null ? null : _), arc) : context;
  };

  return arc;
}