source: Dev/trunk/d3/src/svg/line.js @ 76

function d3_svg_line(projection) {
  var x = d3_svg_lineX,
      y = d3_svg_lineY,
      interpolate = "linear",
      interpolator = d3_svg_lineInterpolators[interpolate],
      tension = .7;

  function line(d) {
    return d.length < 1 ? null : "M" + interpolator(projection(d3_svg_linePoints(this, d, x, y)), tension);
  }

  line.x = function(v) {
    if (!arguments.length) return x;
    x = v;
    return line;
  };

  line.y = function(v) {
    if (!arguments.length) return y;
    y = v;
    return line;
  };

  line.interpolate = function(v) {
    if (!arguments.length) return interpolate;
    interpolator = d3_svg_lineInterpolators[interpolate = v];
    return line;
  };

  line.tension = function(v) {
    if (!arguments.length) return tension;
    tension = v;
    return line;
  };

  return line;
}

d3.svg.line = function() {
  return d3_svg_line(Object);
};

// Converts the specified array of data into an array of points
// (x-y tuples), by evaluating the specified `x` and `y` functions on each
// data point. The `this` context of the evaluated functions is the specified
// "self" object; each function is passed the current datum and index.
function d3_svg_linePoints(self, d, x, y) {
  var points = [],
      i = -1,
      n = d.length,
      fx = typeof x === "function",
      fy = typeof y === "function",
      value;
  if (fx && fy) {
    while (++i < n) points.push([
      x.call(self, value = d[i], i),
      y.call(self, value, i)
    ]);
  } else if (fx) {
    while (++i < n) points.push([x.call(self, d[i], i), y]);
  } else if (fy) {
    while (++i < n) points.push([x, y.call(self, d[i], i)]);
  } else {
    while (++i < n) points.push([x, y]);
  }
  return points;
}

// The default `x` property, which references d[0].
function d3_svg_lineX(d) {
  return d[0];
}

// The default `y` property, which references d[1].
function d3_svg_lineY(d) {
  return d[1];
}

// The various interpolators supported by the `line` class.
var d3_svg_lineInterpolators = {
  "linear": d3_svg_lineLinear,
  "step-before": d3_svg_lineStepBefore,
  "step-after": d3_svg_lineStepAfter,
  "basis": d3_svg_lineBasis,
  "basis-open": d3_svg_lineBasisOpen,
  "basis-closed": d3_svg_lineBasisClosed,
  "bundle": d3_svg_lineBundle,
  "cardinal": d3_svg_lineCardinal,
  "cardinal-open": d3_svg_lineCardinalOpen,
  "cardinal-closed": d3_svg_lineCardinalClosed,
  "monotone": d3_svg_lineMonotone
};

// Linear interpolation; generates "L" commands.
function d3_svg_lineLinear(points) {
  var path = [],
      i = 0,
      n = points.length,
      p = points[0];
  path.push(p[0], ",", p[1]);
  while (++i < n) path.push("L", (p = points[i])[0], ",", p[1]);
  return path.join("");
}

// Step interpolation; generates "H" and "V" commands.
function d3_svg_lineStepBefore(points) {
  var path = [],
      i = 0,
      n = points.length,
      p = points[0];
  path.push(p[0], ",", p[1]);
  while (++i < n) path.push("V", (p = points[i])[1], "H", p[0]);
  return path.join("");
}

// Step interpolation; generates "H" and "V" commands.
function d3_svg_lineStepAfter(points) {
  var path = [],
      i = 0,
      n = points.length,
      p = points[0];
  path.push(p[0], ",", p[1]);
  while (++i < n) path.push("H", (p = points[i])[0], "V", p[1]);
  return path.join("");
}

// Open cardinal spline interpolation; generates "C" commands.
function d3_svg_lineCardinalOpen(points, tension) {
  return points.length < 4
      ? d3_svg_lineLinear(points)
      : points[1] + d3_svg_lineHermite(points.slice(1, points.length - 1),
        d3_svg_lineCardinalTangents(points, tension));
}

// Closed cardinal spline interpolation; generates "C" commands.
function d3_svg_lineCardinalClosed(points, tension) {
  return points.length < 3
      ? d3_svg_lineLinear(points)
      : points[0] + d3_svg_lineHermite((points.push(points[0]), points),
        d3_svg_lineCardinalTangents([points[points.length - 2]]
        .concat(points, [points[1]]), tension));
}

// Cardinal spline interpolation; generates "C" commands.
function d3_svg_lineCardinal(points, tension, closed) {
  return points.length < 3
      ? d3_svg_lineLinear(points)
      : points[0] + d3_svg_lineHermite(points,
        d3_svg_lineCardinalTangents(points, tension));
}

// Hermite spline construction; generates "C" commands.
function d3_svg_lineHermite(points, tangents) {
  if (tangents.length < 1
      || (points.length != tangents.length
      && points.length != tangents.length + 2)) {
    return d3_svg_lineLinear(points);
  }

  var quad = points.length != tangents.length,
      path = "",
      p0 = points[0],
      p = points[1],
      t0 = tangents[0],
      t = t0,
      pi = 1;

  if (quad) {
    path += "Q" + (p[0] - t0[0] * 2 / 3) + "," + (p[1] - t0[1] * 2 / 3)
        + "," + p[0] + "," + p[1];
    p0 = points[1];
    pi = 2;
  }

  if (tangents.length > 1) {
    t = tangents[1];
    p = points[pi];
    pi++;
    path += "C" + (p0[0] + t0[0]) + "," + (p0[1] + t0[1])
        + "," + (p[0] - t[0]) + "," + (p[1] - t[1])
        + "," + p[0] + "," + p[1];
    for (var i = 2; i < tangents.length; i++, pi++) {
      p = points[pi];
      t = tangents[i];
      path += "S" + (p[0] - t[0]) + "," + (p[1] - t[1])
          + "," + p[0] + "," + p[1];
    }
  }

  if (quad) {
    var lp = points[pi];
    path += "Q" + (p[0] + t[0] * 2 / 3) + "," + (p[1] + t[1] * 2 / 3)
        + "," + lp[0] + "," + lp[1];
  }

  return path;
}

// Generates tangents for a cardinal spline.
function d3_svg_lineCardinalTangents(points, tension) {
  var tangents = [],
      a = (1 - tension) / 2,
      p0,
      p1 = points[0],
      p2 = points[1],
      i = 1,
      n = points.length;
  while (++i < n) {
    p0 = p1;
    p1 = p2;
    p2 = points[i];
    tangents.push([a * (p2[0] - p0[0]), a * (p2[1] - p0[1])]);
  }
  return tangents;
}

// B-spline interpolation; generates "C" commands.
function d3_svg_lineBasis(points) {
  if (points.length < 3) return d3_svg_lineLinear(points);
  var path = [],
      i = 1,
      n = points.length,
      pi = points[0],
      x0 = pi[0],
      y0 = pi[1],
      px = [x0, x0, x0, (pi = points[1])[0]],
      py = [y0, y0, y0, pi[1]];
  path.push(x0, ",", y0);
  d3_svg_lineBasisBezier(path, px, py);
  while (++i < n) {
    pi = points[i];
    px.shift(); px.push(pi[0]);
    py.shift(); py.push(pi[1]);
    d3_svg_lineBasisBezier(path, px, py);
  }
  i = -1;
  while (++i < 2) {
    px.shift(); px.push(pi[0]);
    py.shift(); py.push(pi[1]);
    d3_svg_lineBasisBezier(path, px, py);
  }
  return path.join("");
}

// Open B-spline interpolation; generates "C" commands.
function d3_svg_lineBasisOpen(points) {
  if (points.length < 4) return d3_svg_lineLinear(points);
  var path = [],
      i = -1,
      n = points.length,
      pi,
      px = [0],
      py = [0];
  while (++i < 3) {
    pi = points[i];
    px.push(pi[0]);
    py.push(pi[1]);
  }
  path.push(d3_svg_lineDot4(d3_svg_lineBasisBezier3, px)
    + "," + d3_svg_lineDot4(d3_svg_lineBasisBezier3, py));
  --i; while (++i < n) {
    pi = points[i];
    px.shift(); px.push(pi[0]);
    py.shift(); py.push(pi[1]);
    d3_svg_lineBasisBezier(path, px, py);
  }
  return path.join("");
}

// Closed B-spline interpolation; generates "C" commands.
function d3_svg_lineBasisClosed(points) {
  var path,
      i = -1,
      n = points.length,
      m = n + 4,
      pi,
      px = [],
      py = [];
  while (++i < 4) {
    pi = points[i % n];
    px.push(pi[0]);
    py.push(pi[1]);
  }
  path = [
    d3_svg_lineDot4(d3_svg_lineBasisBezier3, px), ",",
    d3_svg_lineDot4(d3_svg_lineBasisBezier3, py)
  ];
  --i; while (++i < m) {
    pi = points[i % n];
    px.shift(); px.push(pi[0]);
    py.shift(); py.push(pi[1]);
    d3_svg_lineBasisBezier(path, px, py);
  }
  return path.join("");
}

function d3_svg_lineBundle(points, tension) {
  var n = points.length - 1,
      x0 = points[0][0],
      y0 = points[0][1],
      dx = points[n][0] - x0,
      dy = points[n][1] - y0,
      i = -1,
      p,
      t;
  while (++i <= n) {
    p = points[i];
    t = i / n;
    p[0] = tension * p[0] + (1 - tension) * (x0 + t * dx);
    p[1] = tension * p[1] + (1 - tension) * (y0 + t * dy);
  }
  return d3_svg_lineBasis(points);
}

// Returns the dot product of the given four-element vectors.
function d3_svg_lineDot4(a, b) {
  return a[0] * b[0] + a[1] * b[1] + a[2] * b[2] + a[3] * b[3];
}

// Matrix to transform basis (b-spline) control points to bezier
// control points. Derived from FvD 11.2.8.
var d3_svg_lineBasisBezier1 = [0, 2/3, 1/3, 0],
    d3_svg_lineBasisBezier2 = [0, 1/3, 2/3, 0],
    d3_svg_lineBasisBezier3 = [0, 1/6, 2/3, 1/6];

// Pushes a "C" Bézier curve onto the specified path array, given the
// two specified four-element arrays which define the control points.
function d3_svg_lineBasisBezier(path, x, y) {
  path.push(
      "C", d3_svg_lineDot4(d3_svg_lineBasisBezier1, x),
      ",", d3_svg_lineDot4(d3_svg_lineBasisBezier1, y),
      ",", d3_svg_lineDot4(d3_svg_lineBasisBezier2, x),
      ",", d3_svg_lineDot4(d3_svg_lineBasisBezier2, y),
      ",", d3_svg_lineDot4(d3_svg_lineBasisBezier3, x),
      ",", d3_svg_lineDot4(d3_svg_lineBasisBezier3, y));
}

// Computes the slope from points p0 to p1.
function d3_svg_lineSlope(p0, p1) {
  return (p1[1] - p0[1]) / (p1[0] - p0[0]);
}

// Compute three-point differences for the given points.
// http://en.wikipedia.org/wiki/Cubic_Hermite_spline#Finite_difference
function d3_svg_lineFiniteDifferences(points) {
  var i = 0,
      j = points.length - 1,
      m = [],
      p0 = points[0],
      p1 = points[1],
      d = m[0] = d3_svg_lineSlope(p0, p1);
  while (++i < j) {
    m[i] = d + (d = d3_svg_lineSlope(p0 = p1, p1 = points[i + 1]));
  }
  m[i] = d;
  return m;
}

// Interpolates the given points using Fritsch-Carlson Monotone cubic Hermite
// interpolation. Returns an array of tangent vectors. For details, see
// http://en.wikipedia.org/wiki/Monotone_cubic_interpolation
function d3_svg_lineMonotoneTangents(points) {
  var tangents = [],
      d,
      a,
      b,
      s,
      m = d3_svg_lineFiniteDifferences(points),
      i = -1,
      j = points.length - 1;

  // The first two steps are done by computing finite-differences:
  // 1. Compute the slopes of the secant lines between successive points.
  // 2. Initialize the tangents at every point as the average of the secants.

  // Then, for each segment

  while (++i < j) {
    d = d3_svg_lineSlope(points[i], points[i + 1]);

    // 3. If two successive yk = y{k + 1} are equal (i.e., d is zero), then set
    // mk = m{k + 1} = 0 as the spline connecting these points must be flat to
    // preserve monotonicity. Ignore step 4 and 5 for those k.

    if (Math.abs(d) < 1e-6) {
      m[i] = m[i + 1] = 0;
    } else {
      // 4. Let ak = mk / dk and bk = m{k + 1} / dk.
      a = m[i] / d;
      b = m[i + 1] / d;

      // 5. Prevent overshoot and ensure monotonicity by restricting the
      // magnitude of vector <ak, bk> to a circle of radius 3.
      s = a * a + b * b;
      if (s > 9) {
        s = d * 3 / Math.sqrt(s);
        m[i] = s * a;
        m[i + 1] = s * b;
      }
    }
  }

  // Compute the normalized tangent vector from the slopes. Note that if x is
  // not monotonic, it's possible that the slope will be infinite, so we protect
  // against NaN by setting the coordinate to zero.
  i = -1; while (++i <= j) {
    s = (points[Math.min(j, i + 1)][0] - points[Math.max(0, i - 1)][0])
      / (6 * (1 + m[i] * m[i]));
    tangents.push([s || 0, m[i] * s || 0]);
  }

  return tangents;
}

function d3_svg_lineMonotone(points) {
  return points.length < 3
      ? d3_svg_lineLinear(points)
      : points[0] +
        d3_svg_lineHermite(points, d3_svg_lineMonotoneTangents(points));
}