--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/toolkit/javascript/d3/src/svg/line.js Thu Apr 10 14:20:23 2014 +0200
@@ -0,0 +1,415 @@
+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 i = 0,
+ n = points.length,
+ p = points[0],
+ path = [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 i = 0,
+ n = points.length,
+ p = points[0],
+ path = [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 i = 0,
+ n = points.length,
+ p = points[0],
+ path = [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 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 = [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));
+}