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484 lines
16 KiB
484 lines
16 KiB
/* The MIT License
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Copyright (c) 2011 by Michael Zinsmaier and nergal.dev
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Copyright (c) 2012 by Thomas Ritou
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Permission is hereby granted, free of charge, to any person obtaining a copy
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of this software and associated documentation files (the "Software"), to deal
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in the Software without restriction, including without limitation the rights
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to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in
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all copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
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THE SOFTWARE.
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*/
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/*
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____________________________________________________
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what it is:
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____________________________________________________
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curvedLines is a plugin for flot, that tries to display lines in a smoother way.
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This is achieved through adding of more data points. The plugin is a data processor and can thus be used
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in combination with standard line / point rendering options.
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=> 1) with large data sets you may get trouble
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=> 2) if you want to display the points too, you have to plot them as 2nd data series over the lines
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=> 3) consecutive x data points are not allowed to have the same value
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Feel free to further improve the code
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____________________________________________________
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how to use it:
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____________________________________________________
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var d1 = [[5,5],[7,3],[9,12]];
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var options = { series: { curvedLines: { active: true }}};
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$.plot($("#placeholder"), [{data: d1, lines: { show: true}, curvedLines: {apply: true}}], options);
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_____________________________________________________
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options:
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_____________________________________________________
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active: bool true => plugin can be used
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apply: bool true => series will be drawn as curved line
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monotonicFit: bool true => uses monotone cubic interpolation (preserve monotonicity)
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tension: int defines the tension parameter of the hermite spline interpolation (no effect if monotonicFit is set)
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nrSplinePoints: int defines the number of sample points (of the spline) in between two consecutive points
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deprecated options from flot prior to 1.0.0:
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------------------------------------------------
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legacyOverride bool true => use old default
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OR
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legacyOverride optionArray
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{
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fit: bool true => forces the max,mins of the curve to be on the datapoints
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curvePointFactor int defines how many "virtual" points are used per "real" data point to
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emulate the curvedLines (points total = real points * curvePointFactor)
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fitPointDist: int defines the x axis distance of the additional two points that are used
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} to enforce the min max condition.
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*/
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/*
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* v0.1 initial commit
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* v0.15 negative values should work now (outcommented a negative -> 0 hook hope it does no harm)
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* v0.2 added fill option (thanks to monemihir) and multi axis support (thanks to soewono effendi)
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* v0.3 improved saddle handling and added basic handling of Dates
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* v0.4 rewritten fill option (thomas ritou) mostly from original flot code (now fill between points rather than to graph bottom), corrected fill Opacity bug
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* v0.5 rewritten instead of implementing a own draw function CurvedLines is now based on the processDatapoints flot hook (credits go to thomas ritou).
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* This change breakes existing code however CurvedLines are now just many tiny straight lines to flot and therefore all flot lines options (like gradient fill,
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* shadow) are now supported out of the box
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* v0.6 flot 0.8 compatibility and some bug fixes
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* v0.6.x changed versioning schema
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*
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* v1.0.0 API Break marked existing implementation/options as deprecated
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* v1.1.0 added the new curved line calculations based on hermite splines
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* v1.1.1 added a rough parameter check to make sure the new options are used
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*/
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(function($) {
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var options = {
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series : {
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curvedLines : {
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active : false,
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apply : false,
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monotonicFit : false,
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tension : 0.5,
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nrSplinePoints : 20,
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legacyOverride : undefined
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}
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}
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};
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function init(plot) {
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plot.hooks.processOptions.push(processOptions);
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//if the plugin is active register processDatapoints method
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function processOptions(plot, options) {
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if (options.series.curvedLines.active) {
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plot.hooks.processDatapoints.unshift(processDatapoints);
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}
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}
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//only if the plugin is active
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function processDatapoints(plot, series, datapoints) {
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var nrPoints = datapoints.points.length / datapoints.pointsize;
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var EPSILON = 0.005;
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//detects missplaced legacy parameters (prior v1.x.x) in the options object
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//this can happen if somebody upgrades to v1.x.x without adjusting the parameters or uses old examples
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var invalidLegacyOptions = hasInvalidParameters(series.curvedLines);
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if (!invalidLegacyOptions && series.curvedLines.apply == true && series.originSeries === undefined && nrPoints > (1 + EPSILON)) {
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if (series.lines.fill) {
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var pointsTop = calculateCurvePoints(datapoints, series.curvedLines, 1);
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var pointsBottom = calculateCurvePoints(datapoints, series.curvedLines, 2);
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//flot makes sure for us that we've got a second y point if fill is true !
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//Merge top and bottom curve
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datapoints.pointsize = 3;
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datapoints.points = [];
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var j = 0;
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var k = 0;
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var i = 0;
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var ps = 2;
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while (i < pointsTop.length || j < pointsBottom.length) {
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if (pointsTop[i] == pointsBottom[j]) {
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datapoints.points[k] = pointsTop[i];
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datapoints.points[k + 1] = pointsTop[i + 1];
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datapoints.points[k + 2] = pointsBottom[j + 1];
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j += ps;
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i += ps;
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} else if (pointsTop[i] < pointsBottom[j]) {
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datapoints.points[k] = pointsTop[i];
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datapoints.points[k + 1] = pointsTop[i + 1];
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datapoints.points[k + 2] = k > 0 ? datapoints.points[k - 1] : null;
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i += ps;
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} else {
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datapoints.points[k] = pointsBottom[j];
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datapoints.points[k + 1] = k > 1 ? datapoints.points[k - 2] : null;
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datapoints.points[k + 2] = pointsBottom[j + 1];
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j += ps;
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}
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k += 3;
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}
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} else if (series.lines.lineWidth > 0) {
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datapoints.points = calculateCurvePoints(datapoints, series.curvedLines, 1);
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datapoints.pointsize = 2;
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}
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}
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}
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function calculateCurvePoints(datapoints, curvedLinesOptions, yPos) {
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if ( typeof curvedLinesOptions.legacyOverride != 'undefined' && curvedLinesOptions.legacyOverride != false) {
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var defaultOptions = {
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fit : false,
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curvePointFactor : 20,
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fitPointDist : undefined
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};
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var legacyOptions = jQuery.extend(defaultOptions, curvedLinesOptions.legacyOverride);
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return calculateLegacyCurvePoints(datapoints, legacyOptions, yPos);
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}
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return calculateSplineCurvePoints(datapoints, curvedLinesOptions, yPos);
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}
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function calculateSplineCurvePoints(datapoints, curvedLinesOptions, yPos) {
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var points = datapoints.points;
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var ps = datapoints.pointsize;
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//create interpolant fuction
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var splines = createHermiteSplines(datapoints, curvedLinesOptions, yPos);
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var result = [];
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//sample the function
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// (the result is intependent from the input data =>
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// it is ok to alter the input after this method)
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var j = 0;
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for (var i = 0; i < points.length - ps; i += ps) {
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var curX = i;
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var curY = i + yPos;
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var xStart = points[curX];
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var xEnd = points[curX + ps];
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var xStep = (xEnd - xStart) / Number(curvedLinesOptions.nrSplinePoints);
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//add point
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result.push(points[curX]);
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result.push(points[curY]);
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//add curve point
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for (var x = (xStart += xStep); x < xEnd; x += xStep) {
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result.push(x);
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result.push(splines[j](x));
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}
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j++;
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}
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//add last point
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result.push(points[points.length - ps]);
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result.push(points[points.length - ps + yPos]);
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return result;
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}
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// Creates an array of splines, one for each segment of the original curve. Algorithm based on the wikipedia articles:
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//
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// http://de.wikipedia.org/w/index.php?title=Kubisch_Hermitescher_Spline&oldid=130168003 and
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// http://en.wikipedia.org/w/index.php?title=Monotone_cubic_interpolation&oldid=622341725 and the description of Fritsch-Carlson from
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// http://math.stackexchange.com/questions/45218/implementation-of-monotone-cubic-interpolation
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// for a detailed description see https://github.com/MichaelZinsmaier/CurvedLines/docu
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function createHermiteSplines(datapoints, curvedLinesOptions, yPos) {
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var points = datapoints.points;
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var ps = datapoints.pointsize;
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// preparation get length (x_{k+1} - x_k) and slope s=(p_{k+1} - p_k) / (x_{k+1} - x_k) of the segments
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var segmentLengths = [];
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var segmentSlopes = [];
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for (var i = 0; i < points.length - ps; i += ps) {
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var curX = i;
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var curY = i + yPos;
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var dx = points[curX + ps] - points[curX];
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var dy = points[curY + ps] - points[curY];
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segmentLengths.push(dx);
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segmentSlopes.push(dy / dx);
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}
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//get the values for the desired gradients m_k for all points k
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//depending on the used method the formula is different
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var gradients = [segmentSlopes[0]];
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if (curvedLinesOptions.monotonicFit) {
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// Fritsch Carlson
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for (var i = 1; i < segmentLengths.length; i++) {
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var slope = segmentSlopes[i];
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var prev_slope = segmentSlopes[i - 1];
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if (slope * prev_slope <= 0) { // sign(prev_slope) != sign(slpe)
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gradients.push(0);
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} else {
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var length = segmentLengths[i];
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var prev_length = segmentLengths[i - 1];
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var common = length + prev_length;
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//m = 3 (prev_length + length) / ((2 length + prev_length) / prev_slope + (length + 2 prev_length) / slope)
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gradients.push(3 * common / ((common + length) / prev_slope + (common + prev_length) / slope));
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}
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}
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} else {
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// Cardinal spline with t € [0,1]
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// Catmull-Rom for t = 0
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for (var i = ps; i < points.length - ps; i += ps) {
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var curX = i;
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var curY = i + yPos;
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gradients.push(Number(curvedLinesOptions.tension) * (points[curY + ps] - points[curY - ps]) / (points[curX + ps] - points[curX - ps]));
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}
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}
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gradients.push(segmentSlopes[segmentSlopes.length - 1]);
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//get the two major coefficients (c'_{oef1} and c'_{oef2}) for each segment spline
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var coefs1 = [];
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var coefs2 = [];
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for (i = 0; i < segmentLengths.length; i++) {
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var m_k = gradients[i];
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var m_k_plus = gradients[i + 1];
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var slope = segmentSlopes[i];
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var invLength = 1 / segmentLengths[i];
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var common = m_k + m_k_plus - slope - slope;
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coefs1.push(common * invLength * invLength);
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coefs2.push((slope - common - m_k) * invLength);
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}
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//create functions with from the coefficients and capture the parameters
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var ret = [];
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for (var i = 0; i < segmentLengths.length; i ++) {
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var spline = function (x_k, coef1, coef2, coef3, coef4) {
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// spline for a segment
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return function (x) {
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var diff = x - x_k;
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var diffSq = diff * diff;
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return coef1 * diff * diffSq + coef2 * diffSq + coef3 * diff + coef4;
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};
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};
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ret.push(spline(points[i * ps], coefs1[i], coefs2[i], gradients[i], points[i * ps + yPos]));
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}
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return ret;
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};
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//no real idea whats going on here code mainly from https://code.google.com/p/flot/issues/detail?id=226
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//if fit option is selected additional datapoints get inserted before the curve calculations in nergal.dev s code.
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function calculateLegacyCurvePoints(datapoints, curvedLinesOptions, yPos) {
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var points = datapoints.points;
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var ps = datapoints.pointsize;
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var num = Number(curvedLinesOptions.curvePointFactor) * (points.length / ps);
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var xdata = new Array;
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var ydata = new Array;
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var curX = -1;
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var curY = -1;
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var j = 0;
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if (curvedLinesOptions.fit) {
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//insert a point before and after the "real" data point to force the line
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//to have a max,min at the data point.
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var fpDist;
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if ( typeof curvedLinesOptions.fitPointDist == 'undefined') {
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//estimate it
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var minX = points[0];
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var maxX = points[points.length - ps];
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fpDist = (maxX - minX) / (500 * 100);
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//x range / (estimated pixel length of placeholder * factor)
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} else {
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//use user defined value
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fpDist = Number(curvedLinesOptions.fitPointDist);
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}
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for (var i = 0; i < points.length; i += ps) {
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var frontX;
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var backX;
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curX = i;
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curY = i + yPos;
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//add point X s
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frontX = points[curX] - fpDist;
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backX = points[curX] + fpDist;
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var factor = 2;
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while (frontX == points[curX] || backX == points[curX]) {
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//inside the ulp
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frontX = points[curX] - (fpDist * factor);
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backX = points[curX] + (fpDist * factor);
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factor++;
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}
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//add curve points
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xdata[j] = frontX;
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ydata[j] = points[curY];
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j++;
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xdata[j] = points[curX];
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ydata[j] = points[curY];
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j++;
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xdata[j] = backX;
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ydata[j] = points[curY];
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j++;
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}
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} else {
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//just use the datapoints
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for (var i = 0; i < points.length; i += ps) {
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curX = i;
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curY = i + yPos;
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xdata[j] = points[curX];
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ydata[j] = points[curY];
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j++;
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}
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}
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var n = xdata.length;
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var y2 = new Array();
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var delta = new Array();
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y2[0] = 0;
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y2[n - 1] = 0;
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delta[0] = 0;
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for (var i = 1; i < n - 1; ++i) {
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var d = (xdata[i + 1] - xdata[i - 1]);
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if (d == 0) {
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//point before current point and after current point need some space in between
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return [];
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}
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var s = (xdata[i] - xdata[i - 1]) / d;
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var p = s * y2[i - 1] + 2;
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y2[i] = (s - 1) / p;
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delta[i] = (ydata[i + 1] - ydata[i]) / (xdata[i + 1] - xdata[i]) - (ydata[i] - ydata[i - 1]) / (xdata[i] - xdata[i - 1]);
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delta[i] = (6 * delta[i] / (xdata[i + 1] - xdata[i - 1]) - s * delta[i - 1]) / p;
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}
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for (var j = n - 2; j >= 0; --j) {
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y2[j] = y2[j] * y2[j + 1] + delta[j];
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}
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// xmax - xmin / #points
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var step = (xdata[n - 1] - xdata[0]) / (num - 1);
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var xnew = new Array;
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var ynew = new Array;
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var result = new Array;
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xnew[0] = xdata[0];
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ynew[0] = ydata[0];
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result.push(xnew[0]);
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result.push(ynew[0]);
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for ( j = 1; j < num; ++j) {
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//new x point (sampling point for the created curve)
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xnew[j] = xnew[0] + j * step;
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var max = n - 1;
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var min = 0;
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while (max - min > 1) {
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var k = Math.round((max + min) / 2);
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if (xdata[k] > xnew[j]) {
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max = k;
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} else {
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min = k;
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}
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}
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//found point one to the left and one to the right of generated new point
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var h = (xdata[max] - xdata[min]);
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if (h == 0) {
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//similar to above two points from original x data need some space between them
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return [];
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}
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var a = (xdata[max] - xnew[j]) / h;
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var b = (xnew[j] - xdata[min]) / h;
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ynew[j] = a * ydata[min] + b * ydata[max] + ((a * a * a - a) * y2[min] + (b * b * b - b) * y2[max]) * (h * h) / 6;
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result.push(xnew[j]);
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result.push(ynew[j]);
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}
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return result;
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}
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function hasInvalidParameters(curvedLinesOptions) {
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if (typeof curvedLinesOptions.fit != 'undefined' ||
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typeof curvedLinesOptions.curvePointFactor != 'undefined' ||
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typeof curvedLinesOptions.fitPointDist != 'undefined') {
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throw new Error("CurvedLines detected illegal parameters. The CurvedLines API changed with version 1.0.0 please check the options object.");
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return true;
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}
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return false;
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}
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}//end init
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$.plot.plugins.push({
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init : init,
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options : options,
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name : 'curvedLines',
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version : '1.1.1'
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});
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})(jQuery);
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