dygraphs
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dygraphs is a fast, flexible open source JavaScript charting library.
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JavaScript
/**
* @license
* Copyright 2011 Robert Konigsberg (konigsberg@google.com)
* MIT-licenced: https://opensource.org/licenses/MIT
*/
/**
* @fileoverview The default interaction model for Dygraphs. This is kept out
* of dygraph.js for better navigability.
* @author Robert Konigsberg (konigsberg@google.com)
*/
/*global Dygraph:false */
"use strict";
import * as utils from './dygraph-utils';
/**
* You can drag this many pixels past the edge of the chart and still have it
* be considered a zoom. This makes it easier to zoom to the exact edge of the
* chart, a fairly common operation.
*/
var DRAG_EDGE_MARGIN = 100;
/**
* A collection of functions to facilitate build custom interaction models.
* @class
*/
var DygraphInteraction = {};
/**
* Checks whether the beginning & ending of an event were close enough that it
* should be considered a click. If it should, dispatch appropriate events.
* Returns true if the event was treated as a click.
*
* @param {Event} event
* @param {Dygraph} g
* @param {Object} context
*/
DygraphInteraction.maybeTreatMouseOpAsClick = function(event, g, context) {
context.dragEndX = utils.dragGetX_(event, context);
context.dragEndY = utils.dragGetY_(event, context);
var regionWidth = Math.abs(context.dragEndX - context.dragStartX);
var regionHeight = Math.abs(context.dragEndY - context.dragStartY);
if (regionWidth < 2 && regionHeight < 2 &&
g.lastx_ !== undefined && g.lastx_ !== null) {
DygraphInteraction.treatMouseOpAsClick(g, event, context);
}
context.regionWidth = regionWidth;
context.regionHeight = regionHeight;
};
/**
* Called in response to an interaction model operation that
* should start the default panning behavior.
*
* It's used in the default callback for "mousedown" operations.
* Custom interaction model builders can use it to provide the default
* panning behavior.
*
* @param {Event} event the event object which led to the startPan call.
* @param {Dygraph} g The dygraph on which to act.
* @param {Object} context The dragging context object (with
* dragStartX/dragStartY/etc. properties). This function modifies the
* context.
*/
DygraphInteraction.startPan = function(event, g, context) {
var i, axis;
context.isPanning = true;
var xRange = g.xAxisRange();
if (g.getOptionForAxis("logscale", "x")) {
context.initialLeftmostDate = utils.log10(xRange[0]);
context.dateRange = utils.log10(xRange[1]) - utils.log10(xRange[0]);
} else {
context.initialLeftmostDate = xRange[0];
context.dateRange = xRange[1] - xRange[0];
}
context.xUnitsPerPixel = context.dateRange / (g.plotter_.area.w - 1);
if (g.getNumericOption("panEdgeFraction")) {
var maxXPixelsToDraw = g.width_ * g.getNumericOption("panEdgeFraction");
var xExtremes = g.xAxisExtremes(); // I REALLY WANT TO CALL THIS xTremes!
var boundedLeftX = g.toDomXCoord(xExtremes[0]) - maxXPixelsToDraw;
var boundedRightX = g.toDomXCoord(xExtremes[1]) + maxXPixelsToDraw;
var boundedLeftDate = g.toDataXCoord(boundedLeftX);
var boundedRightDate = g.toDataXCoord(boundedRightX);
context.boundedDates = [boundedLeftDate, boundedRightDate];
var boundedValues = [];
var maxYPixelsToDraw = g.height_ * g.getNumericOption("panEdgeFraction");
for (i = 0; i < g.axes_.length; i++) {
axis = g.axes_[i];
var yExtremes = axis.extremeRange;
var boundedTopY = g.toDomYCoord(yExtremes[0], i) + maxYPixelsToDraw;
var boundedBottomY = g.toDomYCoord(yExtremes[1], i) - maxYPixelsToDraw;
var boundedTopValue = g.toDataYCoord(boundedTopY, i);
var boundedBottomValue = g.toDataYCoord(boundedBottomY, i);
boundedValues[i] = [boundedTopValue, boundedBottomValue];
}
context.boundedValues = boundedValues;
} else {
// undo effect if it was once set
context.boundedDates = null;
context.boundedValues = null;
}
// Record the range of each y-axis at the start of the drag.
// If any axis has a valueRange, then we want a 2D pan.
// We can't store data directly in g.axes_, because it does not belong to us
// and could change out from under us during a pan (say if there's a data
// update).
context.is2DPan = false;
context.axes = [];
for (i = 0; i < g.axes_.length; i++) {
axis = g.axes_[i];
var axis_data = {};
var yRange = g.yAxisRange(i);
// TODO(konigsberg): These values should be in |context|.
// In log scale, initialTopValue, dragValueRange and unitsPerPixel are log scale.
var logscale = g.attributes_.getForAxis("logscale", i);
if (logscale) {
axis_data.initialTopValue = utils.log10(yRange[1]);
axis_data.dragValueRange = utils.log10(yRange[1]) - utils.log10(yRange[0]);
} else {
axis_data.initialTopValue = yRange[1];
axis_data.dragValueRange = yRange[1] - yRange[0];
}
axis_data.unitsPerPixel = axis_data.dragValueRange / (g.plotter_.area.h - 1);
context.axes.push(axis_data);
// While calculating axes, set 2dpan.
if (axis.valueRange) context.is2DPan = true;
}
};
/**
* Called in response to an interaction model operation that
* responds to an event that pans the view.
*
* It's used in the default callback for "mousemove" operations.
* Custom interaction model builders can use it to provide the default
* panning behavior.
*
* @param {Event} event the event object which led to the movePan call.
* @param {Dygraph} g The dygraph on which to act.
* @param {Object} context The dragging context object (with
* dragStartX/dragStartY/etc. properties). This function modifies the
* context.
*/
DygraphInteraction.movePan = function(event, g, context) {
context.dragEndX = utils.dragGetX_(event, context);
context.dragEndY = utils.dragGetY_(event, context);
var minDate = context.initialLeftmostDate -
(context.dragEndX - context.dragStartX) * context.xUnitsPerPixel;
if (context.boundedDates) {
minDate = Math.max(minDate, context.boundedDates[0]);
}
var maxDate = minDate + context.dateRange;
if (context.boundedDates) {
if (maxDate > context.boundedDates[1]) {
// Adjust minDate, and recompute maxDate.
minDate = minDate - (maxDate - context.boundedDates[1]);
maxDate = minDate + context.dateRange;
}
}
if (g.getOptionForAxis("logscale", "x")) {
g.dateWindow_ = [ Math.pow(utils.LOG_SCALE, minDate),
Math.pow(utils.LOG_SCALE, maxDate) ];
} else {
g.dateWindow_ = [minDate, maxDate];
}
// y-axis scaling is automatic unless this is a full 2D pan.
if (context.is2DPan) {
var pixelsDragged = context.dragEndY - context.dragStartY;
// Adjust each axis appropriately.
for (var i = 0; i < g.axes_.length; i++) {
var axis = g.axes_[i];
var axis_data = context.axes[i];
var unitsDragged = pixelsDragged * axis_data.unitsPerPixel;
var boundedValue = context.boundedValues ? context.boundedValues[i] : null;
// In log scale, maxValue and minValue are the logs of those values.
var maxValue = axis_data.initialTopValue + unitsDragged;
if (boundedValue) {
maxValue = Math.min(maxValue, boundedValue[1]);
}
var minValue = maxValue - axis_data.dragValueRange;
if (boundedValue) {
if (minValue < boundedValue[0]) {
// Adjust maxValue, and recompute minValue.
maxValue = maxValue - (minValue - boundedValue[0]);
minValue = maxValue - axis_data.dragValueRange;
}
}
if (g.attributes_.getForAxis("logscale", i)) {
axis.valueRange = [ Math.pow(utils.LOG_SCALE, minValue),
Math.pow(utils.LOG_SCALE, maxValue) ];
} else {
axis.valueRange = [ minValue, maxValue ];
}
}
}
g.drawGraph_(false);
};
/**
* Called in response to an interaction model operation that
* responds to an event that ends panning.
*
* It's used in the default callback for "mouseup" operations.
* Custom interaction model builders can use it to provide the default
* panning behavior.
*
* @param {Event} event the event object which led to the endPan call.
* @param {Dygraph} g The dygraph on which to act.
* @param {Object} context The dragging context object (with
* dragStartX/dragStartY/etc. properties). This function modifies the
* context.
*/
DygraphInteraction.endPan = DygraphInteraction.maybeTreatMouseOpAsClick;
/**
* Called in response to an interaction model operation that
* responds to an event that starts zooming.
*
* It's used in the default callback for "mousedown" operations.
* Custom interaction model builders can use it to provide the default
* zooming behavior.
*
* @param {Event} event the event object which led to the startZoom call.
* @param {Dygraph} g The dygraph on which to act.
* @param {Object} context The dragging context object (with
* dragStartX/dragStartY/etc. properties). This function modifies the
* context.
*/
DygraphInteraction.startZoom = function(event, g, context) {
context.isZooming = true;
context.zoomMoved = false;
};
/**
* Called in response to an interaction model operation that
* responds to an event that defines zoom boundaries.
*
* It's used in the default callback for "mousemove" operations.
* Custom interaction model builders can use it to provide the default
* zooming behavior.
*
* @param {Event} event the event object which led to the moveZoom call.
* @param {Dygraph} g The dygraph on which to act.
* @param {Object} context The dragging context object (with
* dragStartX/dragStartY/etc. properties). This function modifies the
* context.
*/
DygraphInteraction.moveZoom = function(event, g, context) {
context.zoomMoved = true;
context.dragEndX = utils.dragGetX_(event, context);
context.dragEndY = utils.dragGetY_(event, context);
var xDelta = Math.abs(context.dragStartX - context.dragEndX);
var yDelta = Math.abs(context.dragStartY - context.dragEndY);
// drag direction threshold for y axis is twice as large as x axis
context.dragDirection = (xDelta < yDelta / 2) ? utils.VERTICAL : utils.HORIZONTAL;
g.drawZoomRect_(
context.dragDirection,
context.dragStartX,
context.dragEndX,
context.dragStartY,
context.dragEndY,
context.prevDragDirection,
context.prevEndX,
context.prevEndY);
context.prevEndX = context.dragEndX;
context.prevEndY = context.dragEndY;
context.prevDragDirection = context.dragDirection;
};
/**
* TODO(danvk): move this logic into dygraph.js
* @param {Dygraph} g
* @param {Event} event
* @param {Object} context
*/
DygraphInteraction.treatMouseOpAsClick = function(g, event, context) {
var clickCallback = g.getFunctionOption('clickCallback');
var pointClickCallback = g.getFunctionOption('pointClickCallback');
var selectedPoint = null;
// Find out if the click occurs on a point.
var closestIdx = -1;
var closestDistance = Number.MAX_VALUE;
// check if the click was on a particular point.
for (var i = 0; i < g.selPoints_.length; i++) {
var p = g.selPoints_[i];
var distance = Math.pow(p.canvasx - context.dragEndX, 2) +
Math.pow(p.canvasy - context.dragEndY, 2);
if (!isNaN(distance) &&
(closestIdx == -1 || distance < closestDistance)) {
closestDistance = distance;
closestIdx = i;
}
}
// Allow any click within two pixels of the dot.
var radius = g.getNumericOption('highlightCircleSize') + 2;
if (closestDistance <= radius * radius) {
selectedPoint = g.selPoints_[closestIdx];
}
if (selectedPoint) {
var e = {
cancelable: true,
point: selectedPoint,
canvasx: context.dragEndX,
canvasy: context.dragEndY
};
var defaultPrevented = g.cascadeEvents_('pointClick', e);
if (defaultPrevented) {
// Note: this also prevents click / clickCallback from firing.
return;
}
if (pointClickCallback) {
pointClickCallback.call(g, event, selectedPoint);
}
}
var e = {
cancelable: true,
xval: g.lastx_, // closest point by x value
pts: g.selPoints_,
canvasx: context.dragEndX,
canvasy: context.dragEndY
};
if (!g.cascadeEvents_('click', e)) {
if (clickCallback) {
// TODO(danvk): pass along more info about the points, e.g. 'x'
clickCallback.call(g, event, g.lastx_, g.selPoints_);
}
}
};
/**
* Called in response to an interaction model operation that
* responds to an event that performs a zoom based on previously defined
* bounds..
*
* It's used in the default callback for "mouseup" operations.
* Custom interaction model builders can use it to provide the default
* zooming behavior.
*
* @param {Event} event the event object which led to the endZoom call.
* @param {Dygraph} g The dygraph on which to end the zoom.
* @param {Object} context The dragging context object (with
* dragStartX/dragStartY/etc. properties). This function modifies the
* context.
*/
DygraphInteraction.endZoom = function(event, g, context) {
g.clearZoomRect_();
context.isZooming = false;
DygraphInteraction.maybeTreatMouseOpAsClick(event, g, context);
// The zoom rectangle is visibly clipped to the plot area, so its behavior
// should be as well.
// See http://code.google.com/p/dygraphs/issues/detail?id=280
var plotArea = g.getArea();
if (context.regionWidth >= 10 &&
context.dragDirection == utils.HORIZONTAL) {
var left = Math.min(context.dragStartX, context.dragEndX),
right = Math.max(context.dragStartX, context.dragEndX);
left = Math.max(left, plotArea.x);
right = Math.min(right, plotArea.x + plotArea.w);
if (left < right) {
g.doZoomX_(left, right);
}
context.cancelNextDblclick = true;
} else if (context.regionHeight >= 10 &&
context.dragDirection == utils.VERTICAL) {
var top = Math.min(context.dragStartY, context.dragEndY),
bottom = Math.max(context.dragStartY, context.dragEndY);
top = Math.max(top, plotArea.y);
bottom = Math.min(bottom, plotArea.y + plotArea.h);
if (top < bottom) {
g.doZoomY_(top, bottom);
}
context.cancelNextDblclick = true;
}
context.dragStartX = null;
context.dragStartY = null;
};
/**
* @private
*/
DygraphInteraction.startTouch = function(event, g, context) {
event.preventDefault(); // touch browsers are all nice.
if (event.touches.length > 1) {
// If the user ever puts two fingers down, it's not a double tap.
context.startTimeForDoubleTapMs = null;
}
var touches = [];
for (var i = 0; i < event.touches.length; i++) {
var t = event.touches[i];
var rect = t.target.getBoundingClientRect()
// we dispense with 'dragGetX_' because all touchBrowsers support pageX
touches.push({
pageX: t.pageX,
pageY: t.pageY,
dataX: g.toDataXCoord(t.clientX - rect.left),
dataY: g.toDataYCoord(t.clientY - rect.top)
// identifier: t.identifier
});
}
context.initialTouches = touches;
if (touches.length == 1) {
// This is just a swipe.
context.initialPinchCenter = touches[0];
context.touchDirections = { x: true, y: true };
} else if (touches.length >= 2) {
// It's become a pinch!
// In case there are 3+ touches, we ignore all but the "first" two.
// only screen coordinates can be averaged (data coords could be log scale).
context.initialPinchCenter = {
pageX: 0.5 * (touches[0].pageX + touches[1].pageX),
pageY: 0.5 * (touches[0].pageY + touches[1].pageY),
// TODO(danvk): remove
dataX: 0.5 * (touches[0].dataX + touches[1].dataX),
dataY: 0.5 * (touches[0].dataY + touches[1].dataY)
};
// Make pinches in a 45-degree swath around either axis 1-dimensional zooms.
var initialAngle = 180 / Math.PI * Math.atan2(
context.initialPinchCenter.pageY - touches[0].pageY,
touches[0].pageX - context.initialPinchCenter.pageX);
// use symmetry to get it into the first quadrant.
initialAngle = Math.abs(initialAngle);
if (initialAngle > 90) initialAngle = 90 - initialAngle;
context.touchDirections = {
x: (initialAngle < (90 - 45/2)),
y: (initialAngle > 45/2)
};
}
// save the full x & y ranges.
context.initialRange = {
x: g.xAxisRange(),
y: g.yAxisRange()
};
};
/**
* @private
*/
DygraphInteraction.moveTouch = function(event, g, context) {
// If the tap moves, then it's definitely not part of a double-tap.
context.startTimeForDoubleTapMs = null;
var i, touches = [];
for (i = 0; i < event.touches.length; i++) {
var t = event.touches[i];
touches.push({
pageX: t.pageX,
pageY: t.pageY
});
}
var initialTouches = context.initialTouches;
var c_now;
// old and new centers.
var c_init = context.initialPinchCenter;
if (touches.length == 1) {
c_now = touches[0];
} else {
c_now = {
pageX: 0.5 * (touches[0].pageX + touches[1].pageX),
pageY: 0.5 * (touches[0].pageY + touches[1].pageY)
};
}
// this is the "swipe" component
// we toss it out for now, but could use it in the future.
var swipe = {
pageX: c_now.pageX - c_init.pageX,
pageY: c_now.pageY - c_init.pageY
};
var dataWidth = context.initialRange.x[1] - context.initialRange.x[0];
var dataHeight = context.initialRange.y[0] - context.initialRange.y[1];
swipe.dataX = (swipe.pageX / g.plotter_.area.w) * dataWidth;
swipe.dataY = (swipe.pageY / g.plotter_.area.h) * dataHeight;
var xScale, yScale;
// The residual bits are usually split into scale & rotate bits, but we split
// them into x-scale and y-scale bits.
if (touches.length == 1) {
xScale = 1.0;
yScale = 1.0;
} else if (touches.length >= 2) {
var initHalfWidth = (initialTouches[1].pageX - c_init.pageX);
xScale = (touches[1].pageX - c_now.pageX) / initHalfWidth;
var initHalfHeight = (initialTouches[1].pageY - c_init.pageY);
yScale = (touches[1].pageY - c_now.pageY) / initHalfHeight;
}
// Clip scaling to [1/8, 8] to prevent too much blowup.
xScale = Math.min(8, Math.max(0.125, xScale));
yScale = Math.min(8, Math.max(0.125, yScale));
var didZoom = false;
if (context.touchDirections.x) {
var cFactor = c_init.dataX - swipe.dataX / xScale;
g.dateWindow_ = [
cFactor + (context.initialRange.x[0] - c_init.dataX) / xScale,
cFactor + (context.initialRange.x[1] - c_init.dataX) / xScale
];
didZoom = true;
}
if (context.touchDirections.y) {
for (i = 0; i < 1 /*g.axes_.length*/; i++) {
var axis = g.axes_[i];
var logscale = g.attributes_.getForAxis("logscale", i);
if (logscale) {
// TODO(danvk): implement
} else {
var cFactor = c_init.dataY - swipe.dataY / yScale;
axis.valueRange = [
cFactor + (context.initialRange.y[0] - c_init.dataY) / yScale,
cFactor + (context.initialRange.y[1] - c_init.dataY) / yScale
];
didZoom = true;
}
}
}
g.drawGraph_(false);
// We only call zoomCallback on zooms, not pans, to mirror desktop behavior.
if (didZoom && touches.length > 1 && g.getFunctionOption('zoomCallback')) {
var viewWindow = g.xAxisRange();
g.getFunctionOption("zoomCallback").call(g, viewWindow[0], viewWindow[1], g.yAxisRanges());
}
};
/**
* @private
*/
DygraphInteraction.endTouch = function(event, g, context) {
if (event.touches.length !== 0) {
// this is effectively a "reset"
DygraphInteraction.startTouch(event, g, context);
} else if (event.changedTouches.length == 1) {
// Could be part of a "double tap"
// The heuristic here is that it's a double-tap if the two touchend events
// occur within 500ms and within a 50x50 pixel box.
var now = new Date().getTime();
var t = event.changedTouches[0];
if (context.startTimeForDoubleTapMs &&
now - context.startTimeForDoubleTapMs < 500 &&
context.doubleTapX && Math.abs(context.doubleTapX - t.screenX) < 50 &&
context.doubleTapY && Math.abs(context.doubleTapY - t.screenY) < 50) {
g.resetZoom();
} else {
context.startTimeForDoubleTapMs = now;
context.doubleTapX = t.screenX;
context.doubleTapY = t.screenY;
}
}
};
// Determine the distance from x to [left, right].
var distanceFromInterval = function(x, left, right) {
if (x < left) {
return left - x;
} else if (x > right) {
return x - right;
} else {
return 0;
}
};
/**
* Returns the number of pixels by which the event happens from the nearest
* edge of the chart. For events in the interior of the chart, this returns zero.
*/
var distanceFromChart = function(event, g) {
var chartPos = utils.findPos(g.canvas_);
var box = {
left: chartPos.x,
right: chartPos.x + g.canvas_.offsetWidth,
top: chartPos.y,
bottom: chartPos.y + g.canvas_.offsetHeight
};
var pt = {
x: utils.pageX(event),
y: utils.pageY(event)
};
var dx = distanceFromInterval(pt.x, box.left, box.right),
dy = distanceFromInterval(pt.y, box.top, box.bottom);
return Math.max(dx, dy);
};
/**
* Default interation model for dygraphs. You can refer to specific elements of
* this when constructing your own interaction model, e.g.:
* g.updateOptions( {
* interactionModel: {
* mousedown: DygraphInteraction.defaultInteractionModel.mousedown
* }
* } );
*/
DygraphInteraction.defaultModel = {
// Track the beginning of drag events
mousedown: function(event, g, context) {
// Right-click should not initiate a zoom.
if (event.button && event.button == 2) return;
context.initializeMouseDown(event, g, context);
if (event.altKey || event.shiftKey) {
DygraphInteraction.startPan(event, g, context);
} else {
DygraphInteraction.startZoom(event, g, context);
}
// Note: we register mousemove/mouseup on document to allow some leeway for
// events to move outside of the chart. Interaction model events get
// registered on the canvas, which is too small to allow this.
var mousemove = function(event) {
if (context.isZooming) {
// When the mouse moves >200px from the chart edge, cancel the zoom.
var d = distanceFromChart(event, g);
if (d < DRAG_EDGE_MARGIN) {
DygraphInteraction.moveZoom(event, g, context);
} else {
if (context.dragEndX !== null) {
context.dragEndX = null;
context.dragEndY = null;
g.clearZoomRect_();
}
}
} else if (context.isPanning) {
DygraphInteraction.movePan(event, g, context);
}
};
var mouseup = function(event) {
if (context.isZooming) {
if (context.dragEndX !== null) {
DygraphInteraction.endZoom(event, g, context);
} else {
DygraphInteraction.maybeTreatMouseOpAsClick(event, g, context);
}
} else if (context.isPanning) {
DygraphInteraction.endPan(event, g, context);
}
utils.removeEvent(document, 'mousemove', mousemove);
utils.removeEvent(document, 'mouseup', mouseup);
context.destroy();
};
g.addAndTrackEvent(document, 'mousemove', mousemove);
g.addAndTrackEvent(document, 'mouseup', mouseup);
},
willDestroyContextMyself: true,
touchstart: function(event, g, context) {
DygraphInteraction.startTouch(event, g, context);
},
touchmove: function(event, g, context) {
DygraphInteraction.moveTouch(event, g, context);
},
touchend: function(event, g, context) {
DygraphInteraction.endTouch(event, g, context);
},
// Disable zooming out if panning.
dblclick: function(event, g, context) {
if (context.cancelNextDblclick) {
context.cancelNextDblclick = false;
return;
}
// Give plugins a chance to grab this event.
var e = {
canvasx: context.dragEndX,
canvasy: context.dragEndY,
cancelable: true,
};
if (g.cascadeEvents_('dblclick', e)) {
return;
}
if (event.altKey || event.shiftKey) {
return;
}
g.resetZoom();
}
};
/*
Dygraph.DEFAULT_ATTRS.interactionModel = DygraphInteraction.defaultModel;
// old ways of accessing these methods/properties
Dygraph.defaultInteractionModel = DygraphInteraction.defaultModel;
Dygraph.endZoom = DygraphInteraction.endZoom;
Dygraph.moveZoom = DygraphInteraction.moveZoom;
Dygraph.startZoom = DygraphInteraction.startZoom;
Dygraph.endPan = DygraphInteraction.endPan;
Dygraph.movePan = DygraphInteraction.movePan;
Dygraph.startPan = DygraphInteraction.startPan;
*/
DygraphInteraction.nonInteractiveModel_ = {
mousedown: function(event, g, context) {
context.initializeMouseDown(event, g, context);
},
mouseup: DygraphInteraction.maybeTreatMouseOpAsClick
};
// Default interaction model when using the range selector.
DygraphInteraction.dragIsPanInteractionModel = {
mousedown: function(event, g, context) {
context.initializeMouseDown(event, g, context);
DygraphInteraction.startPan(event, g, context);
},
mousemove: function(event, g, context) {
if (context.isPanning) {
DygraphInteraction.movePan(event, g, context);
}
},
mouseup: function(event, g, context) {
if (context.isPanning) {
DygraphInteraction.endPan(event, g, context);
}
}
};
export default DygraphInteraction;