diff --git a/src/controllers/controller.line.js b/src/controllers/controller.line.js
index fffb1ce55d2..03f7faf96d2 100644
--- a/src/controllers/controller.line.js
+++ b/src/controllers/controller.line.js
@@ -5,6 +5,8 @@ var defaults = require('../core/core.defaults');
 var elements = require('../elements/index');
 var helpers = require('../helpers/index');
 
+var _isPointInArea = helpers.canvas._isPointInArea;
+
 defaults._set('line', {
 	showLines: true,
 	spanGaps: false,
@@ -243,13 +245,15 @@ module.exports = DatasetController.extend({
 
 	updateBezierControlPoints: function() {
 		var me = this;
+		var chart = me.chart;
 		var meta = me.getMeta();
-		var area = me.chart.chartArea;
-		var points = (meta.data || []);
+		var lineModel = meta.dataset._model;
+		var area = chart.chartArea;
+		var points = meta.data || [];
 		var i, ilen, point, model, controlPoints;
 
 		// Only consider points that are drawn in case the spanGaps option is used
-		if (meta.dataset._model.spanGaps) {
+		if (lineModel.spanGaps) {
 			points = points.filter(function(pt) {
 				return !pt._model.skip;
 			});
@@ -259,7 +263,7 @@ module.exports = DatasetController.extend({
 			return Math.max(Math.min(pt, max), min);
 		}
 
-		if (meta.dataset._model.cubicInterpolationMode === 'monotone') {
+		if (lineModel.cubicInterpolationMode === 'monotone') {
 			helpers.splineCurveMonotone(points);
 		} else {
 			for (i = 0, ilen = points.length; i < ilen; ++i) {
@@ -269,7 +273,7 @@ module.exports = DatasetController.extend({
 					helpers.previousItem(points, i)._model,
 					model,
 					helpers.nextItem(points, i)._model,
-					meta.dataset._model.tension
+					lineModel.tension
 				);
 				model.controlPointPreviousX = controlPoints.previous.x;
 				model.controlPointPreviousY = controlPoints.previous.y;
@@ -278,13 +282,19 @@ module.exports = DatasetController.extend({
 			}
 		}
 
-		if (me.chart.options.elements.line.capBezierPoints) {
+		if (chart.options.elements.line.capBezierPoints) {
 			for (i = 0, ilen = points.length; i < ilen; ++i) {
 				model = points[i]._model;
-				model.controlPointPreviousX = capControlPoint(model.controlPointPreviousX, area.left, area.right);
-				model.controlPointPreviousY = capControlPoint(model.controlPointPreviousY, area.top, area.bottom);
-				model.controlPointNextX = capControlPoint(model.controlPointNextX, area.left, area.right);
-				model.controlPointNextY = capControlPoint(model.controlPointNextY, area.top, area.bottom);
+				if (_isPointInArea(model, area)) {
+					if (i > 0 && _isPointInArea(points[i - 1]._model, area)) {
+						model.controlPointPreviousX = capControlPoint(model.controlPointPreviousX, area.left, area.right);
+						model.controlPointPreviousY = capControlPoint(model.controlPointPreviousY, area.top, area.bottom);
+					}
+					if (i < points.length - 1 && _isPointInArea(points[i + 1]._model, area)) {
+						model.controlPointNextX = capControlPoint(model.controlPointNextX, area.left, area.right);
+						model.controlPointNextY = capControlPoint(model.controlPointNextY, area.top, area.bottom);
+					}
+				}
 			}
 		}
 	},
diff --git a/src/elements/element.point.js b/src/elements/element.point.js
index b7909116a7c..8ae37eb8a28 100644
--- a/src/elements/element.point.js
+++ b/src/elements/element.point.js
@@ -65,14 +65,12 @@ module.exports = Element.extend({
 
 	draw: function(chartArea) {
 		var vm = this._view;
-		var model = this._model;
 		var ctx = this._chart.ctx;
 		var pointStyle = vm.pointStyle;
 		var rotation = vm.rotation;
 		var radius = vm.radius;
 		var x = vm.x;
 		var y = vm.y;
-		var epsilon = 0.0000001; // 0.0000001 is margin in pixels for Accumulated error.
 		var globalDefaults = defaults.global;
 		var defaultColor = globalDefaults.defaultColor; // eslint-disable-line no-shadow
 
@@ -81,7 +79,7 @@ module.exports = Element.extend({
 		}
 
 		// Clipping for Points.
-		if (chartArea === undefined || (model.x > chartArea.left - epsilon && chartArea.right + epsilon > model.x && model.y > chartArea.top - epsilon && chartArea.bottom + epsilon > model.y)) {
+		if (chartArea === undefined || helpers.canvas._isPointInArea(vm, chartArea)) {
 			ctx.strokeStyle = vm.borderColor || defaultColor;
 			ctx.lineWidth = helpers.valueOrDefault(vm.borderWidth, globalDefaults.elements.point.borderWidth);
 			ctx.fillStyle = vm.backgroundColor || defaultColor;
diff --git a/src/helpers/helpers.canvas.js b/src/helpers/helpers.canvas.js
index b1212dff46d..1513386a8cb 100644
--- a/src/helpers/helpers.canvas.js
+++ b/src/helpers/helpers.canvas.js
@@ -172,6 +172,20 @@ var exports = {
 		ctx.stroke();
 	},
 
+	/**
+	 * Returns true if the point is inside the rectangle
+	 * @param {Object} point - The point to test
+	 * @param {Object} area - The rectangle
+	 * @returns {Boolean}
+	 * @private
+	 */
+	_isPointInArea: function(point, area) {
+		var epsilon = 1e-6; // 1e-6 is margin in pixels for accumulated error.
+
+		return point.x > area.left - epsilon && point.x < area.right + epsilon &&
+			point.y > area.top - epsilon && point.y < area.bottom + epsilon;
+	},
+
 	clipArea: function(ctx, area) {
 		ctx.save();
 		ctx.beginPath();
diff --git a/test/specs/helpers.canvas.tests.js b/test/specs/helpers.canvas.tests.js
index ee42a414e6f..9654ef28e7b 100644
--- a/test/specs/helpers.canvas.tests.js
+++ b/test/specs/helpers.canvas.tests.js
@@ -86,4 +86,18 @@ describe('Chart.helpers.canvas', function() {
 			expect(context.getCalls()).toEqual([{name: 'rect', args: [10, 20, 30, 40]}]);
 		});
 	});
+
+	describe('isPointInArea', function() {
+		it('should determine if a point is in the area', function() {
+			var isPointInArea = helpers.canvas._isPointInArea;
+			var area = {left: 0, top: 0, right: 512, bottom: 256};
+
+			expect(isPointInArea({x: 0, y: 0}, area)).toBe(true);
+			expect(isPointInArea({x: -1e-12, y: -1e-12}, area)).toBe(true);
+			expect(isPointInArea({x: 512, y: 256}, area)).toBe(true);
+			expect(isPointInArea({x: 512 + 1e-12, y: 256 + 1e-12}, area)).toBe(true);
+			expect(isPointInArea({x: -1e-3, y: 0}, area)).toBe(false);
+			expect(isPointInArea({x: 0, y: 256 + 1e-3}, area)).toBe(false);
+		});
+	});
 });