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/* *
* (c) 2010-2019 Torstein Honsi
*
* License: www.highcharts.com/license
*/
'use strict';
import H from '../parts/Globals.js';
import '../parts/Utilities.js';
// Mathematical Functionility
var deg2rad = H.deg2rad,
pick = H.pick;
/* eslint-disable max-len */
/**
* Apply 3-D rotation
* Euler Angles (XYZ):
* cosA = cos(Alfa|Roll)
* cosB = cos(Beta|Pitch)
* cosG = cos(Gamma|Yaw)
*
* Composite rotation:
* | cosB * cosG | cosB * sinG | -sinB |
* | sinA * sinB * cosG - cosA * sinG | sinA * sinB * sinG + cosA * cosG | sinA * cosB |
* | cosA * sinB * cosG + sinA * sinG | cosA * sinB * sinG - sinA * cosG | cosA * cosB |
*
* Now, Gamma/Yaw is not used (angle=0), so we assume cosG = 1 and sinG = 0, so
* we get:
* | cosB | 0 | - sinB |
* | sinA * sinB | cosA | sinA * cosB |
* | cosA * sinB | - sinA | cosA * cosB |
*
* But in browsers, y is reversed, so we get sinA => -sinA. The general result
* is:
* | cosB | 0 | - sinB | | x | | px |
* | - sinA * sinB | cosA | - sinA * cosB | x | y | = | py |
* | cosA * sinB | sinA | cosA * cosB | | z | | pz |
*
* @private
* @function rotate3D
*/
/* eslint-enable max-len */
function rotate3D(x, y, z, angles) {
return {
x: angles.cosB * x - angles.sinB * z,
y: -angles.sinA * angles.sinB * x + angles.cosA * y -
angles.cosB * angles.sinA * z,
z: angles.cosA * angles.sinB * x + angles.sinA * y +
angles.cosA * angles.cosB * z
};
}
// Perspective3D function is available in global Highcharts scope because is
// needed also outside of perspective() function (#8042).
H.perspective3D = function (coordinate, origin, distance) {
var projection = ((distance > 0) && (distance < Number.POSITIVE_INFINITY)) ?
distance / (coordinate.z + origin.z + distance) :
1;
return {
x: coordinate.x * projection,
y: coordinate.y * projection
};
};
/**
* Transforms a given array of points according to the angles in chart.options.
*
* @private
* @function Highcharts.perspective
*
* @param {Array<Highcharts.Point>} points
* The array of points
*
* @param {Highcharts.Chart} chart
* The chart
*
* @param {boolean} [insidePlotArea]
* Wether to verifiy the points are inside the plotArea
*
* @return {Array<Highcharts.Point>}
* An array of transformed points
*/
H.perspective = function (points, chart, insidePlotArea) {
var options3d = chart.options.chart.options3d,
inverted = insidePlotArea ? chart.inverted : false,
origin = {
x: chart.plotWidth / 2,
y: chart.plotHeight / 2,
z: options3d.depth / 2,
vd: pick(options3d.depth, 1) * pick(options3d.viewDistance, 0)
},
scale = chart.scale3d || 1,
beta = deg2rad * options3d.beta * (inverted ? -1 : 1),
alpha = deg2rad * options3d.alpha * (inverted ? -1 : 1),
angles = {
cosA: Math.cos(alpha),
cosB: Math.cos(-beta),
sinA: Math.sin(alpha),
sinB: Math.sin(-beta)
};
if (!insidePlotArea) {
origin.x += chart.plotLeft;
origin.y += chart.plotTop;
}
// Transform each point
return points.map(function (point) {
var rotated = rotate3D(
(inverted ? point.y : point.x) - origin.x,
(inverted ? point.x : point.y) - origin.y,
(point.z || 0) - origin.z,
angles
),
// Apply perspective
coordinate = H.perspective3D(rotated, origin, origin.vd);
// Apply translation
coordinate.x = coordinate.x * scale + origin.x;
coordinate.y = coordinate.y * scale + origin.y;
coordinate.z = rotated.z * scale + origin.z;
return {
x: (inverted ? coordinate.y : coordinate.x),
y: (inverted ? coordinate.x : coordinate.y),
z: coordinate.z
};
});
};
/**
* Calculate a distance from camera to points - made for calculating zIndex of
* scatter points.
*
* @private
* @function Highcharts.pointCameraDistance
*
* @param {object} coordinates
* The coordinates of the specific point
*
* @param {Highcharts.Chart} chart
* The chart
*
* @return {number}
* A distance from camera to point
*/
H.pointCameraDistance = function (coordinates, chart) {
var options3d = chart.options.chart.options3d,
cameraPosition = {
x: chart.plotWidth / 2,
y: chart.plotHeight / 2,
z: pick(options3d.depth, 1) * pick(options3d.viewDistance, 0) +
options3d.depth
},
distance = Math.sqrt(
Math.pow(cameraPosition.x - coordinates.plotX, 2) +
Math.pow(cameraPosition.y - coordinates.plotY, 2) +
Math.pow(cameraPosition.z - coordinates.plotZ, 2)
);
return distance;
};
/**
* Calculate area of a 2D polygon using Shoelace algorithm
* http://en.wikipedia.org/wiki/Shoelace_formula
*
* @private
* @function Highcharts.shapeArea
*
* @param {Array<object>} vertexes
*
* @return {number}
*/
H.shapeArea = function (vertexes) {
var area = 0,
i,
j;
for (i = 0; i < vertexes.length; i++) {
j = (i + 1) % vertexes.length;
area += vertexes[i].x * vertexes[j].y - vertexes[j].x * vertexes[i].y;
}
return area / 2;
};
/**
* Calculate area of a 3D polygon after perspective projection
*
* @private
* @function Highcharts.shapeArea3d
*
* @param {Array<object>} vertexes
*
* @param {Highcharts.Chart} chart
*
* @param {boolean} [insidePlotArea]
*
* @return {number}
*/
H.shapeArea3d = function (vertexes, chart, insidePlotArea) {
return H.shapeArea(H.perspective(vertexes, chart, insidePlotArea));
};