tupali/librerias/gantt/code/es-modules/parts-3d/Math.js

/* *
 *
 *  (c) 2010-2020 Torstein Honsi
 *
 *  License: www.highcharts.com/license
 *
 *  !!!!!!! SOURCE GETS TRANSPILED BY TYPESCRIPT. EDIT TS FILE ONLY. !!!!!!!
 *
 * */
'use strict';
import H from '../parts/Globals.js';
import U from '../parts/Utilities.js';
var pick = U.pick;
// Mathematical Functionility
var deg2rad = H.deg2rad;
/* 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 */
/**
 * @private
 * @param {number} x
 *        X coordinate
 * @param {number} y
 *        Y coordinate
 * @param {number} z
 *        Z coordinate
 * @param {Highcharts.Rotation3dObject} angles
 *        Rotation angles
 * @return {Highcharts.Rotation3dObject}
 *         Rotated position
 */
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).
 * @private
 * @function Highcharts.perspective3D
 *
 * @param {Highcharts.Position3dObject} coordinate
 * 3D position
 *
 * @param {Highcharts.Position3dObject} origin
 * 3D root position
 *
 * @param {number} distance
 * Perspective distance
 *
 * @return {Highcharts.PositionObject}
 * Perspective 3D Position
 *
 * @requires highcharts-3d
 */
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.Position3dObject>} points
 * The array of points
 *
 * @param {Highcharts.Chart} chart
 * The chart
 *
 * @param {boolean} [insidePlotArea]
 * Whether to verifiy that the points are inside the plotArea
 *
 * @param {boolean} [useInvertedPersp]
 * Whether to use inverted perspective in calculations
 *
 * @return {Array<Highcharts.Position3dObject>}
 * An array of transformed points
 *
 * @requires highcharts-3d
 */
H.perspective = function (points, chart, insidePlotArea, useInvertedPersp) {
    var options3d = chart.options.chart.options3d, 
    /* The useInvertedPersp argument is used for
     * inverted charts with already inverted elements,
     * such as dataLabels or tooltip positions.
     */
    inverted = pick(useInvertedPersp, 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 {Highcharts.Dictionary<number>} coordinates
 * Coordinates of the specific point
 *
 * @param {Highcharts.Chart} chart
 * Related chart
 *
 * @return {number}
 * Distance from camera to point
 *
 * @requires highcharts-3d
 */
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
    }, 
    // Added support for objects with plotX or x coordinates.
    distance = Math.sqrt(Math.pow(cameraPosition.x - pick(coordinates.plotX, coordinates.x), 2) +
        Math.pow(cameraPosition.y - pick(coordinates.plotY, coordinates.y), 2) +
        Math.pow(cameraPosition.z - pick(coordinates.plotZ, coordinates.z), 2));
    return distance;
};
/**
 * Calculate area of a 2D polygon using Shoelace algorithm
 * https://en.wikipedia.org/wiki/Shoelace_formula
 *
 * @private
 * @function Highcharts.shapeArea
 *
 * @param {Array<Highcharts.PositionObject>} vertexes
 * 2D Polygon
 *
 * @return {number}
 * Calculated area
 *
 * @requires highcharts-3d
 */
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<Highcharts.Position3dObject>} vertexes
 * 3D Polygon
 *
 * @param {Highcharts.Chart} chart
 * Related chart
 *
 * @param {boolean} [insidePlotArea]
 * Whether to verifiy that the points are inside the plotArea
 *
 * @return {number}
 * Calculated area
 *
 * @requires highcharts-3d
 */
H.shapeArea3d = function (vertexes, chart, insidePlotArea) {
    return H.shapeArea(H.perspective(vertexes, chart, insidePlotArea));
};