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/* *
*
* (c) 2010-2024 Torstein Honsi
*
* License: www.highcharts.com/license
*
* !!!!!!! SOURCE GETS TRANSPILED BY TYPESCRIPT. EDIT TS FILE ONLY. !!!!!!!
*
* */
'use strict';
import H from './Globals.js';
const { deg2rad } = H;
import U from './Utilities.js';
const { pick } = U;
/* *
*
* Functions
*
* */
/* 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 */
/**
* Rotates the position as defined in angles.
* @private
* @param {number} x
* X coordinate
* @param {number} y
* Y coordinate
* @param {number} z
* Z coordinate
* @param {Highcharts.Rotation3DObject} angles
* Rotation angles
* @return {Highcharts.Position3DObject}
* 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
};
}
/**
* Transforms a given array of points according to the angles in chart.options.
*
* @private
* @function Highcharts.perspective
*
* @param {Array} points
* The array of points
*
* @param {Highcharts.Chart} chart
* The chart
*
* @param {boolean} [insidePlotArea]
* Whether to verify that the points are inside the plotArea
*
* @param {boolean} [useInvertedPersp]
* Whether to use inverted perspective in calculations
*
* @return {Array}
* An array of transformed points
*
* @requires highcharts-3d
*/
function perspective(points, chart, insidePlotArea, useInvertedPersp) {
const 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) {
const 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 = 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
};
});
}
/**
* 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
*/
function perspective3D(coordinate, origin, distance) {
const projection = ((distance > 0) &&
(distance < Number.POSITIVE_INFINITY)) ?
distance / (coordinate.z + origin.z + distance) :
1;
return {
x: coordinate.x * projection,
y: coordinate.y * projection
};
}
/**
* Calculate a distance from camera to points - made for calculating zIndex of
* scatter points.
*
* @private
* @function Highcharts.pointCameraDistance
*
* @param {Highcharts.Dictionary} coordinates
* Coordinates of the specific point
*
* @param {Highcharts.Chart} chart
* Related chart
*
* @return {number}
* Distance from camera to point
*
* @requires highcharts-3d
*/
function pointCameraDistance(coordinates, chart) {
const 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} vertexes
* 2D Polygon
*
* @return {number}
* Calculated area
*
* @requires highcharts-3d
*/
function shapeArea(vertexes) {
let 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} vertexes
* 3D Polygon
*
* @param {Highcharts.Chart} chart
* Related chart
*
* @param {boolean} [insidePlotArea]
* Whether to verify that the points are inside the plotArea
*
* @return {number}
* Calculated area
*
* @requires highcharts-3d
*/
function shapeArea3D(vertexes, chart, insidePlotArea) {
return shapeArea(perspective(vertexes, chart, insidePlotArea));
}
/* *
*
* Default Export
*
* */
const Math3D = {
perspective,
perspective3D,
pointCameraDistance,
shapeArea,
shapeArea3D
};
export default Math3D;