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import * as THREE from 'three';
import { RandomColor } from 'ray-visutil/lib/ColorUtils';
import tools from './tools';
import R3DTools from './R3DTools';
const ThreeMath = THREE.Math;
const R3DMath = {
ThreeMath,
toInteger(n) {
// 转化为 Number， +'1'， +null (0)
// +'a', +'1a', +undefined 均为 NaN
n = +n;
// NaN !== NaN -> true, 可用 n !== n 来判断 NaN
// isNaN(NaN) -> true
if (isNaN(n)) {
// isNaN
n = 0;
} else if (n !== 0 && n !== 1 / 0 && n !== -(1 / 0)) {
n = (n > 0 || -1) * Math.floor(Math.abs(n));
}
return n;
},
clamp(value, min, max) {
return ThreeMath.clamp(value, min, max);
},
/**
* Returns a random number between min (inclusive) and max (exclusive)
* 获取随机浮点数值[最小值, 最大值]
* @param {Number} min 最小值
* @param {Number} max 最大值
* @return {Number}
*/
randomFloat(min, max) {
return Math.random() * (max - min) + min;
},
/**
* Returns a random integer between min (inclusive) and x (inclusive)
* Using Math.round() will give you a non-uniform distribution!
* 获取随机整数数值[最小值, 最大值]
* @param {Number} min 最小值
* @param {Number} max 最大值
* @return {Number}
*/
randomInt(min, max) {
const args = arguments;
if (args.length === 0) {
min = 0;
max = 10;
} else if (args.length === 1) {
min = 0;
max = args[0];
}
return Math.floor(Math.random() * (max - min + 1)) + min;
},
randomBoolean() {
return !!(this.randomInt() % 2);
},
randomColorHex(){
return RandomColor.hexColorStr();
},
/** 获取随机颜色, 返回 number 类型 */
randomColor() {
return RandomColor.intColor();
},
randomTColor() {
const color = RandomColor.intColor();
return new THREE.Color(color);
},
/** 从数组随机挑选出任一元素 */
randomFromArray(arr) {
const i = R3DMath.randomInt(0, arr.length - 1);
return arr[i];
},
/**
* 产生随机下标值 [0, number - 1]
* @param {Number} number 总数
* @return {Number}
*/
randomIndex(number) {
if (!number) {
return 0;
}
return R3DMath.randomInt(0, number - 1);
},
/**
* 随机产生坐标信息
* @param {Number} rx? x 坐标会在[-rx, rx]之间进行随机
* @param {Number} ry? y 坐标会在[-ry, ry]之间进行随机
* @param {Number} rz? z 坐标会在[-rz, rz]之间进行随机
* @return {Array<Number>}
* @example
* // xyz 会在 [-10, 10] 之间随机
* R3DMath.randomVector3(10, 10, 10);
* // 也可用如下的方式调用(xyz 用同一个数值)
* R3DMath.randomVector3(10);
*/
randomVector3(...args) {
if (args.length === 1) {
const range = args[0];
const x = ThreeMath.randFloat(-range, range);
const y = ThreeMath.randFloat(-range, range);
const z = ThreeMath.randFloat(-range, range);
return new THREE.Vector3(x, y, z);
}
// 只有两个参数时，表示 x - z 平面，y 值默认为 0
else if (args.length === 2) {
const rx = args[0];
const rz = args[1];
const x = ThreeMath.randFloat(-rx, rx);
const z = ThreeMath.randFloat(-rz, rz);
return new THREE.Vector3(x, 0, z);
} else if (args.length === 3) {
const rx = args[0];
const ry = args[1];
const rz = args[2];
const x = ThreeMath.randFloat(-rx, rx);
const y = ThreeMath.randFloat(-ry, ry);
const z = ThreeMath.randFloat(-rz, rz);
return new THREE.Vector3(x, y, z);
}
},
/**
* 随机 position
* @param {*} max
* @param {*} radius
* @returns {Number[]}
*/
randomPosition(max, radius) {
const vec3 = R3DMath.randomVector3(max);
// 同 vec3.normalize().multiplyScalar(radius || 1);
vec3.setLength(radius || 1);
return vec3.toArray();
},
/**
* 随机产生 Vector2 坐标信息
* @param {Number} rx? x 坐标会在[-rx, rx]之间进行随机
* @param {Number} ry? y 坐标会在[-ry, ry]之间进行随机
* @return {Array<Number>}
* @example
* // xy 会在 [-10, 10] 之间随机
* R3DMath.randomVector2(10, 10);
* // 也可用如下的方式调用(xy 用同一个数值)
* R3DMath.randomVector2(10);
*/
randomVector2(...args) {
if (args.length === 1) {
const range = args[0];
const x = ThreeMath.randFloat(-range, range);
const y = ThreeMath.randFloat(-range, range);
return new THREE.Vector2(x, y);
} else if (args.length === 2) {
const rx = args[0];
const ry = args[1];
const x = ThreeMath.randFloat(-rx, rx);
const y = ThreeMath.randFloat(-ry, ry);
return new THREE.Vector2(x, y);
}
return new THREE.Vector2(ThreeMath.randFloat(0, 1), ThreeMath.randFloat(0, 1));
},
/**
* 获取随机的 scale
* @param {Number} modulus 模数, 0.5 表示取值为 [0.5, 1.5] 之间的数
* @return {Number}
*/
randomScale(modulus = 0.5){
return Math.random() * Math.random() + modulus;
},
/**
* 随机生成一系列点
* @param {number} [count=5] 点集合总数， 除去默认 [0, 0, 0]
* @param {number} [space=10] 每个点间距最大值，用于生成 offset 系数
* @returns array
*/
randomPoints(count = 5, space = 10) {
const points = [[0, 0, 0]];
let oldType = 2;
for (let i = 0; i < count; i++) {
const old = points[points.length - 1];
let type = R3DMath.randomInt(100) % 3;
while (oldType === type) {
type = R3DMath.randomInt(100) % 3;
}
oldType = type;
const offset = R3DMath.randomInt(1, space) * (Math.random() > 0.5 ? 1 : -1);
points.push([type === 0 ? old[0] + offset : old[0], type === 1 ? old[1] + offset : old[1], type === 2 ? old[2] + offset : old[2]]);
}
return points;
},
/**
* 向上取数值的2次幂
* @param {Number} v 数值
* @return {Number}
*/
roundUpPowerOf2(v) {
v--;
v |= v >> 1;
v |= v >> 2;
v |= v >> 4;
v |= v >> 8;
v |= v >> 16;
v++;
return v;
},
/**
* 返回小数部分
* @param {Number} x 数值
* @return {Number}
*/
fract(x) {
return x - Math.floor(x);
},
/**
* 抛物线路径
* @param {*} vecStart
* @param {*} vecEnd
* @returns
*/
parabolaPath(vecStart, vecEnd) {
const pathArr = [];
const vec1 = R3DTools.parseNumber3(vecStart);
const vec2 = R3DTools.parseNumber3(vecEnd);
let start = R3DMath.addVector(vec1, vec2);
start = R3DMath.scaleVector(start, 0.5);
start[1] = R3DMath.getDistance(vec1, vec2) * 0.6;
for (let i = 0; i < 1; i += 0.001) {
const v1 = R3DMath.scaleVector(vec1, Math.pow(1 - i, 2));
const v2 = R3DMath.scaleVector(start, 2 * i * (1 - i));
const v3 = R3DMath.scaleVector(vec2, Math.pow(i, 2));
const v4 = R3DMath.addVector(v1, v2);
const point = R3DMath.addVector(v4, v3);
pathArr.push(point);
}
return pathArr;
},
/**
* 创建圆 路径
*
* @param {number} [radius=100]
*/
createCirclePath(radius = 100) {
const pathArr = [];
for (let degree = 0; degree <= 360; degree += 10) {
const x = Math.cos((degree * 2 * Math.PI) / 360) * radius;
const z = Math.sin((degree * 2 * Math.PI) / 360) * radius;
pathArr.push([x, 0, z]);
}
return pathArr;
},
/**
* 创建圆形平面点
* @param {*} center 中心点
* @param {Number} radius 半径
* @param {Number} spaceDegree 每个点间隔 默认 10
* @param {Number} raiseHeight 提高高度
*/
circlePlanePoints(center, radius = 100, raiseHeight = 0, spaceDegree = 10){
center = R3DTools.parseNumber3(center, [0, 0, 0]);
const pathArr = [];
const planeCenter = [center[0], center[1] + raiseHeight, center[2]]; // 圆心世界坐标
// 根据圆形和半径计算坐标点
for (let degree = 0, y = 0; degree <= 360; degree += 10) {
const x = Math.cos((degree * 2 * Math.PI) / 360) * radius;
const z = Math.sin((degree * 2 * Math.PI) / 360) * radius;
const pos = R3DMath.addVector([x, y, z], planeCenter);
pathArr.push(pos);
}
return pathArr;
},
/**
* 创建矩形平面点
* @param {String|Array<Number>|Object|THREE.Vector3} center 中心点 如 `x,y,z`、`[x,y,z]`、{x, y, z}、、
* @param {Number} width 矩形长
* @param {Number} height 矩形宽
* @param {Number} raiseHeight 提高高度
*/
rectPlanePoints(center, width = 100, height = 100, raiseHeight = 0){
center = R3DTools.parseNumber3(center, [0, 0, 0]);
const pathArr = [];
const [x, y, z] = [center[0], center[1] + raiseHeight, center[2]]; // 中心世界坐标
const halfW = width / 2;
const halfH = height / 2;
// 根据圆形和半径计算坐标点
const v1 = [x - halfW, y, z - halfH];
const v2 = [x + halfW, y, z - halfH];
const v3 = [x + halfW, y, z + halfH];
const v4 = [x - halfW, y, z + halfH];
pathArr.push(v1, v2, v3, v4);
return pathArr;
},
/**
* 线性插值
* @param {Number} start 起始值
* @param {Number} end 终止值
* @param {Number} percent 百分比(0~1)
* @return {Number}
* @example
* R3DMath.lerp(2,10,0.5) // 6
*/
lerp(start, end, percent) {
return start + percent * (end - start);
},
matrixLerp($from, to, time) {
const ret = new THREE.Matrix4();
for (let i = 0; i < 16; i++) {
ret[i] = $from.elements[i] + (to.elements[i] - $from.elements[i]) * time;
}
return ret;
},
getArrayIndexFromProgress(array, progress, steps) {
if (!array.length) {
return -1;
}
if (progress >= 1) {
return array.length - 1;
}
if (steps) {
let curProgress = 0;
for (let i = 0; i < steps.length; i++) {
const step = steps[i];
const endProgress = curProgress + step;
if (endProgress >= progress) {
return i;
}
curProgress += step;
}
} else {
const step = 1 / array.length;
const index = Math.floor(progress / step);
return Math.min(index, array.length - 1);
}
},
getArrayProgress(array, progress, steps) {
if (!array.length) {
return 0;
}
if (progress >= 1) {
return 1;
}
if (steps) {
let curProgress = 0;
for (let i = 0; i < steps.length; i++) {
const step = steps[i];
const endProgress = curProgress + step;
const deltaProgress = endProgress - progress;
if (deltaProgress >= 0) {
return 1 - deltaProgress / step;
}
curProgress += step;
}
} else {
const step = 1 / array.length;
return this.fract(progress / step);
}
},
getConsumeTime(params = {}, defaultTime) {
const { total, from: $from, to, distance, duration, speed, defaultTime: df } = params;
// 如果使用了速度, 用速度计算消耗时间
if (speed) {
let d = distance;
if (!distance) {
const fromPos = tools.parseVector3([$from.x, $from.y, $from.z]);
const toPos = tools.parseVector3([to.x, to.y, to.z]);
d = fromPos.distanceTo(toPos);
}
return (d / speed) * 1000;
}
// 直接使用时间
else if (duration !== undefined) {
if (total) {
return duration / total.length;
} else {
return duration;
}
}
// 时间和速度都没有提供，那么就返回默认时间
else {
return defaultTime || df;
}
},
/**
* return the distance between two points.
* 获取两点间距离
*
* @param {number} x1 x position of first point
* @param {number} y1 y position of first point
* @param {number} x2 x position of second point
* @param {number} y2 y position of second point
* @return {number} distance between given points
*/
getDistance(...args) {
let x1;
let y1;
let x2;
let y2;
if (args.length === 2) {
x1 = args[0][0];
y1 = args[0][1];
x2 = args[1][0];
y2 = args[1][1];
} else Eif (args.length === 4) {
x1 = args[0];
y1 = args[1];
x2 = args[2];
y2 = args[3];
}
let xs = x2 - x1;
let ys = y2 - y1;
xs *= xs;
ys *= ys;
return Math.sqrt(xs + ys);
},
distance(...args) {
return R3DMath.getDistance(args);
},
degToRad(degrees) {
return ThreeMath.degToRad(degrees);
},
radToDeg(radians) {
return ThreeMath.radToDeg(radians);
},
/**
* 生成唯一的 UUID
* @return {String}
*/
generateUUID(simpilfy) {
let uuid = ThreeMath.generateUUID();
if (simpilfy) {
uuid = uuid.replaceAll('-', '');
}
return uuid;
},
/**
* 交换坐标 x, y 值
* @param {Array<Number>} v 坐标
*/
swapXY(v) {
return [v[1], v[0]];
},
/**
* 坐标相加
* @param {Array<Number>} v1 坐标
* @param {Array<Number>} v2 坐标
* @return {Array<Number>}
*/
addVector3(v1, v2) {
return [v1[0] + v2[0], v1[1] + v2[1], v1[2] + v2[2]];
},
/**
* 坐标相加
* @param {Array<Number>} v1 坐标
* @param {Array<Number> | Number} v2 坐标 或 值
* @return {Array<Number>}
*/
addVector(v1, v2) {
if (tools.isArray(v2)) {
return [v1[0] + v2[0], v1[1] + v2[1], v1[2] + v2[2]];
} else if (tools.isNumber(v2)) {
return [v1[0] + v2, v1[1] + v2, v1[2] + v2];
}
},
/**
* 坐标相减
* @param {Array<Number>} v1 坐标
* @param {Array<Number>} v2 坐标
* @return {Array<Number>}
*/
subVector3(v1, v2) {
return [v1[0] - v2[0], v1[1] - v2[1], v1[2] - v2[2]];
},
/**
* 坐标相减
* @param {Array<Number>} v1 坐标
* @param {Array<Number> | Number} v2 坐标 或 值
* @return {Array<Number>}
*/
subVector(v1, v2) {
if (tools.isArray(v2)) {
return [v1[0] - v2[0], v1[1] - v2[1], v1[2] - v2[2]];
} else if (tools.isNumber(v2)) {
return [v1[0] - v2, v1[1] - v2, v1[2] - v2];
}
},
/**
* 获取面积
* @param {Array<Number>} positions 坐标列表
* @return {Number}
*/
getArea(positions) {
const points = [];
for (let i = 0, len = positions.length; i < len; i++) {
points.push(R3DTools.parseVector3(positions[i]));
}
const area = THREE.ShapeUtils.area(points);
return Math.abs(area);
},
/**
* 检测坐标点是否在多边形内部
* @param {Array<Number>} point 坐标点
* @param {Array<Array<Number>>} vs 多边形区域
* @return {Boolean}
*/
pointInPolygon(point, vs) {
// ray-casting algorithm based on
// http://www.ecse.rpi.edu/Homepages/wrf/Research/Short_Notes/pnpoly.html
const x = point[0];
const y = point[1];
let inside = false;
for (let i = 0, j = vs.length - 1; i < vs.length; j = i++) {
const xi = vs[i][0];
const yi = vs[i][1];
const xj = vs[j][0];
const yj = vs[j][1];
const intersect = yi > y !== yj > y && x < ((xj - xi) * (y - yi)) / (yj - yi) + xi;
if (intersect) {
inside = !inside;
}
}
return inside;
},
Vector3: THREE.Vector3,
/**
* Convert alpha beta rotation to direction.
* @param {number} alpha 垂直方向上与z轴的夹角
* @param {number} beta x-y平面上的夹角
* @return {THREE.Vector3} new vector3 or new out
*/
directionFromAlphaBeta(alpha, beta) {
const theta = (alpha / 180) * Math.PI + Math.PI / 2;
const phi = (-beta / 180) * Math.PI + Math.PI / 2;
const dir = new THREE.Vector3();
const r = Math.sin(theta);
dir.x = r * Math.cos(phi);
dir.y = -Math.cos(theta);
dir.z = r * Math.sin(phi);
return dir;
},
/**
* 从角度获取方向 点
* @param {number} yAngle
* @param {number} xAngle
* @param {number} distance
* @returns {THREE.Vector3}
*/
getDirectionFromAngles(yAngle, xAngle, distance) {
const dir = R3DMath.directionFromAlphaBeta(yAngle, xAngle);
dir.normalize();
dir.multiplyScalar(distance);
return dir;
},
/**
* 获取相对于自己坐标系的位置
*
* @param {object} [params={}] 参数列表
* @property {number} params.xAngle X 轴角度值
* @property {number} params.yAngle Y 轴角度值
* @property {number} params.distance 距离
* @property {number} params.factor 系数
* @returns {Array<Number>} 自身坐标系下的坐标位置
*/
getOffsetPosition(params = {}) {
const { xAngle = 0, yAngle = 0, distance = 10, factor } = params;
let radius = distance;
if (factor) {
radius = radius * factor;
}
return R3DMath.getDirectionFromAngles(yAngle, xAngle, radius).toArray();
},
/**
* 获取屏幕渲染位置
* @param {Array<Number>} position 对齐坐标位置[0,0]~[1,1](百分比)
* @param {Array<Number>} size 元素像素尺寸
* @param {Array<Number>} screenSize 屏幕像素尺寸
*/
getRenderPosition(position, size, screenSize) {
screenSize = screenSize || [window.innerWidth, window.innerHeight];
const halfWidth = screenSize[0] / 2;
const halfHeight = screenSize[1] / 2;
const center = [position[0] * halfWidth, position[1] * halfHeight];
const halfSize = [size[0] / 2, size[1] / 2];
center[0] = R3DMath.clamp(center[0], -halfWidth + halfSize[0], halfWidth - halfSize[0]);
center[1] = R3DMath.clamp(center[1], -halfHeight + halfSize[1], halfHeight - halfSize[1]);
return [center[0], -center[1]];
},
/**
* 获取向量长度
* @param {Array<Number>} v 坐标
* @return {Number}
*/
getVectorLength(v) {
return Math.sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
},
/** 判断数值是否2次幂 */
isPowOf2(num) {
return num > 0 && (num & (num - 1)) === 0;
},
/** 往大取2次幂数值 */
floorPowOf2(value) {
return Math.pow(2, Math.floor(Math.log(value) / Math.LN2));
},
/**
* 向量数乘
* @param {Array<Number>} v 坐标
* @param {Number} scale 缩放系数
* @return {Array<Number>}
*/
scaleVector(v, scale) {
if (tools.isArray(scale)) {
return [v[0] * scale[0], v[1] * scale[1], v[2] * scale[2]];
} else Eif (tools.isNumber(scale)) {
return [v[0] * scale, v[1] * scale, v[2] * scale];
}
},
/**
* 向量数除
* @param {Array<Number>} v 坐标
* @param {Number} scale 缩放系数
* @return {Array<Number>}
*/
divideVector(v, scale) {
if (tools.isArray(scale)) {
return [v[0] / scale[0], v[1] / scale[1], v[2] / scale[2]];
} else Eif (tools.isNumber(scale)) {
return [v[0] / scale, v[1] / scale, v[2] / scale];
}
},
/**
* 求单位向量
* @param {Array<Number>} v 坐标
* @return {Array<Number>}
*/
normalizeVector(v) {
const m = 1.0 / this.getVectorLength(v);
return [v[0] * m, v[1] * m, v[2] * m];
},
/**
* 四舍五入，保留位数为 digit
* @param {Number} tarNumber
* @param {Number} digit
*/
roundDigit(tarNumber, digit = 0) {
if (digit < 1) {
const result = parseInt(tarNumber);
return isNaN(result) ? 0 : result;
}
// why not Number(tarNumber)? Number('111aa') -> NaN
tarNumber = parseFloat(tarNumber);
if (isNaN(tarNumber)) {
return 0;
}
let result;
if (tarNumber >= 0) {
result = parseInt(tarNumber * Math.pow(10, digit) + 0.5) / Math.pow(10, digit);
} else E{
const negNumber = -tarNumber;
result = parseInt(negNumber * Math.pow(10, digit) + 0.5) / Math.pow(10, digit);
}
return result;
},
/**
* 将极坐标(p, θ) 转化为 直角坐标 (x, y)
* !!! 在 Math 的三角函数中，参数均为弧度
* sin0°=0,sin90°=1,sin180°=0,sin270°=﹣1,sin360°=0;
* cos0°=1,cos90°=0,cos180°=﹣1,cos270°=0,cos360°=1;
* @param {Number} p 极坐标系中的 p
* @param {Number} angle 极坐标系中的 θ 单位为 度
*/
polarToXY(p, angle) {
// 将度转化为弧度
const radian = R3DMath.degToRad(angle);
const x = p * Math.cos(radian);
const y = p * Math.sin(radian);
return [x, y];
},
/**
* 将极坐标(p, θ) 转化为 坐标 (x, y, z) x：正东， z:正北，y 高度
* @param {Number} p 极坐标系中的 p
* @param {Number} angle 极坐标系中的 θ
*/
polarToVector3(p, angle, high = 0) {
// 将度转化为弧度
const radian = R3DMath.degToRad(angle);
const x = p * Math.cos(radian);
const z = p * Math.sin(radian);
return [x, high, z];
},
/**
* 通过时间、和 x-y 平面夹角 获取太阳的位置，以及设置光照颜色
* @param {Number} time
* @param {Number} angleOnXYPlane 角度
*/
getSunConfig(time, angleOnXYPlane) {
const alpha = (time / 24) * 360 - 90;
const sunPos = R3DMath.directionFromAlphaBeta(alpha, angleOnXYPlane);
// 中午和晚上的颜色设置
const noonColor = new THREE.Color().setHex(0xffffff);
const earlyEveningColor = new THREE.Color().setHex(0xff8940);
const lightColor = new THREE.Color();
// 设置主光源数据
const night = time < 6 || time > 18;
const lerp = 1 - Math.abs(time - 12) / 6;
const dirColor = lightColor.copy(earlyEveningColor).lerp(noonColor, lerp);
// hemisphereLight 光照颜色
const hemisphereLight = {
intensity: Math.min(Math.max(night ? 0 : lerp + 0.3, 0.2), 0.7)
};
const mainLight = {
color: dirColor.getHex(),
alpha,
beta: angleOnXYPlane
};
return {
sunPosition: R3DTools.parseVector3(sunPos),
hemisphereLight,
mainLight
};
}
};
export { ThreeMath };
export default R3DMath;
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