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添加一个生成匀速Bezier曲线

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leo
2021-03-31 01:22:55 +08:00
parent ec3248ba98
commit e1995046bc
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BezierPathsDemo/.gitignore vendored Normal file
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#///////////////////////////
# Cocos Creator 3D Project
#///////////////////////////
library/
temp/
local/
build/
profiles/
native
#//////////////////////////
# NPM
#//////////////////////////
node_modules/
#//////////////////////////
# VSCode
#//////////////////////////
.vscode/
#//////////////////////////
# WebStorm
#//////////////////////////
.idea/

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# 生成匀速Bezier曲线
> 实现2d与3d的三阶匀速曲线
## 参考
* https://blog.csdn.net/iSunwish/article/details/78935257
* https://blog.csdn.net/iSunwish/article/details/112127363

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import { v2, Vec2, Vec3 } from "cc";
export class BezierCurvesKit {
private static _instance: BezierCurvesKit;
public static get Instacne() {
if (this._instance == null) {
this._instance = new BezierCurvesKit();
}
return this._instance;
}
/**
* 计算三阶曲线 三维坐标
* @param t
* @param p0
* @param p1
* @param p2
* @param p3
*/
private calculateBezierPoint3(t: number, p0: Vec3, p1: Vec3, p2: Vec3, p3: Vec3) {
let u = 1 - t;
let tt = t * t;
let uu = u * u;
let uuu = uu * u;
let ttt = tt * t;
let point = new Vec3();
let x = uuu * p0.x + 3 * uu * t * p1.x + 3 * u * tt * p2.x + ttt * p3.x;
let y = uuu * p0.y + 3 * uu * t * p1.y + 3 * u * tt * p2.y + ttt * p3.y;
let z = uuu * p0.z + 3 * uu * t * p1.z + 3 * u * tt * p2.z + ttt * p3.z;
Vec3.set(point, x, y, z);
return point;
}
/**
* 计算三阶曲线 二维坐标
* @param t
* @param p0
* @param p1
* @param p2
* @param p3
*/
private calculateBezierPoint2(t: number, p0: Vec2, p1: Vec2, p2: Vec2, p3: Vec2) {
let u = 1 - t;
let tt = t * t;
let uu = u * u;
let uuu = uu * u;
let ttt = tt * t;
let point = new Vec2();
let x = uuu * p0.x + 3 * uu * t * p1.x + 3 * u * tt * p2.x + ttt * p3.x;
let y = uuu * p0.y + 3 * uu * t * p1.y + 3 * u * tt * p2.y + ttt * p3.y;
Vec2.set(point, x, y);
return point;
}
public calculateBezierPoint(t: number, p0: Vec2 | Vec3, p1: Vec2 | Vec3, p2: Vec2 | Vec3, p3: Vec2 | Vec3) {
if (p0 instanceof Vec2) {
return this.calculateBezierPoint2(t, p0, p1, p2, p3);
} else {
return this.calculateBezierPoint3(t, p0, p1, p2, p3);
}
}
//
private speedX(points: Vec3[] | Vec2[], t: number) {
let a = -3 * points[0].x * Math.pow(1 - t, 2) + 3 * points[1].x * Math.pow(1 - t, 2) - 6 * points[1].x * (1 - t) * t + 6 * points[2].x * (1 - t) * t - 3 * points[2].x * Math.pow(t, 2) + 3 * points[3].x * Math.pow(t, 2);
return a;
}
private speedY(points: Vec3[] | Vec2[], t: number) {
let a = -3 * points[0].y * Math.pow(1 - t, 2) + 3 * points[1].y * Math.pow(1 - t, 2) - 6 * points[1].y * (1 - t) * t + 6 * points[2].y * (1 - t) * t - 3 * points[2].y * Math.pow(t, 2) + 3 * points[3].y * Math.pow(t, 2);
return a;
}
private speedZ(points: Vec3[], t: number) {
let a = -3 * points[0].z * Math.pow(1 - t, 2) + 3 * points[1].z * Math.pow(1 - t, 2) - 6 * points[1].z * (1 - t) * t + 6 * points[2].z * (1 - t) * t - 3 * points[2].z * Math.pow(t, 2) + 3 * points[3].z * Math.pow(t, 2);
return a;
}
private speedMerge2(points: Vec2[], t: number) {
let v_x = this.speedX(points, t);
let v_y = this.speedY(points, t);
return Math.sqrt(Math.pow(v_x, 2) + Math.pow(v_y, 2));
}
private speedMerge3(points: Vec3[], t: number) {
let v_x = this.speedX(points, t);
let v_y = this.speedY(points, t);
let v_z = this.speedZ(points, t);
return Math.sqrt(Math.pow(v_x, 2) + Math.pow(v_y, 2) + Math.pow(v_z, 2));
}
private speedMerge(points: Vec2[] | Vec3[], t: number) {
if (points[0] instanceof Vec2) {
return this.speedMerge2(points, t);
} else {
return this.speedMerge3(points, t);
}
}
/**
* 求 0~t 段的三阶贝塞尔曲线长度
* t为realTime
* @param points
*/
private pathLength(points: Vec2[] | Vec3[], t: number) {
let total_step = 100000;
let step_counts = total_step;
let half_counts;
let i = 0;
let sum_1 = 0, sum_2 = 0, t_step;
if (step_counts == 0) {
return 0;
}
if (step_counts % 2 == 0) {
step_counts++;
}
half_counts = step_counts / 2;
t_step = t / step_counts;
while (i < half_counts) {
sum_1 += this.speedMerge(points, (2 * i + 1) * t_step);
i++;
}
i = 1;
while (i < half_counts) {
sum_2 += this.speedMerge(points, (2 * i * t_step));
i++;
}
return (this.speedMerge(points, 0) + this.speedMerge(points, 1) + 2 * sum_2 + 4 * sum_1) * t_step / 3;
}
/**
* 通过对应的弧长来取得rt
* @param points
* @param length
*/
private realTimeByLength(points: Vec2[] | Vec3[], length: number) {
let real_time = 0;
let rt_length = 0;
let delta_length = 0;
let delta_time = 0;
let low = 0, high = 1;
do {
if (delta_length > 0) {
real_time -= (real_time - low) / 2;
delta_time = real_time - low;
} else {
real_time += (high - real_time) / 2;
delta_time = high - real_time;
}
rt_length = this.pathLength(points, real_time);
delta_length = rt_length - length;
if (delta_length > 0) {
high = real_time;
} else {
low = real_time;
}
// 0.01 的误差已经很小了，可视为此时的 rt 就是真实的 rt
// 或者 rt 的更新量足够小时也应跳出，防止梯度消失造成死循环
} while (Math.abs(delta_length) > 0.01 && delta_time > 0.000000001)
return real_time;
}
/**
* 取得匀速点数组
* @param points
* @param step
*/
public getUniformPoints(points: Vec2[] | Vec3[],step:number=100) {
let lengthTotal = this.pathLength(points, 1);
let deltaStep = lengthTotal / step;
let drawingPoints: Vec2[] | Vec3[] = [];
for (let i = 0; i < points.length - 3; i += 3) {
let p0: Vec2 | Vec3 = points[i];
let p1: Vec2 | Vec3 = points[i + 1];
let p2: Vec2 | Vec3 = points[i + 2];
let p3: Vec2 | Vec3 = points[i + 3];
if (i == 0) {
drawingPoints.push(p0);
}
for (let j = 1; j <= step; j++) {
let length = deltaStep * j;
let t = this.realTimeByLength([p0, p1, p2, p3], length);
drawingPoints.push(this.calculateBezierPoint(t, p0, p1, p2, p3));
}
}
return drawingPoints;
}
}
/**
* 参考文章
* https://blog.csdn.net/iSunwish/article/details/78935257
* https://blog.csdn.net/iSunwish/article/details/112127363
*/

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import { _decorator, Component, Node, Vec2, Graphics, v2 } from 'cc';
const { ccclass, property } = _decorator;
@ccclass('GraphicsHelper')
export class GraphicsHelper extends Component {
private graphics: Graphics = null!;
onLoad() {
this.graphics = this.node.getComponent(Graphics);
console.log('graphics=', this.graphics);
}
start() {
// [3]
// this.drawPoints([v2(10, 10), v2(-10, 10), v2(10, -10), v2(-10, -10)], 5);
// this.drawFill();
}
drawPoints(points: Vec2[], radius: number) {
for (let i = 0; i < points.length; i++) {
let point = points[i];
this.graphics.circle(point.x, point.y, radius);
}
}
drawPointsLine(points: Vec2[], isClose: boolean = false) {
let length = points.length;
if (length < 2) {
console.warn('point num less than one')
return;
}
this.graphics.moveTo(points[0].x, points[0].y);
for (let i = 1; i < length; i++) {
let point = points[i];
this.graphics.lineTo(point.x, point.y);
}
if (isClose) {
this.graphics.close();
}
}
drawFill() {
this.graphics.fill();
}
drawStroke() {
this.graphics.stroke();
}
}

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import { _decorator, Component, Node, v2, Vec2 } from 'cc';
import { BezierCurvesKit } from './BezierCurvesKit';
import { GraphicsHelper } from './GraphicsHelper';
const { ccclass, property } = _decorator;
@ccclass('Main')
export class Main extends Component {
@property(GraphicsHelper)
graphicsHelper: GraphicsHelper = null!
start() {
// [3]
let points = [v2(-300, -100), v2(-150, 700), v2(50, 600), v2(300, -200)];
this.graphicsHelper.drawPoints(points, 10);
this.graphicsHelper.drawFill();
// let paths: Vec2[] = BezierCurves.getDrawingPoints2(points, 100);
let paths:Vec2[]=BezierCurvesKit.Instacne.getUniformPoints(points,20);
// this.graphicsHelper.drawPointsLine(paths);
// this.graphicsHelper.drawStroke();
this.graphicsHelper.drawPoints(paths, 3);
this.graphicsHelper.drawFill();
}
// update (deltaTime: number) {
// // [4]
// }
}
/**
* [1] Class member could be defined like this.
* [2] Use `property` decorator if your want the member to be serializable.
* [3] Your initialization goes here.
* [4] Your update function goes here.
*
* Learn more about scripting: https://docs.cocos.com/creator/3.0/manual/en/scripting/
* Learn more about CCClass: https://docs.cocos.com/creator/3.0/manual/en/scripting/ccclass.html
* Learn more about life-cycle callbacks: https://docs.cocos.com/creator/3.0/manual/en/scripting/life-cycle-callbacks.html
*/

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/**
* UI 的渲染在 v3.0 变为使用 node.layer 来判断可见性，为了保证老版本项目升级后表现一致，
* Creator 会在运行时动态分配一个未使用的 layer 给常驻节点的 UI，避免常驻节点的 UI 与场景中
* 的其他 UI 的 layer 发生冲突，当你确定不会发生冲突时，你可以移除此脚本.
*
* UI rendering has changed in v3.0 to use node.layer to determine visibility.
* To ensure consistent performance after upgrading old projects.
* Creator will dynamically assign an unused layer to the UI node in the persist node at
* runtime to avoid conflicts between the layer of UI in the persist node and the
* layer of other UI in the scene. You can remove this script when you
* are sure there is no conflict
*/
import { _decorator, Node, director, Director, game, BaseNode, Canvas, Camera } from 'cc';
const customLayerMask = 0x000fffff;
const builtinLayerMask = 0xfff00000;
director.on(Director.EVENT_AFTER_SCENE_LAUNCH, () => {
const roots = director.getScene()?.children as BaseNode[];
let allCanvases = director.getScene()?.getComponentsInChildren(Canvas) as Canvas[];
if (allCanvases.length <= 1) return;
allCanvases = allCanvases.filter(x => !!x.cameraComponent);
let allCameras = director.getScene()?.getComponentsInChildren(Camera) as Camera[];
let usedLayer = 0;
allCameras.forEach(x => usedLayer |= (x.visibility & customLayerMask));
const persistCanvas: Canvas[] = [];
for (let i = 0, l = roots.length; i < l; i++) {
const root = roots[i];
if (!game.isPersistRootNode(root)) continue;
const canvases = root.getComponentsInChildren(Canvas);
if (canvases.length === 0) continue;
persistCanvas.push(...canvases.filter(x => !!x.cameraComponent));
}
persistCanvas.forEach((val) => {
const isLayerCollided = allCanvases.find(x => x !== val && (x.cameraComponent!.visibility & val.cameraComponent!.visibility & customLayerMask));
if (isLayerCollided) {
const availableLayers = ~usedLayer;
const lastAvailableLayer = availableLayers & ~(availableLayers - 1);
val.cameraComponent!.visibility = lastAvailableLayer | (val.cameraComponent!.visibility & builtinLayerMask);
setChildrenLayer(val.node, lastAvailableLayer);
usedLayer |= availableLayers;
}
});
});
function setChildrenLayer (node: Node, layer: number) {
for (let i = 0, l = node.children.length; i < l; i++) {
node.children[i].layer = layer;
setChildrenLayer(node.children[i], layer);
}
}
let setParentEngine = cc.Node.prototype.setParent;
cc.Node.prototype.setParent = function(value, keepWorldTransform) {
setParentEngine.call(this, value, keepWorldTransform);
if (!value) return;
// find canvas
let layer = getCanvasCameraLayer(this);
if (layer) {
this.layer = layer;
setChildrenLayer(this, layer);
}
}
function getCanvasCameraLayer (node: Node) {
let layer = null;
let canvas = node.getComponent(Canvas);
if (canvas && canvas.cameraComponent) {
if (canvas.cameraComponent.visibility & canvas.node.layer) {
layer = canvas.node.layer;
} else {
layer = canvas.cameraComponent.visibility & ~(canvas.cameraComponent.visibility - 1);
}
return layer;
}
if (node.parent) {
layer = getCanvasCameraLayer(node.parent);
}
return layer;
}

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6
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{
"name": "BezierDemo",
"type": "3d",
"uuid": "c30b28da-749e-479b-bcb6-cecd8d7be9e3",
"version": "3.0.0"
}

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{
"__version__": "1.2.4"
}

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BezierPathsDemo/settings/1.2.0/packages/engine.json Normal file
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{
"modules": {
"cache": {},
"includeModules": [
"base",
"gfx-webgl",
"gfx-webgl2",
"ui",
"particle",
"physics-cannon",
"physics-framework",
"audio",
"tween",
"terrain"
]
},
"__version__": "1.0.1"
}

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BezierPathsDemo/settings/1.2.0/packages/project.json Normal file
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{
"__version__": "1.0.1",
"script": {
"useDefineForClassFields": false,
"allowDeclareFields": false
}
}

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{
"__version__": "1.2.6"
}

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{
"modules": {
"cache": {},
"includeModules": [
"base",
"gfx-webgl",
"3d",
"2d",
"ui",
"particle",
"physics-ammo",
"physics-2d-box2d",
"intersection-2d",
"primitive",
"profiler",
"particle-2d",
"audio",
"video",
"webview",
"tween",
"terrain",
"tiled-map",
"spine",
"dragon-bones"
]
},
"__version__": "1.0.5"
}

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{
"__version__": "1.0.1",
"script": {
"useDefineForClassFields": false,
"allowDeclareFields": false
},
"general": {
"designResolution": {
"width": 720,
"height": 1280
}
}
}

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BezierPathsDemo/tsconfig.json Normal file
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{
/* Base configuration. Do not edit this field. */
"extends": "./temp/tsconfig.cocos.json"
/* Add your custom configuration here. */
}