增加一篇博客

docs/.vuepress/public/js/bezier_app.js

@@ -0,0 +1,78 @@
+class QuadBezierLine {
+	constructor(_p0, _p1, _p2, _step, _uniformSpeed) {
+		this.step=_step;
+		this.points=[];
+		this.uniformSpeed=_uniformSpeed;
+		this.updatePoints(_p0, _p1, _p2);
+	}
+	
+	//Speed(t_) = Sqrt[A*t*t+B*t+C]
+	speed(t) {
+		return Math.sqrt(this.A * t * t + this.B * t + this.C);
+	}
+	
+	//Length(t) = Integrate[Speed[t], t]
+	//Length(t_)=((2*Sqrt[A]*(2*A*t*Sqrt[C+t*(B+A*t)]+B*(Sqrt[C + t*(B + A*t)]-Sqrt[C])) +
+	//	(B^2-4*A*C)(Log[B+2*Sqrt[A]*Sqrt[C]]-Log[B+2*A*t+2*Sqrt[A]*Sqrt[C+t*(B+A*t)]]))/
+	//	(8* A^(3/2)));
+	length(t) {
+		let temp1 = Math.sqrt(this.C + t * (this.B + this.A * t));
+		let temp2 = (2 * this.A * t * temp1 + this.B * (temp1 - Math.sqrt(this.C)));
+		let temp3 = Math.log(this.B + 2 * Math.sqrt(this.A) * Math.sqrt(this.C));
+		let temp4 = Math.log(this.B + 2 * this.A * t + 2 * Math.sqrt(this.A) * temp1);
+		let temp5 = 2 * Math.sqrt(this.A) * temp2;
+		let temp6 = (this.B * this.B - 4 * this.A * this.C) * (temp3 - temp4);
+		return (temp5 + temp6) / (8 * Math.pow(this.A, 1.5));
+	}
+	
+	//X(n+1) = Xn - F(Xn)/F'(Xn)
+	invertLength(t, len) {
+		let t1 = t, t2;
+		do {
+			t2 = t1 - (this.length(t1) - len) / this.speed(t1);
+			if (Math.abs(t1 - t2) < 0.000001)
+				break;
+			t1 = t2;
+		} while (true);
+		return t2;
+	}
+	
+	updatePoints(_p0, _p1, _p2) {
+		this.p0=_p0;
+		this.p1=_p1;
+		this.p2=_p2;
+		
+		let ax = this.p0.x - 2 * this.p1.x + this.p2.x;
+		let ay = this.p0.y - 2 * this.p1.y + this.p2.y;
+		let bx = 2 * this.p1.x - 2 * this.p0.x;
+		let by = 2 * this.p1.y - 2 * this.p0.y;
+
+		this.A = 4 * (ax * ax + ay *ay);
+		this.B = 4 * (ax * bx + ay *by);
+		this.C = bx * bx + by * by;
+		
+		this.points.length = 0;
+		let totalLength = this.length(1);
+		
+		for (let index = 1; index < this.step; index++) {  
+			let t = index / this.step;
+			
+			if(this.uniformSpeed) {
+				//根据 L 函数的反函数，求得 l 对应的 t 值
+				t = this.invertLength(t, totalLength*t);
+			}
+			
+			let x = (1-t)*(1-t)*this.p0.x+2*(1-t)*t*this.p1.x+t*t*this.p2.x;
+			let y = (1-t)*(1-t)*this.p0.y+2*(1-t)*t*this.p1.y+t*t*this.p2.y;
+			
+			this.points.push({x:x, y:y});
+		}
+	}
+	
+	draw() {
+		this.points.forEach(pt => {
+			fill('green');
+			ellipse(pt.x, pt.y, 5, 5);
+		});
+	}
+}

docs/.vuepress/public/js/bezier_base.js

@@ -0,0 +1,82 @@
+
+class Point {
+	constructor(x, y){
+		this.pos = createVector(x, y);
+		this.radius = 10;
+		this.isDragged = false;
+		this.isBeingDragged = false;
+	}
+
+	get x(){ return this.pos.x; }
+	get y(){ return this.pos.y; }
+	set x(newVal){ this.pos.x = newVal; }
+	set y(newVal){ this.pos.y = newVal; }
+	set(x, y){ this.x = x; this.y = y; }
+
+	containsXY(x, y){
+		return dist(x, y, this.x, this.y) < this.radius;
+	}
+
+	handleMousePressed(){
+		this.isDragged = this.containsXY(mouseX, mouseY);
+		return this.isDragged;
+	}
+
+	handleMouseDragged(){
+		this.set(mouseX, mouseY);
+	}
+
+	handleMouseReleased(){
+		this.isDragged = false;
+	}
+
+	draw(){
+		if (this.containsXY(mouseX, mouseY)){
+			fill('red');
+		}else {
+			fill('gray');
+		}
+		stroke('black')
+		ellipse(this.x, this.y, this.radius, this.radius);
+	}
+}
+
+class LineSegments {
+	constructor() {
+		this.points = [];
+	}
+	
+	addPoint(x,y) {
+		this.points.push(new Point(x, y));
+	}
+	
+	draw(){
+		stroke('black')
+		if(this.points.length>1) {
+			for(let index=0; index<this.points.length-1; index++) {
+				line(this.points[index].x, this.points[index].y, this.points[index+1].x, this.points[index+1].y);
+			}
+			this.points.forEach(pt => pt.draw())
+		}
+	}
+
+	handleMousePressed(){
+		const pointPressed = this.points.find(pt => pt.containsXY(mouseX, mouseY));
+		if (pointPressed){
+			pointPressed.isBeingDragged = true;
+			return true;
+		}
+		return false;
+	}
+
+	handleMouseDragged(){
+		const pointDragged = this.points.find(p => p.isBeingDragged);
+		if (pointDragged) {
+			pointDragged.set(mouseX, mouseY);
+		}
+	}
+
+	handleMouseReleased(){
+		this.points.forEach(p => { p.isBeingDragged = false; });
+	}
+}