增加一篇博客

2025-03-08 00:14:09 +08:00
parent da75a56037
commit 2eea319e54
7 changed files with 290 additions and 3 deletions
@@ -3,9 +3,11 @@ import { defaultTheme } from '@vuepress/theme-default'
 import { markdownMathPlugin } from '@vuepress/plugin-markdown-math'
 import { markdownImagePlugin } from '@vuepress/plugin-markdown-image'
 import { defineUserConfig } from 'vuepress'
+import { getDirname, path } from 'vuepress/utils'

 const navbar_def = require('./config/nav.js');
 const sidebar_def = require('./config/sidebar.js');
+const __dirname = getDirname(import.meta.url)

 export default defineUserConfig({
 	bundler: viteBundler({
@@ -37,7 +39,7 @@ export default defineUserConfig({
 		markdownMathPlugin({
 			// options
 			type: 'mathjax',
-			output: 'chtml'
+			output: 'svg'
 		}),
 		
 		markdownImagePlugin({
@@ -52,6 +54,10 @@ export default defineUserConfig({
 		}),
 	],
 	markdown: {
-		lineNumbers: false
+		lineNumbers: false,
+		importCode: {
+			handleImportPath: (str) =>
+			str.replace(/^@public/, path.resolve(__dirname, 'public/')),
+		},
 	}
 })
@@ -0,0 +1,51 @@
+<html>
+<head>
+<script src="https://cdn.jsdelivr.net/npm/p5@1.4.2/lib/p5.js"></script>
+<script src="/js/bezier_app.js"></script>
+<script src="/js/bezier_base.js"></script>
+</head>
+<body style="margin:0px; padding:0px; overflow: hidden">
+<script>
+
+var lineSegments;
+var quadBezierLine;
+var P0={x:10.0, y:10.0}, P1={x:260.0, y:235.0}, P2={x:300.0, y:80.0};
+
+function setup() {
+	const searchParams = new URLSearchParams(window.location.search);
+	let uniformSpeed = searchParams.get('uniformSpeed')!=0;
+	
+	canvas = createCanvas(windowWidth, windowHeight);
+
+	lineSegments = new LineSegments();
+	lineSegments.addPoint(P0.x, P0.y);
+	lineSegments.addPoint(P1.x, P1.y);
+	lineSegments.addPoint(P2.x, P2.y);
+	
+	quadBezierLine = new QuadBezierLine(P0, P1, P2, 20, uniformSpeed)
+}
+
+function draw() {
+	clear();
+	background('white');
+	noStroke();
+
+	lineSegments.draw();
+	quadBezierLine.draw()
+}
+
+function mousePressed(){
+	lineSegments.handleMousePressed();
+}
+
+function mouseDragged(){
+	lineSegments.handleMouseDragged();
+}
+
+function mouseReleased(){
+	lineSegments.handleMouseReleased();
+	quadBezierLine.updatePoints(lineSegments.points[0], lineSegments.points[1], lineSegments.points[2]);
+}
+</script>
+</body>
+</html>
@@ -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);
+		});
+	}
+}
@@ -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; });
+	}
+}