WebGL的繪製三次方貝茲曲線( Cubic bezier curve )
前言
續之前的 WebGL的繪製曲線( Curve ) ,該篇所繪製的曲線為二次貝茲曲線(Quadratic bezier curve),但常見的貝茲曲線是三次方貝茲曲線( Cubic bezier curve ),這次會製作繪製三次方貝茲曲線( Cubic bezier curve )的範例,在此做個紀錄。內容
二次貝茲曲線(Quadratic bezier curve)與三次方貝茲曲線( Cubic bezier curve )的差異在於前者的控制點是3個,後者的控制點是4個。為什麼說三次方貝茲曲線( Cubic bezier curve )比較常見呢?手上的繪圖軟體 Painter.NET 與 Blender 的貝茲曲線工具都是4個控制點,如下圖Painter.NET 的曲線工具 |
Blender的曲線工具 |
HTML 的部分
<!DOCTYPE html> <html> <head> <meta charset="utf-8"> <meta name="viewport" content="width=device-width"> <title>JS Bin</title> </head> <body> <canvas id="myCanvas1" width=400 height=300></canvas> <br> <input id="btnDrawCtrlPoints"type="button" value="DrawCtrlPoints"/> <br> <input id="btnDrawCurve"type="button" value="DrawCurve"/> <input type="range" min="2" max="100" value="30" class="slider" id="sliderLerp"> <label id="labelLerpValue">30</label> </body> </html>
Javascript 的部分
let canvas1 = document.getElementById('myCanvas1'); let glCTX1 = canvas1.getContext('webgl'); let vboPrimitiveCon = 0; let vbo=createDynamicBuffer(glCTX1); let shaderProg = createShader(glCTX1); // function createShader(glContext){ let vertShader = glContext.createShader(glContext.VERTEX_SHADER); glContext.shaderSource( vertShader , 'attribute vec3 pos;void main(void){gl_Position=vec4(pos, 1.0);}' ); glContext.compileShader(vertShader); let fragShader = glContext.createShader(glContext.FRAGMENT_SHADER); glContext.shaderSource( fragShader, 'void main(void){gl_FragColor=vec4(1,1,1,1);}' ); glContext.compileShader(fragShader); let prog = glContext.createProgram(); glContext.attachShader(prog, vertShader); glContext.attachShader(prog, fragShader); glContext.linkProgram(prog); glContext.useProgram(prog); return prog; } function createDynamicBuffer(glContext){ let vertexBuf = glContext.createBuffer(); glContext.bindBuffer(glContext.ARRAY_BUFFER, vertexBuf); let dataArray=new Float32Array([ 0.0, 0.5, 0.0, -0.5,-0.5, 0.0, -0.5,-0.5, 0.0, 0.5,-0.5, 0.0, 0.5,-0.5, 0.0, 0.0, 0.5, 0.0 ]); glContext.bufferData( glContext.ARRAY_BUFFER, 3000, glContext.DYNAMIC_DRAW ); //write deafult data... glCTX1.bufferSubData(glCTX1.ARRAY_BUFFER,0,dataArray); vboPrimitiveCon = dataArray.length / 3; return vertexBuf; } function simpleDraw(glContext){ glContext.useProgram(shaderProg); // glContext.viewport(0,0,glContext.canvas.width,glContext.canvas.height); glContext.clearColor(0, 0, 1, 1); glContext.clear(glContext.COLOR_BUFFER_BIT); // glContext.bindBuffer(glContext.ARRAY_BUFFER, vbo); let posLoc = glContext.getAttribLocation(shaderProg, "pos"); glContext.vertexAttribPointer(posLoc, 3, glContext.FLOAT, false, 0, 0); glContext.enableVertexAttribArray(posLoc); glContext.drawArrays(glContext.LINES, 0, vboPrimitiveCon); } function generateLineListData(ar){ let tagAr=[]; let mod=ar.length%3; let elementAmount=(ar.length-mod)/3; if(elementAmount>=2 && mod===0){ tagAr.push(ar[0]); tagAr.push(ar[1]); tagAr.push(ar[2]); // for(let i=3;i<(ar.length-3);i+=3){ tagAr.push(ar[i]); tagAr.push(ar[i+1]); tagAr.push(ar[i+2]); // tagAr.push(ar[i]); tagAr.push(ar[i+1]); tagAr.push(ar[i+2]); } // tagAr.push(ar[ar.length-3]); tagAr.push(ar[ar.length-2]); tagAr.push(ar[ar.length-1]); } return new Float32Array(tagAr); } function generateBezierCurve(p0,p1,p2,lerp){ if(lerp < 2) return []; // let tagAr = []; for(let i=0;i < lerp;i++){ let t = i/(lerp-1); let invT = 1.0-t; let part0Value = invT * invT; let part1Value = 2 * t * invT; let part2Value = t * t; let part0 = [part0Value*p0[0], part0Value*p0[1], part0Value*p0[2] ]; let part1 = [part1Value*p1[0], part1Value*p1[1], part1Value*p1[2] ]; let part2 = [part2Value*p2[0], part2Value*p2[1], part2Value*p2[2] ]; tagAr.push(part0[0] + part1[0] + part2[0]); tagAr.push(part0[1] + part1[1] + part2[1]); tagAr.push(part0[2] + part1[2] + part2[2]); } return tagAr; } function generateCubicBezierCurve(p0,p1,p2,p3,lerp){ if(lerp < 2) return []; // let tagAr = []; for(let i=0;i < lerp;i++){ let t = i/(lerp-1); let invT = 1.0-t; let part0Value = invT * invT * invT; let part1Value = 3 * t * invT * invT; let part2Value = 3 * t * t * invT; let part3Value = t * t * t; let part0 = [part0Value*p0[0], part0Value*p0[1], part0Value*p0[2] ]; let part1 = [part1Value*p1[0], part1Value*p1[1], part1Value*p1[2] ]; let part2 = [part2Value*p2[0], part2Value*p2[1], part2Value*p2[2] ]; let part3 = [part3Value*p3[0], part3Value*p3[1], part3Value*p3[2] ]; tagAr.push(part0[0] + part1[0] + part2[0] + part3[0]); tagAr.push(part0[1] + part1[1] + part2[1] + part3[1]); tagAr.push(part0[2] + part1[2] + part2[2] + part3[2]); } return tagAr; } function myRender(){ simpleDraw(glCTX1); // window.requestAnimationFrame(myRender); } // let ctrlPointList=[ [-0.9,0.0,0.0], [-0.45,0.9,0.0], [0.45,0.9,0.0], [0.9,0.0,0.0], ]; let tagLerpValue=document.getElementById("sliderLerp").value; function UpdateCurveData(){ let data=generateCubicBezierCurve( ctrlPointList[0], ctrlPointList[1], ctrlPointList[2], ctrlPointList[3], tagLerpValue); let dataArray=generateLineListData(data); glCTX1.bindBuffer(glCTX1.ARRAY_BUFFER, vbo); glCTX1.bufferSubData(glCTX1.ARRAY_BUFFER,0,dataArray); vboPrimitiveCon = dataArray.length / 3; } document.getElementById("btnDrawCtrlPoints").onclick=function(evt){ let data = []; for(let i=0;i<ctrlPointList.length;i++) data.push(...ctrlPointList[i]); // let dataArray=generateLineListData(data); glCTX1.bindBuffer(glCTX1.ARRAY_BUFFER, vbo); glCTX1.bufferSubData(glCTX1.ARRAY_BUFFER,0,dataArray); vboPrimitiveCon = dataArray.length / 3; } document.getElementById("btnDrawCurve").onclick=function(evt){ UpdateCurveData(); } document.getElementById("sliderLerp").oninput=function(evt){ tagLerpValue=this.value; UpdateCurveData(); document.getElementById("labelLerpValue").innerHTML = this.value; } window.onload = function(){ window.requestAnimationFrame(myRender); }
執行結果如下
繪製控制點 |
繪製曲線 |
這次的範例是由 WebGL的繪製曲線( Curve ) 的範例改來,重複的部分就不再說明。這次多了generateCubicBezierCurve() ,由於控制點多了一個,所以參數多一個 p3 ,曲線的攻勢可以參考 [ Wiki ]貝茲曲線 ,裡面有對應的公式。 ctrlPointList 要多一個控制點,UpdateCurveData()換成用 generateCubicBezierCurve() 來產生資料,最後在 btnDrawCtrlPoints 的事件改了作法,上次直接使用寫3行推入陣列,這次改採使用迴圈的方法。
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