出于某种目的想做这个东西，顺便可以提供给GMA的用户&&放在博客园。
实现上只是简单的描点，加上一个相邻两点连线的开关，完全没有技术含量。而且函数图像一旦多起来就会变卡。
瓶颈在隐函数的绘制，这个超烦，计算量一下子就上去了。我的做法是把画布格成很多个60*60的小方格，先扫一遍方格边框上有没有零点，有就进这个方格绘图，没有就不管它了。绘图的部分也牺牲了精度换取速度，当然相关参数都还给用户自己调。结果还是挺慢的，但还可以接受啦。
效果还行
接下来打算兹兹一下js语句做函数表达式，然后再加上一维时间（动态图）。三维空间的话估计等我读了大学才能来做了……空间几何完全不行啊T_T
诸位聚聚如果有什么更好的函数渲染算法给点点建议啊……
<?php require_once("style.php"); ?> <style> [UnSelect=YES]{ -webkit-touch-callout: none; /* iOS Safari */ -webkit-user-select: none; /* Chrome/Safari/Opera */ -khtml-user-select: none; /* Konqueror */ -moz-user-select: none; /* Firefox */ -ms-user-select: none; /* Internet Explorer/Edge */ } #mask{ width:100%; height:100%; background:#000; opacity:0.5; position:fixed; top:0; left: 0; z-index: 100; display:none; } .notes{ color:#FFFFFF; font-weight:800; font-size:20px; } </style> <body> <div id="mask"></div> <div id="control" class="ui inverted segment" style="background-color:black;position:fixed;margin:auto;left:0;right:0;top:0;bottom:0;z-index:101;600px;height:500px;overflow:auto;display:none;"> <div id="function"> <button class="ui green button" onclick="Add()">Add function</button> <span class="ui divider"></span> <span id="mod" style="display:none" name="0"> <select class="ui dropdown" style="border-radius:5px;" onchange="FunctionChange(this)"> <option value="0">Cartesian</option> <option value="1">Polar</option> <option value="2">Implicit</option> <option value="3">Parameter</option> </select> <input type="color" style="20px;height:20px;border-radius:5px;"/> <span style="display:inline"> <span class="notes">y=</span> <span class="ui input" name="Fun"><input/></span> <span class="notes"></span> <span class="ui input" style="display:none"><input/></span> </span> <button class="ui red button" onclick="Delete(this.parentNode)">Delete</button> <span class="ui checkbox"> <input type="checkbox" onclick="DrawLine(this.parentNode)"/> <label style="color:white;">Draw Line</label> </span> <span style="display:none;margin-top:6px;font-size:80%;"> <span class="notes"></span> <span class="ui input" style="50px;"><input/></span> <span class="notes"></span> <span class="ui input" style="50px;"><input/></span> <span class="notes"></span> <span class="ui input" style="50px;"><input/></span> </span> <span class="ui divider" style="height:40px"></span> </span> </div> <div class="title" UnSelect="YES" onclick="ShowOption(this)" style="color:white;cursor:pointer;font-size:17px;line-height:35px;font-weight:bold;"><i class="Caret Right icon"></i>Advanced Options</div> <div id="option" UnSelect="YES" style="color:white;font-size:50%;font-family: Consolas,Monaco,monospace;display:none;transition:2s;line-height:30px;"> <span class="notes">X:</span> <span class="ui input"><input id="FunLx" style="180px;"/></span> <span class="notes">~</span> <span class="ui input"><input id="FunRx" style="180px;"/></span> <br> <span class="notes">Y:</span> <span class="ui input"><input id="FunLy" style="180px;"/></span> <span class="notes">~</span> <span class="ui input"><input id="FunRy" style="180px;"/></span> <br> <span class="notes">Coordinate:</span> <span class="ui input"><input id="FontStyle" style="200px;" value=""/></span> <br> <span class="ui checkbox"> <input type="checkbox" id="sizelimit" checked="1"/> <label style="color:white;">Size Limit</label> </span> <br> <span class="notes">PointRadii:</span> <span class="ui input"><input id="PointRadii" style="50px;" value="1"/></span> <br> <span class="notes">Scale:</span> <span class="ui input"><input id="Scale" style="50px;" value="0.9"/></span> <br> <span class="ui checkbox"> <input type="checkbox" id="DrawMoving" checked=1/> <label style="color:white;">Draw while moving</label> </span> <br> <span class="notes" id="size"></span> </div> <span class="ui divider"></span> <button class="ui blue button" onclick="change()">Draw</button> </div> <div id="main"> <h1 class="ui header" UnSelect="YES" style=""> <i class="book icon"></i> <div class="content">Tools</div> </h1> <h1 align="center" UnSelect="YES">函数图像绘制工具</h1> <div align="center" style="100%;height:70%;"> <canvas id="graph"></canvas> </div> <div UnSelect="YES"> <button class="ui green button" onclick="mask()">Control</button> <button class="ui green button" onclick="redraw()">Reflash</button> <!--<p id="map"></p>--> </div> <script> function $(id) { return document.getElementById(id); } function getRandomColor(){ return '#'+('00000'+(Math.random()*0x1000000<<0).toString(16)).substr(-6); } function ischar(c){return (c>='a'&&c<='z')||(c>='A'&&c<='Z');} function isdigit(c){return c>='0'&&c<='9';} function ChangeToPointX(x){return parseInt((x-FunLx)/(FunRx-FunLx)*FunW);} function ChangeToPointY(y){return FunH-1-parseInt((y-FunLy)/(FunRy-FunLy)*FunH);} function priority(c){ switch(c){ case '(':{return 0;break;} case '+':{return 1;break;} case '-':{return 1;break;} case '*':{return 2;break;} case '/':{return 2;break;} case '^':{return 3;break;} default:{return -1;break;} } } function isopt(c){return priority(c)!=-1;} function SingleCalc(c,a,b){ if (c=='+') return a+b;else if (c=='-') return a-b;else if (c=='*') return a*b;else if (c=='/') return a/b;else if (c=='^') return Math.pow(a,b);else return NaN } function FunWork(f,x){ switch(f){ case "":{return x;break;} case "SIN":{return Math.sin(x);break;} case "COS":{return Math.cos(x);break;} case "TAN":{return Math.tan(x);break;} case "ABS":{return Math.abs(x);break;} case "SQRT":{return Math.sqrt(x);break;} case "LN":{return Math.log(x);break;} case "LOG":{return Math.log(x)/Math.LN2;break;}//2为底 case "LG":{return Math.log(x)/Math.LN10;break;}//10为底 case "FLOOR":{return Math.floor(x);break;} case "CEIL":{return Math.ceil(x);break;} case "INT":{return parseInt(x);break;} default:{return NaN;break;} } } function FunInit(F){ F=F.replace(/sin/g,"SIN"); F=F.replace(/cos/g,"COS"); F=F.replace(/tan/g,"TAN"); F=F.replace(/abs/g,"ABS"); F=F.replace(/sqrt/g,"SQRT"); F=F.replace(/ln/g,"LN"); F=F.replace(/log/g,"LOG"); F=F.replace(/lg/g,"LG"); F=F.replace(/floor/g,"FLOOR"); F=F.replace(/ceil/g,"CEIL"); F=F.replace(/int/g,"INT"); return F; } var ca=$("graph"),el=ca.getContext("2d"),fun=$("function"),eps=1e-12; var FunW=ca.parentNode.clientWidth,FunH=ca.parentNode.clientHeight,FunLx=-FunW/100,FunRx=FunW/100,FunLy=-FunH/100,FunRy=FunH/100,PR,tableX,tableY,tmp,countX,countY,Funstage=0,MoX,MoY,MIN=1e-4,MAX=1e8,FUN; var dir=[[0,1],[1,0],[0,-1],[-1,0],[1,1],[1,-1],[-1,1],[-1,-1]]; var FontStyle="bold 12px Georgia"; ca.width=FunW;ca.height=FunH;$("size").innerHTML="Size:"+FunW+"*"+FunH; function Calc(fun,X,Value){ var number=new Array(),opt=new Array(),F=new Array(),now=0,f="",tmp,a,b,sign=1,base=0,j; for (var i=0;i<fun.length;i++){ for (j=0;j<X.length;j++) if (X[j]==fun[i]){ if (i==0||isopt(fun[i-1])) now=Value[j];else now*=Value[j]; break; } if (j==X.length) if (fun[i]=='(') F.push(f),f="",opt.push('(');else if (fun[i]==')'){ number.push(now*sign);now=0;sign=1;base=0; while ((tmp=opt.pop())!='('){ b=number.pop();a=number.pop(); tmp=SingleCalc(tmp,a,b); number.push(tmp); } now=FunWork(F.pop(),number.pop()); }else if (fun[i]=='.') base=1;else if (fun[i]=='+'&&(i==0||priority(fun[i-1])!=-1));else if (fun[i]=='-'&&(i==0||priority(fun[i-1])!=-1)) sign=-1;else if (fun[i]=='e') if (i==0||isopt(fun[i-1])) now=Math.E;else now*=Math.E;else if (fun[i]=='p'&&fun[i+1]=='i'){if (i==0||isopt(fun[i-1])) now=Math.PI;else now*=Math.PI;i+=1;}else if (isdigit(fun[i])) if (base==0) now=now*10+(fun[i]-'0');else base/=10,now+=base*(fun[i]-'0');else if (ischar(fun[i])) f+=fun[i];else if (isopt(fun[i])){ number.push(now*sign);now=0;sign=1;base=0; var s=priority(fun[i]); if (s==-1) return 0; while (s<=priority(opt[opt.length-1])){ b=number.pop();a=number.pop(); tmp=SingleCalc(opt.pop(),a,b); number.push(tmp); } opt.push(fun[i]); } } number.push(now*sign); while (opt.length>0){ b=number.pop();a=number.pop(); tmp=SingleCalc(opt.pop(),a,b); number.push(tmp); } return number.pop(); } function drawarc(x,y,R){ el.beginPath(); el.arc(x,y,R,0,Math.PI*2); el.closePath(); el.fill(); } function drawline(lx,ly,px,py){ el.beginPath(); el.moveTo(lx,ly); el.lineTo(px,py); el.closePath(); el.stroke(); } function gettable(){ tmp=(FunRx-FunLx+eps)/20; tableX=1;countX=0;countY=0; while(tableX<tmp) tableX*=10; while(tableX/10>tmp) tableX/=10,countX++; if (tableX>=1) countX=0; if (tableX/5>tmp) tableX/=5,countX++;else if (tableX/2>tmp) tableX/=2,countX++; for (var i=parseInt(FunLx/tableX)+(FunLx>0);i*tableX<FunRx;i++){ el.fillStyle=i==0?"#000000":"#CDB7B5"; tmp=(i*tableX-FunLx)/(FunRx-FunLx)*FunW; el.fillRect(tmp,0,1,FunH); el.fillStyle="#000000"; el.font=FontStyle; el.fillText((i*tableX).toFixed(countX),tmp+2,10); } tmp=(FunRy-FunLy+eps)/20; tableY=1; while(tableY<tmp) tableY*=10; while(tableY/10>tmp) tableY/=10,countY++; if (tableY/5>tmp) tableY/=5,countY++;else if (tableY/2>tmp) tableY/=2,countY++; if (tableY>=1) countY=0; for (var i=parseInt(FunLy/tableY)+(FunLy>0);i*tableY<FunRy;i++){ el.fillStyle=i==0?"#000000":"#CDB7B5"; tmp=(i*tableY-FunLy)/(FunRy-FunLy)*FunH; el.fillRect(0,FunH-1-tmp,FunW,1); el.fillStyle="#000000"; el.font=FontStyle; el.fillText((i*tableY).toFixed(countY),0,FunH-1-tmp); } //$("map").innerHTML=tableX+" "+tableY; } function PCalc(i,j){return Calc(FUN,['x','y'],[FunLx+(FunRx-FunLx)/FunW*i,FunRy-(FunRy-FunLy)/FunH*j]);} function ImpDraw(x,y,X,Y,jump){ if (x+X>FunW) X=FunW-x;if (y+Y>FunH) Y=FunH-y; var Imp=new Array(),tmp; if (X>jump)X/=jump; if (Y>jump)Y/=jump; for (var i=-1;i<=X;i+=1){ Imp[i+1]=new Array(); for (var j=-1;j<=Y;j+=1) Imp[i+1].push(PCalc(i*jump+x,j*jump+y)); } for (var i=0;i<X;i+=1) for (var j=0;j<Y;j+=1) for (var k=0;k<4;k++) if (Imp[i+1][j+1]*Imp[i+1+dir[k][0]][j+1+dir[k][1]]<0) {drawarc(i*jump+x,j*jump+y,PR);break;} } function getfunction(){ var group=document.getElementsByName("Fun"),x,y,R,lax,lay,px,py,color,OutSide,type,ValueL,ValueR,ValueS,DLc,tmp,TMP; PR=$("PointRadii").value; for (var k=1;k<group.length;k++){ var gf=group[k].parentNode.parentNode; OutSide=1;type=gf.children[0].value;DLc=gf.children[4].children[0].checked; FUN=FunInit((group[k].children[0].value).toLowerCase()); color=gf.children[1].value; el.fillStyle=el.strokeStyle=color; switch (type){ case '0':{ for (var i=0;i<FunW;i++){ x=FunLx+(FunRx-FunLx)/FunW*i; y=Calc(FUN,['x'],[x]); if (isNaN(y)) continue; px=i;py=ChangeToPointY(y); if (y>=FunLy&&y<FunRy){ drawarc(px,py,PR); if (DLc) drawline(lax,lay,px,py); OutSide=0; }else{ if (DLc) if (!OutSide) drawline(lax,lay,px,py); OutSide=1; } lax=px;lay=py; } break; } case '1':{ ValueL=Calc(gf.children[5].children[1].children[0].value,[],[]); ValueR=Calc(gf.children[5].children[3].children[0].value,[],[]); ValueS=Calc(gf.children[5].children[5].children[0].value,[],[]); for (var i=ValueL;i<ValueR+ValueS-eps;i+=ValueS){ if (i>ValueR) i=ValueR; R=Calc(FUN,['t'],[i]); x=R*Math.cos(i);y=R*Math.sin(i); px=ChangeToPointX(x);py=ChangeToPointY(y); if (FunLx<=x&&x<FunRx&&FunLy<=y&&y<FunRy){ drawarc(px,py,PR); if (DLc) drawline(lax,lay,px,py); OutSide=0; }else{ if (DLc) if (!OutSide) drawline(lax,lay,px,py); OutSide=1; } lax=px;lay=py; } break; } case '2':{ var SpaceW=Calc(gf.children[5].children[1].children[0].value,[],[]), SpaceH=Calc(gf.children[5].children[3].children[0].value,[],[]), jump=Calc(gf.children[5].children[5].children[0].value,[],[]),Imp=new Array(); for (var i=0;i*SpaceW<FunW;i+=1){ Imp[i]=new Array(); for (var j=0;j*SpaceH<FunH;j+=1) Imp[i].push(0); } for (var i=0,_i=0;i<FunW;i+=SpaceW,_i+=1) for (var j=0,_j=0;j<FunH;j+=SpaceH,_j+=1){ //if (!Imp[_i][_j]||(!_i&&!Imp[_i-1][_j])) { tmp=PCalc(i,j-1); for (var l=0;l<SpaceH&&j+l<FunH;l++) if (TMP=tmp,tmp=PCalc(i,j+l),TMP*tmp<0||Math.abs(tmp)<eps) {Imp[_i][_j]=1;if (_i) Imp[_i-1][_j]=1;break;} } //if (!Imp[_i][_j]||(!_j&&!Imp[_i][_j-1])) { tmp=PCalc(i-1,j); for (var l=0;l<SpaceW&&i+l<FunW;l++) if (TMP=tmp,tmp=PCalc(i+l,j),TMP*tmp<0||Math.abs(tmp)<eps) {Imp[_i][_j]=1;if (_j) Imp[_i][_j-1]=1;break;} } } for (var i=0;i<Imp.length;i+=1) for (var j=0;j<Imp[i].length;j+=1) if (Imp[i][j]) ImpDraw(i*SpaceW,j*SpaceH,SpaceW,SpaceH,jump); break; } case '3':{ ValueL=Calc(gf.children[5].children[1].children[0].value,[],[]); ValueR=Calc(gf.children[5].children[3].children[0].value,[],[]); ValueS=Calc(gf.children[5].children[5].children[0].value,[],[]); _FUN=FunInit((group[k].parentNode.children[3].children[0].value).toLowerCase()); for (var i=ValueL;i<ValueR+ValueS-eps;i+=ValueS){ if (i>ValueR) i=ValueR; x=Calc(FUN,['t'],[i]);y=Calc(_FUN,['t'],[i]); px=ChangeToPointX(x);py=ChangeToPointY(y); if (FunLx<=x&&x<FunRx&&FunLy<=y&&y<FunRy){ drawarc(px,py,PR); if (DLc) drawline(lax,lay,px,py); OutSide=0; }else{ if (DLc) if (!OutSide) drawline(lax,lay,px,py); OutSide=1; } lax=px;lay=py; } break; } } } } function redraw(){ el.clearRect(0,0,FunW,FunH); gettable(); if (Funstage!=1||$("DrawMoving").checked) getfunction(); } function change(){ FunLx=parseFloat($("FunLx").value); FunRx=parseFloat($("FunRx").value); FunLy=parseFloat($("FunLy").value); FunRy=parseFloat($("FunRy").value); FontStyle=$("FontStyle").value; redraw(); } function update(){ $("FunLx").value=FunLx; $("FunRx").value=FunRx; $("FunLy").value=FunLy; $("FunRy").value=FunRy; $("FontStyle").value=FontStyle; } function Scale(x,y,times){ if (x<0||x>=FunW||y<0||y>=FunH) return; if ($("sizelimit").checked){ if (times<1&&(FunRx-FunLx<MIN||FunRy-FunLy<MIN)) return; if (times>1&&(FunRx-FunLx>MAX||FunRy-FunLy>MAX)) return; } x=FunLx+(FunRx-FunLx)/FunW*x; y=FunLy+(FunRy-FunLy)/FunH*y; FunLx=x-(x-FunLx)*times;FunRx=x+(FunRx-x)*times; FunLy=y-(y-FunLy)*times;FunRy=y+(FunRy-y)*times; } ca.onmousedown=function(ob){ MoX=ob.layerX;MoY=ob.layerY; Funstage=1; } ca.onmousemove=function(ob){ if (Funstage!=1) return; var NoX,NoY,det; NoX=ob.layerX;NoY=ob.layerY; det=(MoX-NoX)/FunW*(FunRx-FunLx);FunLx+=det;FunRx+=det; det=(NoY-MoY)/FunH*(FunRy-FunLy);FunLy+=det;FunRy+=det; MoX=NoX;MoY=NoY; redraw();update(); } ca.onmouseup=function(ob){ if (Funstage==1){ Funstage=0; redraw(); } } ca.onmouseleave=function(ob){ if (Funstage==1){ Funstage=0; redraw(); } } ca.onmousewheel=function(ob){ ob=ob||window.event;ob.preventDefault(); var ScaleRate=$("Scale").value; var detail; if(ob.wheelDelta)detail=ob.wheelDelta;else if(ob.detail)detail=ob.detail; if (detail>0) Scale(ob.layerX,FunH-1-ob.layerY,ScaleRate);else Scale(ob.layerX,FunH-1-ob.layerY,1/ScaleRate); redraw();update(); } function Add(){ var New=$("mod").cloneNode(true); New.style.display="block"; New.children[1].value=getRandomColor(); fun.appendChild(New); } function Delete(node){ node.parentNode.removeChild(node); } function DrawLine(ob){ //if (ob.className=="ui checkbox checked") ob.className="ui checkbox";else ob.className="ui checkbox checked"; redraw(); } function ShowOption(obj){ obj=obj.children[0]; if (obj.className=="Caret Right icon") obj.className="Caret Down icon",$("option").style.display="block";else obj.className="Caret Right icon",$("option").style.display="none"; } function FunctionChange(obj){ var fi=0,la=2,v=obj.value; obj=obj.parentNode; obj.children[5].style.display="none"; obj.children[2].style.display="inline"; obj.children[2].children[3].style.display="none"; if (v==0){ obj.children[2].children[fi].innerHTML="y="; obj.children[2].children[la].innerHTML=""; }else if (v==1){ obj.children[2].children[fi].innerHTML="r="; obj.children[2].children[la].innerHTML=""; obj.children[5].style.display="block"; obj.children[5].children[0].innerHTML="t:"; obj.children[5].children[1].children[0].value="0"; obj.children[5].children[2].innerHTML="~"; obj.children[5].children[3].children[0].value="2pi"; obj.children[5].children[4].innerHTML=" Space:"; obj.children[5].children[5].children[0].value="0.02"; }else if (v==2){ obj.children[2].children[fi].innerHTML=""; obj.children[2].children[la].innerHTML="=0"; obj.children[5].style.display="block"; obj.children[5].children[0].innerHTML="SpaceW:"; obj.children[5].children[1].children[0].value="60"; obj.children[5].children[2].innerHTML=" SpaceH:"; obj.children[5].children[3].children[0].value="60"; obj.children[5].children[4].innerHTML=" Jump:"; obj.children[5].children[5].children[0].value="3"; }else if (v==3){ obj.children[2].style.display="block"; obj.children[2].children[3].style.display="inline"; obj.children[2].children[fi].innerHTML="x="; obj.children[2].children[la].innerHTML=" y="; obj.children[5].style.display="block"; obj.children[5].children[0].innerHTML="t:"; obj.children[5].children[1].children[0].value="0"; obj.children[5].children[2].innerHTML="~"; obj.children[5].children[3].children[0].value="1"; obj.children[5].children[4].innerHTML=" Space:"; obj.children[5].children[5].children[0].value="0.1"; } } redraw();update(); var maskobj=$("mask"); var control=$("control"); function mask(){ if (maskobj.style.display=="block") control.style.display=maskobj.style.display="none";else control.style.display=maskobj.style.display="block"; } maskobj.onclick=function(){ mask(); } </script> </div> </body>