使用HTML5 Canvas进行真正的等距投影

Question

我是HTML5 Canvas和JavaScript的新手,但有一种简单的方法可以在HTML5 Canvas元素中进行等距投影吗？

我的意思是真正的等距投影 - http://en.wikipedia.org/wiki/Isometric_projection

谢谢大家的回复.

Answer 1

首先,我建议将游戏世界视为正方形X的Y网格.这使得从碰撞检测,寻路甚至渲染的所有内容都变得更加容易.

要在等轴测投影中渲染地图,只需修改投影矩阵:

var ctx = canvas.getContext('2d');

function render(ctx) {
    var dx = 0, dy = 0;
    ctx.save();

    // change projection to isometric view
    ctx.translate(view.x, view.y);
    ctx.scale(1, 0.5);
    ctx.rotate(45 * Math.PI /180);

    for (var y = 0; i < 10; y++) {
        for (var x = 0; x < 10; x++) {
            ctx.strokeRect(dx, dy, 40, 40);
            dx += 40;
        }
        dx = 0;
        dy += 40;
    }

    ctx.restore(); // back to orthogonal projection

    // Now, figure out which tile is under the mouse cursor... :)
}

这是第一次让它工作时令人兴奋,但你会很快意识到它对于绘制实际的等距地图并不是那么有用......你不能只是旋转你的瓷砖图像,看看即将到来的是什么.转换不是用于绘制,而是用于在屏幕空间和世界空间之间进行转换.

奖励:弄清楚鼠标在哪个区块上

你想要做的是从"视图坐标"(从画布原点的像素偏移)转换为"世界坐标"(沿着对角轴从图块0,0的像素偏移).然后简单地用瓦片宽度和高度划分世界坐标以获得"地图坐标".

理论上,您需要做的就是通过上面投影矩阵的倒数来投影"视图位置"向量,以获得"世界位置".我在理论上说,因为由于某种原因,画布不提供返回当前投影矩阵的方法.有一种setTransform()方法,但没有getTransform(),所以这是你必须推出自己的3x3转换矩阵的地方.

它实际上并不那么难,在绘制对象时,您需要在世界和视图坐标之间进行转换.

希望这可以帮助.

Answer 2

轴测渲染

处理轴测(通常称为等距)渲染的最佳方法是通过投影矩阵.

如下的投影对象可以描述您进行任何形式的轴测投影所需的全部内容

该对象具有3个x,y和z轴变换,每个变换描述x,y,z坐标的2D投影中的比例和方向.深度计算的变换和画布像素中的原点(如果是setTransform(1,0,0,1,0,0)或画布的当前变换)

要投射点,调用函数axoProjMat({x=10,y=10,z=10}),它将返回带有x的3D点,y是顶点的2D坐标,z是深度(深度值接近视图(与3D透视投影相反));

  // 3d 2d points
  const P3 = (x=0, y=0, z=0) => ({x,y,z});
  const P2 = (x=0, y=0) => ({x, y});
  // projection object
  const axoProjMat = {
      xAxis : P2(1 , 0.5) ,
      yAxis :  P2(-1 , 0.5) ,
      zAxis :  P2(0 , -1) ,
      depth :  P3(0.5,0.5,1) , // projections have z as depth
      origin : P2(), // (0,0) default 2D point
      setProjection(name){
        if(projTypes[name]){
          Object.keys(projTypes[name]).forEach(key => {
            this[key]=projTypes[name][key];
          })
          if(!projTypes[name].depth){
            this.depth = P3(
              this.xAxis.y,
              this.yAxis.y,
              -this.zAxis.y
            );
          }
        }
      },
      project (p, retP = P3()) {
          retP.x = p.x * this.xAxis.x + p.y * this.yAxis.x + p.z * this.zAxis.x + this.origin.x;
          retP.y = p.x * this.xAxis.y + p.y * this.yAxis.y + p.z * this.zAxis.y + this.origin.y;
          retP.z = p.x * this.depth.x + p.y * this.depth.y + p.z * this.depth.z; 
          return retP;
      }
  }

使用上述对象,您可以使用该功能axoProjMat.setProjection(name)选择投影类型.

下面是维基轴测投影中概述的相关投影类型, 以及像素艺术和游戏中常用的两种修改(以Pixel为前缀).使用axoProjMat.setProjection(name)name是其中一个projTypes属性名称.

const D2R = (ang) => (ang-90) * (Math.PI/180 );
const Ang2Vec = (ang,len = 1) => P2(Math.cos(D2R(ang)) * len,Math.sin(D2R(ang)) * len);
const projTypes = {
  PixelBimetric : {
    xAxis : P2(1 , 0.5) ,
    yAxis :  P2(-1 , 0.5) ,
    zAxis :  P2(0 , -1) ,
    depth :  P3(0.5,0.5,1) , // projections have z as depth      
  },
  PixelTrimetric : {
    xAxis : P2(1 , 0.5) ,
    yAxis :  P2(-0.5 , 1) ,
    zAxis :  P2(0 , -1) ,
    depth :  P3(0.5,1,1) ,
  },
  Isometric : {
    xAxis : Ang2Vec(120) ,
    yAxis : Ang2Vec(-120) ,
    zAxis : Ang2Vec(0) ,
  },
  Bimetric : {
    xAxis : Ang2Vec(116.57) ,
    yAxis : Ang2Vec(-116.57) ,
    zAxis : Ang2Vec(0) ,
  },
  Trimetric : {
    xAxis : Ang2Vec(126.87,2/3) ,
    yAxis : Ang2Vec(-104.04) ,
    zAxis : Ang2Vec(0) ,
  },
  Military : {
    xAxis : Ang2Vec(135) ,
    yAxis : Ang2Vec(-135) ,
    zAxis : Ang2Vec(0) ,
  },
  Cavalier : {
    xAxis : Ang2Vec(135) ,
    yAxis : Ang2Vec(-90) ,
    zAxis : Ang2Vec(0) ,
  },
  TopDown : {
    xAxis : Ang2Vec(180) ,
    yAxis : Ang2Vec(-90) ,
    zAxis : Ang2Vec(0) ,
  }
}

真等距投影的示例.

该片段是一个简单的示例,投影设置Isometric为OP问题中wiki链接上的详细信息,并使用上述函数和对象.

const ctx = canvas.getContext("2d");

// function creates a 3D point (vertex)
function vertex(x, y, z) { return { x, y, z}};
// an array of vertices
const vertices = []; // an array of vertices

// create the 8 vertices that make up a box
const boxSize = 20; // size of the box
const hs = boxSize / 2; // half size shorthand for easier typing

vertices.push(vertex(-hs, -hs, -hs)); // lower top left  index 0
vertices.push(vertex(hs, -hs, -hs)); // lower top right
vertices.push(vertex(hs, hs, -hs)); // lower bottom right
vertices.push(vertex(-hs, hs, -hs)); // lower bottom left
vertices.push(vertex(-hs, -hs, hs)); // upper top left  index 4
vertices.push(vertex(hs, -hs, hs)); // upper top right
vertices.push(vertex(hs, hs, hs)); // upper bottom right
vertices.push(vertex(-hs, hs, hs)); // upper  bottom left index 7



const colours = {
  dark: "#040",
  shade: "#360",
  light: "#ad0",
  bright: "#ee0",
}

function createPoly(indexes, colour) {
  return {
    indexes,
    colour
  }
}
const polygons = [];

polygons.push(createPoly([1, 2, 6, 5], colours.shade)); // right face
polygons.push(createPoly([2, 3, 7, 6], colours.light)); // front face
polygons.push(createPoly([4, 5, 6, 7], colours.bright)); // top face



// From here in I use P2,P3 to create 2D and 3D points
const P3 = (x = 0, y = 0, z = 0) => ({x,y,z});
const P2 = (x = 0, y = 0) => ({ x, y});
const D2R = (ang) => (ang-90) * (Math.PI/180 );
const Ang2Vec = (ang,len = 1) => P2(Math.cos(D2R(ang)) * len,Math.sin(D2R(ang)) * len);
const projTypes = {
  PixelBimetric : {
    xAxis : P2(1 , 0.5) ,
    yAxis :  P2(-1 , 0.5) ,
    zAxis :  P2(0 , -1) ,
    depth :  P3(0.5,0.5,1) , // projections have z as depth      
  },
  PixelTrimetric : {
    xAxis : P2(1 , 0.5) ,
    yAxis :  P2(-0.5 , 1) ,
    zAxis :  P2(0 , -1) ,
    depth :  P3(0.5,1,1) ,
  },
  Isometric : {
    xAxis : Ang2Vec(120) ,
    yAxis : Ang2Vec(-120) ,
    zAxis : Ang2Vec(0) ,
  },
  Bimetric : {
    xAxis : Ang2Vec(116.57) ,
    yAxis : Ang2Vec(-116.57) ,
    zAxis : Ang2Vec(0) ,
  },
  Trimetric : {
    xAxis : Ang2Vec(126.87,2/3) ,
    yAxis : Ang2Vec(-104.04) ,
    zAxis : Ang2Vec(0) ,
  },
  Military : {
    xAxis : Ang2Vec(135) ,
    yAxis : Ang2Vec(-135) ,
    zAxis : Ang2Vec(0) ,
  },
  Cavalier : {
    xAxis : Ang2Vec(135) ,
    yAxis : Ang2Vec(-90) ,
    zAxis : Ang2Vec(0) ,
  },
  TopDown : {
    xAxis : Ang2Vec(180) ,
    yAxis : Ang2Vec(-90) ,
    zAxis : Ang2Vec(0) ,
  }
}

const axoProjMat = {
  xAxis : P2(1 , 0.5) ,
  yAxis :  P2(-1 , 0.5) ,
  zAxis :  P2(0 , -1) ,
  depth :  P3(0.5,0.5,1) , // projections have z as depth
  origin : P2(150,65), // (0,0) default 2D point
  setProjection(name){
    if(projTypes[name]){
      Object.keys(projTypes[name]).forEach(key => {
        this[key]=projTypes[name][key];
      })
      if(!projTypes[name].depth){
        this.depth = P3(
          this.xAxis.y,
          this.yAxis.y,
          -this.zAxis.y
        );
      }
    }
  },
  project (p, retP = P3()) {
      retP.x = p.x * this.xAxis.x + p.y * this.yAxis.x + p.z * this.zAxis.x + this.origin.x;
      retP.y = p.x * this.xAxis.y + p.y * this.yAxis.y + p.z * this.zAxis.y + this.origin.y;
      retP.z = p.x * this.depth.x + p.y * this.depth.y + p.z * this.depth.z; 
      return retP;
  }
}
axoProjMat.setProjection("Isometric");

var x,y,z;
for(z = 0; z < 4; z++){
   const hz = z/2;
   for(y = hz; y < 4-hz; y++){
       for(x = hz; x < 4-hz; x++){
          // move the box
          const translated = vertices.map(vert => {
               return P3(
                   vert.x + x * boxSize, 
                   vert.y + y * boxSize, 
                   vert.z + z * boxSize, 
               );
          });
                   
          // create a new array of 2D projected verts
          const projVerts = translated.map(vert => axoProjMat.project(vert));
          // and render
          polygons.forEach(poly => {
            ctx.fillStyle = poly.colour;
            ctx.strokeStyle = poly.colour;
            ctx.lineWidth = 1;
            ctx.beginPath();
            poly.indexes.forEach(index => ctx.lineTo(projVerts[index].x , projVerts[index].y));
            ctx.stroke();
            ctx.fill();
            
          });
      }
   }
}

canvas {
  border: 2px solid black;
}
body { font-family: arial; }

True Isometric projection. With x at 120deg, and y at -120deg from up.<br>
<canvas id="canvas"></canvas>