Daniel-Abrecht · June 16, 2018 21:02
diff --git a/faster webgl rendering, rotate camera with arrow keys, move with xy. b/faster webgl rendering, rotate camera with arrow keys, move with xy.
 <!DOCTYPE html>
 <html>
  <head>
  </head>
  <body>
 <canvas id="canvas" width="512" height="512"></canvas>
 <script type="x-shader/x-vertex">
 uniform vec3 direction, ucamera;
 attribute vec3 coordinates;
 varying vec3 ray;
 varying vec3 vcamera;

 const vec3 up = vec3(0,1,0);

 void main(void){
  mat3 rotation = mat3(
    -1,0,0,
    0,0,1,
    0,1,0
  );
  vec3 forward = normalize(direction);
  if(forward != up){
    vec3 left = normalize(cross(forward,up));
    vec3 top = normalize(cross(left,forward));
    rotation = mat3(left,top,forward);
  }
  ray = rotation * vec3(coordinates.xy,1);
  vcamera = ucamera;
  gl_Position = vec4(coordinates, 1.0);
 }
 </script>
 <script type="x-shader/x-fragment">
 precision mediump float;
 varying vec3 ray;
 varying vec3 vcamera;

 const vec3 up = vec3(0,1,0);
 const float depth = 5.;
 const int resolution = 1000;
 const int backtrack = 30;
 const float displacement = 1.5;
 const int overtrace = 2;

 const float step = depth / float(resolution);
 const float backtrack_step = step / float(backtrack);


 bool fur(vec3 p){
  const float n = 10.;
  const float d = 0.75;
  const float r = 0.5;
  const float m = 3.;
  const vec2 t = vec2(-0.6, 1.4);
  p.xyz = p.zxy;
  if(p.z < 0.)
    return false;
  p.xy += vec2(cos(p.z*m*3.14*2.),sin(p.z*m*3.14*2.))/(n*2.);
  p.xy += p.z*p.z * t;
  p.xy = mod(abs(p.xy) * n, 2.) - 1.;
  return 1. > ( dot(p.xy,p.xy) + p.z/d*r) + (1.-r);
 }


 bool sphere(vec3 p){
  return dot(p,p) < 1.;
 }

 bool plotfunc(vec3 p){
  return fur(p);
 }

 float finetune_distance(vec3 ray, vec3 viewpoint, float distance){
  float res = distance;
  for(int i=0; i<backtrack*overtrace; i++){
    float bdist = float(i)*backtrack_step;
    vec3 position = ray * (distance-bdist);
    if(plotfunc(position-viewpoint)){
      res = distance-bdist;
    }else{
      return res;
    }
  }
  return res;
 }

 float finetune_surface_distance(vec3 ray, vec3 viewpoint){
  for(int i=0; i<backtrack*overtrace; i++){
    float bdist = float(i)*backtrack_step;
    vec3 position = ray * bdist;
    if(plotfunc(position+viewpoint))
      return bdist;
  }
  return 1000.;
 }

 float getDisplacement(vec3 ray, vec3 viewpoint){
  if(plotfunc(viewpoint)){
    return finetune_distance(ray,-viewpoint,0.);
  }else{
    return finetune_surface_distance(ray,viewpoint);
  }
 }

 void main(void){
  vec3 viewpoint = vcamera;
  vec3 zray = normalize(ray);
  vec3 xray = ray == up ? vec3(1,0,0) : normalize(cross(zray,up));
  vec3 yray = normalize(cross(zray,xray));
  float distance;
  vec3 position;
  bool found = false;
  for(int i=0; i<resolution; i++){
    distance = float(i)*step;
    position = zray * distance;
    if(plotfunc(position-viewpoint)){
      found = true;
      break;
    }
  }
  if(!found)
    discard;
  distance = finetune_distance(zray,viewpoint,distance);
  position = zray * distance;
  float ld = getDisplacement(zray,position - viewpoint + xray * backtrack_step * displacement);
  float rd = getDisplacement(zray,position - viewpoint - xray * backtrack_step * displacement);
  float td = getDisplacement(zray,position - viewpoint + yray * backtrack_step * displacement);
  float bd = getDisplacement(zray,position - viewpoint - yray * backtrack_step * displacement);
  vec3 dir = vec3(ld-rd,td-bd,0) * float(backtrack) / ( float(step) * displacement);
  if(dir.xy == vec2(0,0)){
    dir.z = 1.;
  }else{
    dir.z = 1. / length(dir.xy);
  }
  dir = normalize(dir);
  gl_FragColor = vec4(dir, 1);
 }
 </script>
 <script>
 var canvas = document.getElementById("canvas");
 var gl = canvas.getContext("webgl");
 var rx=0.14, ry=-0.15, x=0, y=-1.25, z=0, keys=[];

 var vertices = [
  -1, 1, 0,
  -1,-1, 0,
   1,-1, 0, 
  -1, 1, 0,
   1,-1, 0, 
   1, 1, 0,
 ];
 	
 indices = [0,1,2,3,4,5]; 

 var vertex_buffer = gl.createBuffer();
 gl.bindBuffer(gl.ARRAY_BUFFER, vertex_buffer);
 gl.bufferData(gl.ARRAY_BUFFER, new Float32Array(vertices), gl.STATIC_DRAW);
 gl.bindBuffer(gl.ARRAY_BUFFER, null);

 var Index_Buffer = gl.createBuffer();
 gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, Index_Buffer);
 gl.bufferData(gl.ELEMENT_ARRAY_BUFFER, new Uint16Array(indices), gl.STATIC_DRAW);
 gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, null);

 var vertCode = document.querySelector('script[type="x-shader/x-vertex"]').textContent;
 var fragCode = document.querySelector('script[type="x-shader/x-fragment"]').textContent;

 var vertShader = gl.createShader(gl.VERTEX_SHADER);
 gl.shaderSource(vertShader, vertCode);
 gl.compileShader(vertShader);
 var compiled = gl.getShaderParameter(vertShader, gl.COMPILE_STATUS);
 if(!compiled){
  var compilationLog = gl.getShaderInfoLog(vertShader);
  console.log('Vertex shader compile error: ' + compilationLog);
 }

 var fragShader = gl.createShader(gl.FRAGMENT_SHADER);
 gl.shaderSource(fragShader, fragCode); 
 gl.compileShader(fragShader);
 var compiled = gl.getShaderParameter(fragShader, gl.COMPILE_STATUS);
 if(!compiled){
  var compilationLog = gl.getShaderInfoLog(fragShader);
  console.log('Fragment shader compile error: ' + compilationLog);
 }

 var shaderProgram = gl.createProgram();
 gl.attachShader(shaderProgram, vertShader);
 gl.attachShader(shaderProgram, fragShader);
 gl.linkProgram(shaderProgram);
 gl.useProgram(shaderProgram);

 gl.bindBuffer(gl.ARRAY_BUFFER, vertex_buffer);
 gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, Index_Buffer);
 var coord = gl.getAttribLocation(shaderProgram, "coordinates");
 gl.vertexAttribPointer(coord, 3, gl.FLOAT, false, 0, 0); 
 gl.enableVertexAttribArray(coord);
 gl.disable(gl.DEPTH_TEST);

 var direction = gl.getUniformLocation(shaderProgram, 'direction');
 var ucamera = gl.getUniformLocation(shaderProgram, 'ucamera');

 gl.viewport(0,0,canvas.width,canvas.height);

 function draw(){
  var dx = -Math.cos(ry*Math.PI*2)*Math.sin(rx*Math.PI*2),
      dy = Math.sin(ry*Math.PI*2),
      dz = Math.cos(rx*Math.PI*2)*Math.cos(ry*Math.PI*2);
  if(keys[89]){
    x += dx * 0.01;
    y += dy * 0.01;
    z += dz * 0.01;
  }
  if(keys[88]){
    x -= dx * 0.01;
    y -= dy * 0.01;
    z -= dz * 0.01;
  }
  if(keys[37]) rx -= 0.01;
  if(keys[39]) rx += 0.01;
  if(keys[38]) ry -= 0.01;
  if(keys[40]) ry += 0.01;
  if(ry>0.25) ry=0.25;
  if(ry<-0.25) ry=-0.25;
  gl.clearColor(0.0, 0.0, 0.3, 1);
  gl.clear(gl.COLOR_BUFFER_BIT);
  gl.uniform3f(ucamera,x,y,z);
  gl.uniform3f(direction,dx,dy,dz);
  gl.drawElements(gl.TRIANGLES, indices.length, gl.UNSIGNED_SHORT,0);
  requestAnimationFrame(draw);
 }
 draw();

 addEventListener("keydown",function(event){
  keys[event.which] = true;
 });

 addEventListener("keyup",function(event){
  keys[event.which] = false;
 });

 </script>
 </body></html>
diff --git a/slow orthogonal cpu rendering.html b/slow orthogonal cpu rendering.html
 <!DOCTYPE html>
 <html>
  <head>
  </head>
  <body>
    <canvas id="ra" width="512" height="512"></canvas>
    <canvas id="rb" width="512" height="512"></canvas><br/>
    <canvas id="rc" width="512" height="512"></canvas>
    <br/>
    <canvas id="rd" width="512" height="512"></canvas>
    <canvas id="re" width="512" height="512"></canvas><br/>
    <canvas id="rf" width="512" height="512"></canvas>
 <script>
 var rae = document.getElementById("ra");
 var rac = rae.getContext("2d");
 var rbe = document.getElementById("rb");
 var rbc = rbe.getContext("2d");
 var rce = document.getElementById("rc");
 var rcc = rce.getContext("2d");

 var rde = document.getElementById("rd");
 var rdc = rde.getContext("2d");
 var ree = document.getElementById("re");
 var rec = ree.getContext("2d");
 var rfe = document.getElementById("rf");
 var rfc = rfe.getContext("2d");

 function plot(f,w,h,x,y){
  x = x || 0;
  y = y || 0;
  w = w || rae.width;
  h = h || rae.height;
  for(let j=0;j<h;j++){
    let ry = j / h * 2 - 1;
    for(let i=0;i<w;i++){
      let rx = i / w * 2 - 1;
      let green1 = 0;
      let red1 = 0;
      let green2 = 0;
      let red2 = 0;
      let green3 = 0;
      let red3 = 0;
      let d1 = -1;
      let d2 = -1;
      let d3 = -1;
      for(let k=0;k<w;k++){
        let rz = k / w * 2 - 1;
        let r1 = Math.max(-1,Math.min(1,+f([rx,ry,-rz])));
        let r2 = Math.max(-1,Math.min(1,+f([rz,ry,rx])));
        let r3 = Math.max(-1,Math.min(1,+f([rx,rz,ry])));
        if(r1 > 0){
          green1 += r1;
          if(d1 == -1)
            d1 = 1-k/w;
        }else{
          red1 -= r1;
        }
        if(r2 > 0){
          green2 += r2;
          if(d2 == -1)
            d2 = 1-k/w;
        }else{
          red2 -= r2;
        }
        if(r3 > 0){
          green3 += r3;
          if(d3 == -1)
            d3 = 1-k/w;
        }else{
          red3 -= r3;
        }
      }
      green1 /= w;
      red1 /= w;
      green2 /= w;
      red2 /= w;
      green3 /= w;
      red3 /= w;
      rac.fillStyle="rgb("+Math.round(red1*220+35)+","+Math.round(green1*220+35)+",0)";
      rac.fillRect(i+x,j+y,1,1);
      rbc.fillStyle="rgb("+Math.round(red2*220+35)+","+Math.round(green2*220+35)+",0)";
      rbc.fillRect(i+x,j+y,1,1);
      rcc.fillStyle="rgb("+Math.round(red3*220+35)+","+Math.round(green3*220+35)+",0)";
      rcc.fillRect(i+x,j+y,1,1);

      let c = x=>Math.max(Math.round((x*0.9+0.1)*255),0);
      
      rdc.fillStyle="rgb("+c(d1)+","+c(d1)+","+c(d1)+")";
      rdc.fillRect(i+x,j+y,1,1);
      rec.fillStyle="rgb("+c(d2)+","+c(d2)+","+c(d2)+")";
      rec.fillRect(i+x,j+y,1,1);
      rfc.fillStyle="rgb("+c(d3)+","+c(d3)+","+c(d3)+")";
      rfc.fillRect(i+x,j+y,1,1);
    }
  }
 }

 function q(x){return x*x;}

 function fur([x,y,z],n,f,r,d){
  if(z < -1) return;
  z = z * 0.5 + 0.5;
  x += Math.cos(z*f*Math.PI*2)/(n*2) * (1-r);
  y += Math.sin(z*f*Math.PI*2)/(n*2) * (1-r);
  x += z*z *  1;
  y += z*z * -2;
  x = Math.abs(x) * n % 2 - 1;
  y = Math.abs(y) * n % 2 - 1;
  return 1 > ( x*x + y*y + z/d*r) + (1-r);
 }

 function smile([x,y,z]){
  x *= 6;
  y *= 6;
  y = -y;
  return q(x)+q(y)<36 && q(x+2.5)+q(y-2.5)>2.25 && q(x-2.5)+q(y-2.5)>2.25 && q((y+3.5)/1.5-q(x/4))+q(x/4)>1;
 }

 plot(x=>fur(x,15,5,0.5,3/4));
 </script>
  </body>
 </html>
	<!DOCTYPE html>
	<html>
	<head>
	</head>
	<body>
	<canvas id="canvas" width="512" height="512"></canvas>
	<script type="x-shader/x-vertex">
	uniform vec3 direction, ucamera;
	attribute vec3 coordinates;
	varying vec3 ray;
	varying vec3 vcamera;

	const vec3 up = vec3(0,1,0);

	void main(void){
	mat3 rotation = mat3(
	-1,0,0,
	0,0,1,
	0,1,0
	);
	vec3 forward = normalize(direction);
	if(forward != up){
	vec3 left = normalize(cross(forward,up));
	vec3 top = normalize(cross(left,forward));
	rotation = mat3(left,top,forward);
	}
	ray = rotation * vec3(coordinates.xy,1);
	vcamera = ucamera;
	gl_Position = vec4(coordinates, 1.0);
	}
	</script>
	<script type="x-shader/x-fragment">
	precision mediump float;
	varying vec3 ray;
	varying vec3 vcamera;

	const vec3 up = vec3(0,1,0);
	const float depth = 5.;
	const int resolution = 1000;
	const int backtrack = 30;
	const float displacement = 1.5;
	const int overtrace = 2;

	const float step = depth / float(resolution);
	const float backtrack_step = step / float(backtrack);


	bool fur(vec3 p){
	const float n = 10.;
	const float d = 0.75;
	const float r = 0.5;
	const float m = 3.;
	const vec2 t = vec2(-0.6, 1.4);
	p.xyz = p.zxy;
	if(p.z < 0.)
	return false;
	p.xy += vec2(cos(p.zm3.142.),sin(p.zm3.142.))/(n*2.);
	p.xy += p.zp.z t;
	p.xy = mod(abs(p.xy) * n, 2.) - 1.;
	return 1. > ( dot(p.xy,p.xy) + p.z/d*r) + (1.-r);
	}


	bool sphere(vec3 p){
	return dot(p,p) < 1.;
	}

	bool plotfunc(vec3 p){
	return fur(p);
	}

	float finetune_distance(vec3 ray, vec3 viewpoint, float distance){
	float res = distance;
	for(int i=0; i<backtrack*overtrace; i++){
	float bdist = float(i)*backtrack_step;
	vec3 position = ray * (distance-bdist);
	if(plotfunc(position-viewpoint)){
	res = distance-bdist;
	}else{
	return res;
	}
	}
	return res;
	}

	float finetune_surface_distance(vec3 ray, vec3 viewpoint){
	for(int i=0; i<backtrack*overtrace; i++){
	float bdist = float(i)*backtrack_step;
	vec3 position = ray * bdist;
	if(plotfunc(position+viewpoint))
	return bdist;
	}
	return 1000.;
	}

	float getDisplacement(vec3 ray, vec3 viewpoint){
	if(plotfunc(viewpoint)){
	return finetune_distance(ray,-viewpoint,0.);
	}else{
	return finetune_surface_distance(ray,viewpoint);
	}
	}

	void main(void){
	vec3 viewpoint = vcamera;
	vec3 zray = normalize(ray);
	vec3 xray = ray == up ? vec3(1,0,0) : normalize(cross(zray,up));
	vec3 yray = normalize(cross(zray,xray));
	float distance;
	vec3 position;
	bool found = false;
	for(int i=0; i<resolution; i++){
	distance = float(i)*step;
	position = zray * distance;
	if(plotfunc(position-viewpoint)){
	found = true;
	break;
	}
	}
	if(!found)
	discard;
	distance = finetune_distance(zray,viewpoint,distance);
	position = zray * distance;
	float ld = getDisplacement(zray,position - viewpoint + xray * backtrack_step * displacement);
	float rd = getDisplacement(zray,position - viewpoint - xray * backtrack_step * displacement);
	float td = getDisplacement(zray,position - viewpoint + yray * backtrack_step * displacement);
	float bd = getDisplacement(zray,position - viewpoint - yray * backtrack_step * displacement);
	vec3 dir = vec3(ld-rd,td-bd,0) * float(backtrack) / ( float(step) * displacement);
	if(dir.xy == vec2(0,0)){
	dir.z = 1.;
	}else{
	dir.z = 1. / length(dir.xy);
	}
	dir = normalize(dir);
	gl_FragColor = vec4(dir, 1);
	}
	</script>
	<script>
	var canvas = document.getElementById("canvas");
	var gl = canvas.getContext("webgl");
	var rx=0.14, ry=-0.15, x=0, y=-1.25, z=0, keys=[];

	var vertices = [
	-1, 1, 0,
	-1,-1, 0,
	1,-1, 0,
	-1, 1, 0,
	1,-1, 0,
	1, 1, 0,
	];

	indices = [0,1,2,3,4,5];

	var vertex_buffer = gl.createBuffer();
	gl.bindBuffer(gl.ARRAY_BUFFER, vertex_buffer);
	gl.bufferData(gl.ARRAY_BUFFER, new Float32Array(vertices), gl.STATIC_DRAW);
	gl.bindBuffer(gl.ARRAY_BUFFER, null);

	var Index_Buffer = gl.createBuffer();
	gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, Index_Buffer);
	gl.bufferData(gl.ELEMENT_ARRAY_BUFFER, new Uint16Array(indices), gl.STATIC_DRAW);
	gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, null);

	var vertCode = document.querySelector('script[type="x-shader/x-vertex"]').textContent;
	var fragCode = document.querySelector('script[type="x-shader/x-fragment"]').textContent;

	var vertShader = gl.createShader(gl.VERTEX_SHADER);
	gl.shaderSource(vertShader, vertCode);
	gl.compileShader(vertShader);
	var compiled = gl.getShaderParameter(vertShader, gl.COMPILE_STATUS);
	if(!compiled){
	var compilationLog = gl.getShaderInfoLog(vertShader);
	console.log('Vertex shader compile error: ' + compilationLog);
	}

	var fragShader = gl.createShader(gl.FRAGMENT_SHADER);
	gl.shaderSource(fragShader, fragCode);
	gl.compileShader(fragShader);
	var compiled = gl.getShaderParameter(fragShader, gl.COMPILE_STATUS);
	if(!compiled){
	var compilationLog = gl.getShaderInfoLog(fragShader);
	console.log('Fragment shader compile error: ' + compilationLog);
	}

	var shaderProgram = gl.createProgram();
	gl.attachShader(shaderProgram, vertShader);
	gl.attachShader(shaderProgram, fragShader);
	gl.linkProgram(shaderProgram);
	gl.useProgram(shaderProgram);

	gl.bindBuffer(gl.ARRAY_BUFFER, vertex_buffer);
	gl.bindBuffer(gl.ELEMENT_ARRAY_BUFFER, Index_Buffer);
	var coord = gl.getAttribLocation(shaderProgram, "coordinates");
	gl.vertexAttribPointer(coord, 3, gl.FLOAT, false, 0, 0);
	gl.enableVertexAttribArray(coord);
	gl.disable(gl.DEPTH_TEST);

	var direction = gl.getUniformLocation(shaderProgram, 'direction');
	var ucamera = gl.getUniformLocation(shaderProgram, 'ucamera');

	gl.viewport(0,0,canvas.width,canvas.height);

	function draw(){
	var dx = -Math.cos(ryMath.PI2)Math.sin(rxMath.PI*2),
	dy = Math.sin(ryMath.PI2),
	dz = Math.cos(rxMath.PI2)Math.cos(ryMath.PI*2);
	if(keys[89]){
	x += dx * 0.01;
	y += dy * 0.01;
	z += dz * 0.01;
	}
	if(keys[88]){
	x -= dx * 0.01;
	y -= dy * 0.01;
	z -= dz * 0.01;
	}
	if(keys[37]) rx -= 0.01;
	if(keys[39]) rx += 0.01;
	if(keys[38]) ry -= 0.01;
	if(keys[40]) ry += 0.01;
	if(ry>0.25) ry=0.25;
	if(ry<-0.25) ry=-0.25;
	gl.clearColor(0.0, 0.0, 0.3, 1);
	gl.clear(gl.COLOR_BUFFER_BIT);
	gl.uniform3f(ucamera,x,y,z);
	gl.uniform3f(direction,dx,dy,dz);
	gl.drawElements(gl.TRIANGLES, indices.length, gl.UNSIGNED_SHORT,0);
	requestAnimationFrame(draw);
	}
	draw();

	addEventListener("keydown",function(event){
	keys[event.which] = true;
	});

	addEventListener("keyup",function(event){
	keys[event.which] = false;
	});

	</script>
	</body></html>