How does this fake light on an aerovist?

Question

How does this fake light on an aerovist?

I am trying to read this lesson:

https://aerotwist.com/tutorials/an-introduction-to-shaders-part-2/

but I can’t follow. Basically, the code creates directional light using shaders that run directly on the GPU. This is the code:

// same name and type as VS
varying vec3 vNormal;

void main() {

    // calc the dot product and clamp
    // 0 -> 1 rather than -1 -> 1
    vec3 light = vec3(0.5,0.2,1.0);

    // ensure it normalized
    light = normalize(light);

    // calculate the dot product of
    // the light to the vertex normal
    float dProd = max(0.0, dot(vNormal, light));

    // feed into our frag colour
    gl_FragColor = vec4(dProd, dProd, dProd, 1.0);

}

In particular, a line that I don't understand is this:

float dProd = max(0.0, dot(vNormal, light));

As a point product, vNormal peaks and lights create directional light. Can someone explain me schematically. I can’t get it. It looks a little magic to me. I know that in this vertex shader, each vertex is passed as an input, which is called normal, because it is represented in terms of "1", and this shared variable is then used in the fragment fragment shader code above. But other than that, I did not understand how this works.

P.S: , , , 2- . , - three.js .

+1

three.js webgl glsl

TCM 15 . '11 4:35

1

Rabbid76 · Accepted Answer · 2017-07-15T18:50:34+0000

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dot( A, B ) == length( A ) * length( B ) * cos( angle_A_B )

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uA = normalize( A )
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cos( angle_A_B ) == dot( uA, uB )

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WebGL: ,

(function loadscene() {
  
  var gl, progDraw, vp_size;
  var bufSphere = {};
  
  function render(delteMS){

      Camera.create();
      Camera.vp = vp_size;
          
      gl.viewport( 0, 0, vp_size[0], vp_size[1] );
      gl.enable( gl.DEPTH_TEST );
      gl.clearColor( 0.0, 0.0, 0.0, 1.0 );
      gl.clear( gl.COLOR_BUFFER_BIT | gl.DEPTH_BUFFER_BIT );

      // set up draw shader
      ShaderProgram.Use( progDraw.prog );
      ShaderProgram.SetUniformM44( progDraw.prog, "u_projectionMat44", Camera.Perspective() );
      ShaderProgram.SetUniformM44( progDraw.prog, "u_viewMat44", Camera.LookAt() );
      var modelMat = IdentityMat44()
      modelMat = RotateAxis( modelMat, CalcAng( delteMS, 13.0 ), 0 );
      modelMat = RotateAxis( modelMat, CalcAng( delteMS, 17.0 ), 1 );
      ShaderProgram.SetUniformM44( progDraw.prog, "u_modelMat44", modelMat );
      ShaderProgram.SetUniformF3( progDraw.prog, "u_color", [1.0, 0.5, 0.0] );
      ShaderProgram.SetUniformF3( progDraw.prog, "u_lightDir", [-4.0, 0.0, -1.0] )
      
      // draw scene
      VertexBuffer.Draw( bufSphere );

      requestAnimationFrame(render);
  }
  
  function resize() {
      //vp_size = [gl.drawingBufferWidth, gl.drawingBufferHeight];
      vp_size = [window.innerWidth, window.innerHeight]
      canvas.width = vp_size[0];
      canvas.height = vp_size[1];
  }
  
  function initScene() {
  
      canvas = document.getElementById( "canvas");
      gl = canvas.getContext( "experimental-webgl" );
      if ( !gl )
        return null;
  
      progDraw = {}
      progDraw.prog = ShaderProgram.Create( 
        [ { source : "draw-shader-vs", stage : gl.VERTEX_SHADER },
          { source : "draw-shader-fs", stage : gl.FRAGMENT_SHADER }
        ] );
      if ( !progDraw.prog )
          return null;
      progDraw.inPos = gl.getAttribLocation( progDraw.prog, "inPos" );
      
      // create sphere
      var layer_size = 16, circum_size = 32;
      var rad_circum = 1.0;
      var rad_tube = 0.5;
      var sphere_pts = [];
      sphere_pts.push( 0.0, 0.0, -1.0 );
      for ( var i_l = 1; i_l < layer_size; ++ i_l ) {
          var angH = (1.0 - i_l / layer_size) * Math.PI;
          var h = Math.cos( angH );
          var r = Math.sin( angH );
          for ( var i_c = 0; i_c < circum_size; ++ i_c ) {
              var circumX = Math.cos(2 * Math.PI * i_c / circum_size);
              var circumY = Math.sin(2 * Math.PI * i_c / circum_size);
              sphere_pts.push( r * circumX, r * circumY, h );
          }
      }
      sphere_pts.push( 0.0, 0.0, 1.0 );
      var sphere_inx = [];
      for ( var i_c = 0; i_c < circum_size; ++ i_c ) {
          sphere_inx.push( i_c+1, 0, (i_c+1) % circum_size + 1 )
      } 
      for ( var i_l = 0; i_l < layer_size-2; ++ i_l ) {
          var l1 = i_l * circum_size + 1;
          var l2 = (i_l+1) * circum_size + 1
          for ( var i_c = 0; i_c < circum_size; ++ i_c ) {
              var i_n = (i_c+1) % circum_size;
              sphere_inx.push( l1+i_c, l1+i_n, l2+i_c, l1+i_n, l2+i_n, l2+i_c );
          }
      }
      for ( var i_c = 0; i_c < circum_size; ++ i_c ) {
          var i_start = 1 + (layer_size-2) * circum_size;
          var i_n = (i_c+1) % circum_size;
          sphere_inx.push( i_start + i_c, i_start + i_n, sphere_pts.length/3-1 );
      }
      bufSphere = VertexBuffer.Create(
          [ { data : sphere_pts, attrSize : 3, attrLoc : progDraw.inPos } ],
          sphere_inx );
        
      window.onresize = resize;
      resize();
      requestAnimationFrame(render);
  }
  
  function Fract( val ) { 
      return val - Math.trunc( val );
  }
  function CalcAng( deltaTime, intervall ) {
      return Fract( deltaTime / (1000*intervall) ) * 2.0 * Math.PI;
  }
  function CalcMove( deltaTime, intervall, range ) {
      var pos = self.Fract( deltaTime / (1000*intervall) ) * 2.0
      var pos = pos < 1.0 ? pos : (2.0-pos)
      return range[0] + (range[1] - range[0]) * pos;
  }    
  function EllipticalPosition( a, b, angRag ) {
      var a_b = a * a - b * b
      var ea = (a_b <= 0) ? 0 : Math.sqrt( a_b );
      var eb = (a_b >= 0) ? 0 : Math.sqrt( -a_b );
      return [ a * Math.sin( angRag ) - ea, b * Math.cos( angRag ) - eb, 0 ];
  }
  
  glArrayType = typeof Float32Array !="undefined" ? Float32Array : ( typeof WebGLFloatArray != "undefined" ? WebGLFloatArray : Array );
  
  function IdentityMat44() {
    var m = new glArrayType(16);
    m[0]  = 1; m[1]  = 0; m[2]  = 0; m[3]  = 0;
    m[4]  = 0; m[5]  = 1; m[6]  = 0; m[7]  = 0;
    m[8]  = 0; m[9]  = 0; m[10] = 1; m[11] = 0;
    m[12] = 0; m[13] = 0; m[14] = 0; m[15] = 1;
    return m;
  };
  
  function RotateAxis(matA, angRad, axis) {
      var aMap = [ [1, 2], [2, 0], [0, 1] ];
      var a0 = aMap[axis][0], a1 = aMap[axis][1]; 
      var sinAng = Math.sin(angRad), cosAng = Math.cos(angRad);
      var matB = new glArrayType(16);
      for ( var i = 0; i < 16; ++ i ) matB[i] = matA[i];
      for ( var i = 0; i < 3; ++ i ) {
          matB[a0*4+i] = matA[a0*4+i] * cosAng + matA[a1*4+i] * sinAng;
          matB[a1*4+i] = matA[a0*4+i] * -sinAng + matA[a1*4+i] * cosAng;
      }
      return matB;
  }
  
  function Cross( a, b ) { return [ a[1] * b[2] - a[2] * b[1], a[2] * b[0] - a[0] * b[2], a[0] * b[1] - a[1] * b[0], 0.0 ]; }
  function Dot( a, b ) { return a[0]*b[0] + a[1]*b[1] + a[2]*b[2]; }
  function Normalize( v ) {
      var len = Math.sqrt( v[0] * v[0] + v[1] * v[1] + v[2] * v[2] );
      return [ v[0] / len, v[1] / len, v[2] / len ];
  }
  
  var Camera = {};
  Camera.create = function() {
      this.pos    = [0, 1.5, 0.0];
      this.target = [0, 0, 0];
      this.up     = [0, 0, 1];
      this.fov_y  = 90;
      this.vp     = [800, 600];
      this.near   = 0.5;
      this.far    = 100.0;
  }
  Camera.Perspective = function() {
      var fn = this.far + this.near;
      var f_n = this.far - this.near;
      var r = this.vp[0] / this.vp[1];
      var t = 1 / Math.tan( Math.PI * this.fov_y / 360 );
      var m = IdentityMat44();
      m[0]  = t/r; m[1]  = 0; m[2]  =  0;                              m[3]  = 0;
      m[4]  = 0;   m[5]  = t; m[6]  =  0;                              m[7]  = 0;
      m[8]  = 0;   m[9]  = 0; m[10] = -fn / f_n;                       m[11] = -1;
      m[12] = 0;   m[13] = 0; m[14] = -2 * this.far * this.near / f_n; m[15] =  0;
      return m;
  }
  Camera.LookAt = function() {
      var mz = Normalize( [ this.pos[0]-this.target[0], this.pos[1]-this.target[1], this.pos[2]-this.target[2] ] );
      var mx = Normalize( Cross( this.up, mz ) );
      var my = Normalize( Cross( mz, mx ) );
      var tx = Dot( mx, this.pos );
      var ty = Dot( my, this.pos );
      var tz = Dot( [-mz[0], -mz[1], -mz[2]], this.pos ); 
      var m = IdentityMat44();
      m[0]  = mx[0]; m[1]  = my[0]; m[2]  = mz[0]; m[3]  = 0;
      m[4]  = mx[1]; m[5]  = my[1]; m[6]  = mz[1]; m[7]  = 0;
      m[8]  = mx[2]; m[9]  = my[2]; m[10] = mz[2]; m[11] = 0;
      m[12] = tx;    m[13] = ty;    m[14] = tz;    m[15] = 1; 
      return m;
  } 
  
  var ShaderProgram = {};
  ShaderProgram.Create = function( shaderList ) {
      var shaderObjs = [];
      for ( var i_sh = 0; i_sh < shaderList.length; ++ i_sh ) {
          var shderObj = this.CompileShader( shaderList[i_sh].source, shaderList[i_sh].stage );
          if ( shderObj == 0 )
              return 0;
          shaderObjs.push( shderObj );
      }
      var progObj = this.LinkProgram( shaderObjs )
      if ( progObj != 0 ) {
          progObj.attribIndex = {};
          var noOfAttributes = gl.getProgramParameter( progObj, gl.ACTIVE_ATTRIBUTES );
          for ( var i_n = 0; i_n < noOfAttributes; ++ i_n ) {
              var name = gl.getActiveAttrib( progObj, i_n ).name;
              progObj.attribIndex[name] = gl.getAttribLocation( progObj, name );
          }
          progObj.unifomLocation = {};
          var noOfUniforms = gl.getProgramParameter( progObj, gl.ACTIVE_UNIFORMS );
          for ( var i_n = 0; i_n < noOfUniforms; ++ i_n ) {
              var name = gl.getActiveUniform( progObj, i_n ).name;
              progObj.unifomLocation[name] = gl.getUniformLocation( progObj, name );
          }
      }
      return progObj;
  }
  ShaderProgram.AttributeIndex = function( progObj, name ) { return progObj.attribIndex[name]; } 
  ShaderProgram.UniformLocation = function( progObj, name ) { return progObj.unifomLocation[name]; } 
  ShaderProgram.Use = function( progObj ) { gl.useProgram( progObj ); } 
  ShaderProgram.SetUniformI1  = function( progObj, name, val ) { if(progObj.unifomLocation[name]) gl.uniform1i( progObj.unifomLocation[name], val ); }
  ShaderProgram.SetUniformF1  = function( progObj, name, val ) { if(progObj.unifomLocation[name]) gl.uniform1f( progObj.unifomLocation[name], val ); }
  ShaderProgram.SetUniformF2  = function( progObj, name, arr ) { if(progObj.unifomLocation[name]) gl.uniform2fv( progObj.unifomLocation[name], arr ); }
  ShaderProgram.SetUniformF3  = function( progObj, name, arr ) { if(progObj.unifomLocation[name]) gl.uniform3fv( progObj.unifomLocation[name], arr ); }
  ShaderProgram.SetUniformF4  = function( progObj, name, arr ) { if(progObj.unifomLocation[name]) gl.uniform4fv( progObj.unifomLocation[name], arr ); }
  ShaderProgram.SetUniformM33 = function( progObj, name, mat ) { if(progObj.unifomLocation[name]) gl.uniformMatrix3fv( progObj.unifomLocation[name], false, mat ); }
  ShaderProgram.SetUniformM44 = function( progObj, name, mat ) { if(progObj.unifomLocation[name]) gl.uniformMatrix4fv( progObj.unifomLocation[name], false, mat ); }
  ShaderProgram.CompileShader = function( source, shaderStage ) {
      var shaderScript = document.getElementById(source);
      if (shaderScript)
        source = shaderScript.text;
      var shaderObj = gl.createShader( shaderStage );
      gl.shaderSource( shaderObj, source );
      gl.compileShader( shaderObj );
      var status = gl.getShaderParameter( shaderObj, gl.COMPILE_STATUS );
      if ( !status ) alert(gl.getShaderInfoLog(shaderObj));
      return status ? shaderObj : null;
  } 
  ShaderProgram.LinkProgram = function( shaderObjs ) {
      var prog = gl.createProgram();
      for ( var i_sh = 0; i_sh < shaderObjs.length; ++ i_sh )
          gl.attachShader( prog, shaderObjs[i_sh] );
      gl.linkProgram( prog );
      status = gl.getProgramParameter( prog, gl.LINK_STATUS );
      if ( !status ) alert("Could not initialise shaders");
      gl.useProgram( null );
      return status ? prog : null;
  }
  
  var VertexBuffer = {};
  VertexBuffer.Create = function( attributes, indices ) {
      var buffer = {};
      buffer.buf = [];
      buffer.attr = []
      for ( var i = 0; i < attributes.length; ++ i ) {
          buffer.buf.push( gl.createBuffer() );
          buffer.attr.push( { size : attributes[i].attrSize, loc : attributes[i].attrLoc } );
          gl.bindBuffer( gl.ARRAY_BUFFER, buffer.buf[i] );
          gl.bufferData( gl.ARRAY_BUFFER, new Float32Array( attributes[i].data ), gl.STATIC_DRAW );
      }
      buffer.inx = gl.createBuffer();
      gl.bindBuffer( gl.ELEMENT_ARRAY_BUFFER, buffer.inx );
      gl.bufferData( gl.ELEMENT_ARRAY_BUFFER, new Uint16Array( indices ), gl.STATIC_DRAW );
      buffer.inxLen = indices.length;
      gl.bindBuffer( gl.ARRAY_BUFFER, null );
      gl.bindBuffer( gl.ELEMENT_ARRAY_BUFFER, null );
      return buffer;
  }
  VertexBuffer.Draw = function( bufObj ) {
    for ( var i = 0; i < bufObj.buf.length; ++ i ) {
          gl.bindBuffer( gl.ARRAY_BUFFER, bufObj.buf[i] );
          gl.vertexAttribPointer( bufObj.attr[i].loc, bufObj.attr[i].size, gl.FLOAT, false, 0, 0 );
          gl.enableVertexAttribArray( bufObj.attr[i].loc );
      }
      gl.bindBuffer( gl.ELEMENT_ARRAY_BUFFER, bufObj.inx );
      gl.drawElements( gl.TRIANGLES, bufObj.inxLen, gl.UNSIGNED_SHORT, 0 );
      for ( var i = 0; i < bufObj.buf.length; ++ i )
         gl.disableVertexAttribArray( bufObj.attr[i].loc );
      gl.bindBuffer( gl.ARRAY_BUFFER, null );
      gl.bindBuffer( gl.ELEMENT_ARRAY_BUFFER, null );
  }
  
  initScene();
  
  })();

html,body {
    height: 100%;
    width: 100%;
    margin: 0;
    overflow: hidden;
}

#gui {
    position : absolute;
    top : 0;
    left : 0;
}

<script id="draw-shader-vs" type="x-shader/x-vertex">
    precision mediump float;
    
    attribute vec3 inPos;
    
    varying vec3 v_normal;

    uniform mat4 u_projectionMat44;
    uniform mat4 u_viewMat44;
    uniform mat4 u_modelMat44;
    
    void main()
    {
        vec3  modelNV = mat3( u_modelMat44 ) * normalize( inPos );
        vec3  normalV = mat3( u_viewMat44 ) * modelNV;
        v_normal      = normalV;

        vec4 modelPos = u_modelMat44 * vec4( inPos, 1.0 );
        vec4 viewPos  = u_viewMat44 * modelPos;
        gl_Position   = u_projectionMat44 * viewPos;
}
</script>
  
<script id="draw-shader-fs" type="x-shader/x-fragment">
    precision mediump float;
    
    varying vec3 v_normal;
    
    uniform vec3 u_lightDir;
    uniform vec3 u_color;

    void main()
    {
        vec3  normalV  = normalize( v_normal );
        vec3  lightV   = normalize( -u_lightDir );
        float NdotL    = max( 0.0, dot( normalV, lightV ) );

        vec3 lightCol  = (0.2 + 0.8 * NdotL) * u_color;
        gl_FragColor   = vec4( lightCol.rgb, 1.0 );
    }
</script>

<canvas id="canvas" style="border: none;" width="100%" height="100%"></canvas>

How does this fake light on an aerovist?

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