translation

geometry를 업로드하고 shader에서 translation을 수행하여 2D 객체를 이동

<script id="vertex-shader-2d" type="x-shader/x-vertex">
attribute vec2 a_position;

uniform vec2 u_resolution;
uniform vec2 u_translation;

void main() {
    //Add in the translation.
    vec2 position = a_position + u_translation;

    //convert the position from pixels to 0.0 to 1.0
    vec2 zeroToOne = position / u_resolution;

    //convert from 0->1 to 0->2
    vec2 zeroToTwo = zeroToOne * 2.0;

    //convert from 0->2 to -1->+1 (clipspace)
    vec2 clipSpace = zeroToTwo - 1.0;

    gl_Position = vec4(clipSpace * vec2(1, -1), 0, 1);
}
</script>
<script  id="fragment-shader-2d" type="x-shader/x-fragment">
precision mediump float;

uniform vec4 u_color;

void main() {
   gl_FragColor = u_color;
}
"use strict";

function main() {
  // Get A WebGL context
  /** @type {HTMLCanvasElement} */
  var canvas = document.querySelector("#canvas");
  var gl = canvas.getContext("webgl");
  if (!gl) {
    return;
  }

  // setup GLSL program
  var program = webglUtils.createProgramFromScripts(gl, ["vertex-shader-2d", "fragment-shader-2d"]);
  gl.useProgram(program);

  // look up where the vertex data needs to go.
  var positionLocation = gl.getAttribLocation(program, "a_position");

  // lookup uniforms
  var resolutionLocation = gl.getUniformLocation(program, "u_resolution");
  var colorLocation = gl.getUniformLocation(program, "u_color");
  var translationLocation = gl.getUniformLocation(program, "u_translation");

  // Create a buffer to put positions in
  var positionBuffer = gl.createBuffer();
  // Bind it to ARRAY_BUFFER (think of it as ARRAY_BUFFER = positionBuffer)
  gl.bindBuffer(gl.ARRAY_BUFFER, positionBuffer);
  // Put geometry data into buffer
  setGeometry(gl);

  var translation = [0, 0];
  var color = [Math.random(), Math.random(), Math.random(), 1];

  drawScene();

  // Setup a ui.
  webglLessonsUI.setupSlider("#x", {slide: updatePosition(0), max: gl.canvas.width });
  webglLessonsUI.setupSlider("#y", {slide: updatePosition(1), max: gl.canvas.height});

  function updatePosition(index) {
    return function(event, ui) {
      translation[index] = ui.value;
      drawScene();
    };
  }

  // Draw the scene.
  function drawScene() {
    webglUtils.resizeCanvasToDisplaySize(gl.canvas);

    // Tell WebGL how to convert from clip space to pixels
    gl.viewport(0, 0, gl.canvas.width, gl.canvas.height);

    // Clear the canvas.
    gl.clear(gl.COLOR_BUFFER_BIT);

    // Tell it to use our program (pair of shaders)
    gl.useProgram(program);

    // Turn on the attribute
    gl.enableVertexAttribArray(positionLocation);

    // Bind the position buffer.
    gl.bindBuffer(gl.ARRAY_BUFFER, positionBuffer);

    // Tell the attribute how to get data out of positionBuffer (ARRAY_BUFFER)
    var size = 2;          // 2 components per iteration
    var type = gl.FLOAT;   // the data is 32bit floats
    var normalize = false; // don't normalize the data
    var stride = 0;        // 0 = move forward size * sizeof(type) each iteration to get the next position
    var offset = 0;        // start at the beginning of the buffer
    gl.vertexAttribPointer(
        positionLocation, size, type, normalize, stride, offset);

    // set the resolution
    gl.uniform2f(resolutionLocation, gl.canvas.width, gl.canvas.height);

    // set the color
    gl.uniform4fv(colorLocation, color);

    // Set the translation.
    gl.uniform2fv(translationLocation, translation);

    // Draw the geometry.
    var primitiveType = gl.TRIANGLES;
    var offset = 0;
    var count = 18;  // 6 triangles in the 'F', 3 points per triangle
    gl.drawArrays(primitiveType, offset, count);
  }
}

// Fill the buffer with the values that define a letter 'F'.
function setGeometry(gl) {
  gl.bufferData(
      gl.ARRAY_BUFFER,
      new Float32Array([
          // left column
          0, 0,
          30, 0,
          0, 150,
          0, 150,
          30, 0,
          30, 150,

          // top rung
          30, 0,
          100, 0,
          30, 30,
          30, 30,
          100, 0,
          100, 30,

          // middle rung
          30, 60,
          67, 60,
          30, 90,
          30, 90,
          67, 60,
          67, 90,
      ]),
      gl.STATIC_DRAW);
}

main();


Rotation

단위원의 점은 sine consine으로 표현

function printSineAndCosineForAnAngle(angleInDegrees) {
  var angleInRadians = angleInDegrees * Math.PI / 180;
  var s = Math.sin(angleInRadians);
  var c = Math.cos(angleInRadians);
  console.log("s = " + s + " c = " + c);
}
  • degree보다는 radian이 수학에서 쉽게 표현할 수 있다. 360 degree = 2π radian , 90 degree = 1/2π radian

...
uniform vec2 u_rotation;

void main() {
    // Rotate the position
    vec2 rotatedPosition = vec2(
       a_position.x * u_rotation.y + a_position.y * u_rotation.x,
       a_position.y * u_rotation.y - a_position.x * u_rotation.x);
    
    // Add in the translation.
    vec2 position = rotatedPosition + u_translation;
    ...
}


Scale

uniform vec2 u_scale;
void main() {
  // 위치 scale
  vec2 scaledPosition = a_position * u_scale;
 
  // 위치 회전
  vec2 rotatedPosition = vec2(
     scaledPosition.x * u_rotation.y + scaledPosition.y * u_rotation.x,
     scaledPosition.y * u_rotation.y - scaledPosition.x * u_rotation.x);
 
  // translation 추가
  vec2 position = rotatedPosition + u_translation;
...
  ...
  var scaleLocation = gl.getUniformLocation(program, "u_scale");
  ...
  var scale = [1, 1];
  ...
  // 장면 그리기
  function drawScene() {
    ...
    // translation 설정
    gl.uniform2fv(translationLocation, translation);
    // rotation 설정
    gl.uniform2fv(rotationLocation, rotation);
    // scale 설정
    gl.uniform2fv(scaleLocation, scale);
    // geometry 그리기
    var primitiveType = gl.TRIANGLES;
    var offset = 0;
    var count = 18;  // 'F'의 삼각형 6개, 삼각형마다 점 3개
    gl.drawArrays(primitiveType, offset, count);
  }
  • 음수로 크기를 조정하면 geometry가 뒤집힌다.


Matrices

Matrices의 위치를 이용하여 함수를 선언한 후 조합을 사용하여 표현

"use strict";

function main() {
  // Get A WebGL context
  /** @type {HTMLCanvasElement} */
  var canvas = document.querySelector("#canvas");
  var gl = canvas.getContext("webgl");
  if (!gl) {
    return;
  }

  // setup GLSL program
  var program = webglUtils.createProgramFromScripts(gl, ["vertex-shader-2d", "fragment-shader-2d"]);

  // look up where the vertex data needs to go.
  var positionLocation = gl.getAttribLocation(program, "a_position");

  // lookup uniforms
  var colorLocation = gl.getUniformLocation(program, "u_color");
  var matrixLocation = gl.getUniformLocation(program, "u_matrix");

  // Create a buffer to put positions in
  var positionBuffer = gl.createBuffer();
  // Bind it to ARRAY_BUFFER (think of it as ARRAY_BUFFER = positionBuffer)
  gl.bindBuffer(gl.ARRAY_BUFFER, positionBuffer);
  // Put geometry data into buffer
  setGeometry(gl);

  var translation = [100, 150];
  var angleInRadians = 0;
  var scale = [1, 1];
  var color = [Math.random(), Math.random(), Math.random(), 1];

  drawScene();

  // Setup a ui.
  webglLessonsUI.setupSlider("#x", {value: translation[0], slide: updatePosition(0), max: gl.canvas.width });
  webglLessonsUI.setupSlider("#y", {value: translation[1], slide: updatePosition(1), max: gl.canvas.height});
  webglLessonsUI.setupSlider("#angle", {slide: updateAngle, max: 360});
  webglLessonsUI.setupSlider("#scaleX", {value: scale[0], slide: updateScale(0), min: -5, max: 5, step: 0.01, precision: 2});
  webglLessonsUI.setupSlider("#scaleY", {value: scale[1], slide: updateScale(1), min: -5, max: 5, step: 0.01, precision: 2});

  function updatePosition(index) {
    return function(event, ui) {
      translation[index] = ui.value;
      drawScene();
    };
  }

  function updateAngle(event, ui) {
    var angleInDegrees = 360 - ui.value;
    angleInRadians = angleInDegrees * Math.PI / 180;
    drawScene();
  }

  function updateScale(index) {
    return function(event, ui) {
      scale[index] = ui.value;
      drawScene();
    };
  }

  // Draw the scene.
  function drawScene() {
    webglUtils.resizeCanvasToDisplaySize(gl.canvas);

    // Tell WebGL how to convert from clip space to pixels
    gl.viewport(0, 0, gl.canvas.width, gl.canvas.height);

    // Clear the canvas.
    gl.clear(gl.COLOR_BUFFER_BIT);

    // Tell it to use our program (pair of shaders)
    gl.useProgram(program);

    // Turn on the attribute
    gl.enableVertexAttribArray(positionLocation);

    // Bind the position buffer.
    gl.bindBuffer(gl.ARRAY_BUFFER, positionBuffer);

    // Tell the attribute how to get data out of positionBuffer (ARRAY_BUFFER)
    var size = 2;          // 2 components per iteration
    var type = gl.FLOAT;   // the data is 32bit floats
    var normalize = false; // don't normalize the data
    var stride = 0;        // 0 = move forward size * sizeof(type) each iteration to get the next position
    var offset = 0;        // start at the beginning of the buffer
    gl.vertexAttribPointer(
        positionLocation, size, type, normalize, stride, offset);

    // set the color
    gl.uniform4fv(colorLocation, color);

    // Compute the matrices
    var matrix = m3.projection(gl.canvas.clientWidth, gl.canvas.clientHeight);
    matrix = m3.translate(matrix, translation[0], translation[1]);
    matrix = m3.rotate(matrix, angleInRadians);
    matrix = m3.scale(matrix, scale[0], scale[1]);

    // Set the matrix.
    gl.uniformMatrix3fv(matrixLocation, false, matrix);

    // Draw the geometry.
    var primitiveType = gl.TRIANGLES;
    var offset = 0;
    var count = 18;  // 6 triangles in the 'F', 3 points per triangle
    gl.drawArrays(primitiveType, offset, count);

  }
}

var m3 = {
  projection: function(width, height) {
    // Note: This matrix flips the Y axis so that 0 is at the top.
    return [
      2 / width, 0, 0,
      0, -2 / height, 0,
      -1, 1, 1
    ];
  },

  identity: function() {
    return [
      1, 0, 0,
      0, 1, 0,
      0, 0, 1,
    ];
  },

  translation: function(tx, ty) {
    return [
      1, 0, 0,
      0, 1, 0,
      tx, ty, 1,
    ];
  },

  rotation: function(angleInRadians) {
    var c = Math.cos(angleInRadians);
    var s = Math.sin(angleInRadians);
    return [
      c,-s, 0,
      s, c, 0,
      0, 0, 1,
    ];
  },

  scaling: function(sx, sy) {
    return [
      sx, 0, 0,
      0, sy, 0,
      0, 0, 1,
    ];
  },

  multiply: function(a, b) {
    var a00 = a[0 * 3 + 0];
    var a01 = a[0 * 3 + 1];
    var a02 = a[0 * 3 + 2];
    var a10 = a[1 * 3 + 0];
    var a11 = a[1 * 3 + 1];
    var a12 = a[1 * 3 + 2];
    var a20 = a[2 * 3 + 0];
    var a21 = a[2 * 3 + 1];
    var a22 = a[2 * 3 + 2];
    var b00 = b[0 * 3 + 0];
    var b01 = b[0 * 3 + 1];
    var b02 = b[0 * 3 + 2];
    var b10 = b[1 * 3 + 0];
    var b11 = b[1 * 3 + 1];
    var b12 = b[1 * 3 + 2];
    var b20 = b[2 * 3 + 0];
    var b21 = b[2 * 3 + 1];
    var b22 = b[2 * 3 + 2];
    return [
      b00 * a00 + b01 * a10 + b02 * a20,
      b00 * a01 + b01 * a11 + b02 * a21,
      b00 * a02 + b01 * a12 + b02 * a22,
      b10 * a00 + b11 * a10 + b12 * a20,
      b10 * a01 + b11 * a11 + b12 * a21,
      b10 * a02 + b11 * a12 + b12 * a22,
      b20 * a00 + b21 * a10 + b22 * a20,
      b20 * a01 + b21 * a11 + b22 * a21,
      b20 * a02 + b21 * a12 + b22 * a22,
    ];
  },

  translate: function(m, tx, ty) {
    return m3.multiply(m, m3.translation(tx, ty));
  },

  rotate: function(m, angleInRadians) {
    return m3.multiply(m, m3.rotation(angleInRadians));
  },

  scale: function(m, sx, sy) {
    return m3.multiply(m, m3.scaling(sx, sy));
  },
};

// Fill the buffer with the values that define a letter 'F'.
function setGeometry(gl) {
  gl.bufferData(
      gl.ARRAY_BUFFER,
      new Float32Array([
          // left column
          0, 0,
          30, 0,
          0, 150,
          0, 150,
          30, 0,
          30, 150,

          // top rung
          30, 0,
          100, 0,
          30, 30,
          30, 30,
          100, 0,
          100, 30,

          // middle rung
          30, 60,
          67, 60,
          30, 90,
          30, 90,
          67, 60,
          67, 90,
      ]),
      gl.STATIC_DRAW);
}

main();


출처

https://webglfundamentals.org/webgl/lessons/ko/webgl-2d-translation.html https://webglfundamentals.org/webgl/lessons/ko/webgl-2d-rotation.html https://webglfundamentals.org/webgl/lessons/ko/webgl-2d-matrices.html