🔒 👩🏼‍🏫 🗻 The d'Alembert formula in action 😞 🕴️ 🖥️

Good day!

Today I would like to present you a small program that uses the d'Alembert formula:

In my opinion, here there is a shift of the function of one relative to the other, due to which a wave is formed. The function arguments are x and t, you can also use the acceleration a. Two functions fi and ksi, more precisely y (instead of ksi).

The program is written using a browser and WebGL.

Wave.html file:

<!DOCTYPE html>
<html lang="en">
<head>

<meta charset="utf-8" />

<title>Draw a Wave</title>
</head>

<body onload="main()">

<canvas id="webgl" width="1600" height="1000">

Please use a browser that supports "canvas"

</canvas>
<script src="webgl-utils.js"></script>
<script src="webgl-debug.js"></script>
<script src="cuon-utils.js"></script>
<script src="Wave.js"></script>
</body>
</html>

You need to put webgl-utils.js webgl-debug.js cuon-utils.js to the Wave.html file or find them on the net and connect.

Wave.js file:

// Vertex shader program
var VSHADER_SOURCE =
  'attribute vec4 a_Position;\n' +
  'void main() {\n' +
  '  gl_Position = a_Position;\n' +
  '}\n';

// Fragment shader program
var FSHADER_SOURCE =
  'void main() {\n' +
  '  gl_FragColor = vec4(1.0, 0.0, 0.0, 1.0);\n' +
  '}\n';

var xx=0;
function main() {
  // Retrieve <canvas> element
  var canvas = document.getElementById('webgl');

  // Get the rendering context for WebGL
  var gl = getWebGLContext(canvas);
  if (!gl) {
    console.log('Failed to get the rendering context for WebGL');
    return;
  }

  // Initialize shaders
  if (!initShaders(gl, VSHADER_SOURCE, FSHADER_SOURCE)) {
    console.log('Failed to intialize shaders.');
    return;
  }

  // Write the positions of vertices to a vertex shader
  var n = initVertexBuffers(gl);
  if (n < 0) {
    console.log('Failed to set the positions of the vertices');
    return;
  }

  // Specify the color for clearing <canvas>
  gl.clearColor(0, 0, 0, 1);

  var tick = function() {
    draw(gl, n);   // Draw function
    requestAnimationFrame(tick, canvas); // Request that the browser calls tick
  };
  tick();
}
function draw(gl, n) {
  // Clear <canvas>
  gl.clear(gl.COLOR_BUFFER_BIT);
  initVertexBuffers(gl);
    // function
  gl.drawArrays(gl.LINE_STRIP, 0, n);
}
function fi(x)
{
    return Math.cos(x);
}
function ksi(x)
{
    return Math.sin(3*x);
}
function Dalamber(x,t)
{
    return 0.5*(fi(x-t) + fi(x+t))+0.5*(ksi(x+t)-ksi(x-t));
}
function initVertexBuffers(gl) {

  var vertices = new Float32Array(400);
  var i=0;
  for(var t=-1.0;t<1.0;t+=0.01)
  {
      vertices[i]=t;
      vertices[i+1]=Dalamber(t,xx)/2;
      //document.write("x=",vertices[i],"y=",vertices[i+1]+"<br>");
      i+=2;
  }
  xx+=0.01;
  var n = vertices.length/2;
  // Create a buffer object
  var vertexBuffer = gl.createBuffer();
  if (!vertexBuffer) {
    console.log('Failed to create the buffer object');
    return -1;
  }

  // Bind the buffer object to target
  gl.bindBuffer(gl.ARRAY_BUFFER, vertexBuffer);
  // Write date into the buffer object
  gl.bufferData(gl.ARRAY_BUFFER, vertices, gl.STATIC_DRAW);

  var a_Position = gl.getAttribLocation(gl.program, 'a_Position');
  if (a_Position < 0) {
    console.log('Failed to get the storage location of a_Position');
    return -1;
  }
  // Assign the buffer object to a_Position variable
  gl.vertexAttribPointer(a_Position, 2, gl.FLOAT, false, 0, 0);

  // Enable the assignment to a_Position variable
  gl.enableVertexAttribArray(a_Position);

  return n;
}

You can experiment with the fi and ksi functions, change parameters and add other functions, sum them, multiply them.

Result:

Do not judge strictly and thank you for your attention!

PS If you squeeze my karma into 0 at least, I'll post something else interesting.

The d'Alembert formula in action

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