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Activation des boutons Précédent et Suivant

S’appuyant sur les informations présentées dans Ajout de nuances de gris à une image de Mandelbrot, cette rubrique décrit comment activer les boutons Précédent et Suivant du navigateur.

La technique employée pour activer les boutons Précédent et Suivant du navigateur consiste à obtenir et à définir la chaîne de hachage d’URL de la page, comme dans :


http://samples.msdn.microsoft.com/Workshop/samples/mandelbrot/mandelbrotExplorer.html#0.722,-0.178,0.846,0.246,1

En général, quand l’URL change, les boutons Précédent et Suivant du navigateur deviennent activés. Ainsi, chaque image (page) de Mandelbrot unique aura une chaîne de hachage unique.

La chaîne de hachage, #0.722,-0.178,0.846,0.246,1, peut être interprétée comme suit :

  • globals.reMax = 0.722
  • globals.reMin = -0.178
  • globals.ImMax = 0.846
  • globals.ImMin = 0.246
  • globals.grayscaleFactor = 1

Nous discuterons en détail de cette interprétation un peu plus loin, mais pour le moment globals.grayscaleFactor indique dans quelle mesure éclaircir une image donnée (une valeur de 1 n’a aucun effet).

Mandelbrot 4 est semblable à Mandelbrot 5, comme indiqué ici :

Mandelbrot 5


<!DOCTYPE html>
<html>

<head>
  <meta http-equiv="X-UA-Compatible" content="IE=10" />
  <meta content="text/html; charset=utf-8" http-equiv="Content-Type">
  <title>Mandelbrot 5</title>
  <style>
    html, body {
      margin: 0;
      padding: 0;
      text-align: center;
    }
    
    canvas {
      border: 2px solid black;
    }    
    
    table {
      margin: 0 auto; /* Center the table. */
    }
    
    #messageBox {
      text-align: left;
    }
        
    #elapsedTime {
      width: 23em;
      text-align: right;
    }    

    button {
      width: 5em;
    }
    
    #filenameForm {
      visibility: hidden; /* As opposed to "display: none", keep room for this hidden element in the layout. */
    }
}
  </style>      
</head>

<body>
  <h1>Mandelbrot 5</h1>
  <p>This example demonstrates how to enable the browser's back and forward buttons.</p>      
  <table>
    <tr>
      <td id="messageBox"></td>
      <td id="elapsedTime"></td>
    </tr>
  </table>
  <canvas width="600" height="400" oncontextmenu="return false;"> <!-- Because the hold gesture event can fire more than once, the 'oncontextmenu="return false;"' attribute is used to stop the right-click context menu from appearing inappropriately. -->
    Canvas not supported - upgrade your browser (after checking that your browser is in the correct mode).
  </canvas><br>
  <button type="button" id="resetButton">Reset</button>  
  <button type="button" id="lightenButton">Lighten</button>    
  <button type="button" id="saveButton">Save</button>
  <form id="filenameForm"> 
    Extensionless filename: <input id="filename" type="text"> <input type="submit" value="Submit">
  </form>
  <script>
    var RE_MAX = 1.1; // This value will be adjusted as necessary to ensure that the rendered Mandelbrot set is never skewed (that is, true to it's actual shape).
    var RE_MIN = -2.5;
    var IM_MAX = 1.2;
    var IM_MIN = -1.2;
    var MAX_ITERATIONS = 1200; // Increase this value to improve detection of complex c values that belong to the Mandelbrot set.
    var STATIC_ZOOM_BOX_FACTOR = 0.25; // Increase to make the double-click and hold gesture zoom box bigger.
    var DEFAULT_MESSAGE = "Click or click-and-drag to zoom."
      
      
      var globals = {}; // See the handleLoad function.
      
      window.addEventListener('load', handleLoad, false);
                
    /************************************************************************************************************************************************************/
    
    Number.prototype.format = function() {
    /* 
      Formats this integer so that it has commas in the expected places.
    */
    	var numberString = Math.round(this).toString(); // An integer value is assumed, so we ensure that it is indeed an integer.
    	var precompiledRegularExpression = /(\d+)(\d{3})/;
    	
    	while ( precompiledRegularExpression.test(numberString) ) {
    		numberString = numberString.replace(precompiledRegularExpression, '$1' + ',' + '$2'); // For this integer, inject ","'s at the appropriate locations.
    	} // while
    	
    	return numberString;
    } // Number.prototype.format

    /*----------------------------------------------------------------------------------------------------------------------------------------------------------*/    

    function handleLoad() {          
      var canvas = document.getElementsByTagName('canvas')[0];
      var canvasWidth = canvas.width;
      var canvasHeight = canvas.height;      
      var ctx = canvas.getContext('2d');
      
      document.getElementsByTagName('table')[0].width = canvasWidth; // Make the table's width the same as the canvas's width. 
      document.getElementById('messageBox').innerHTML = DEFAULT_MESSAGE;            

      globals.canvas = canvas;
      globals.canvas.context = ctx;
      globals.canvas.context.imageDataObject = ctx.createImageData(canvasWidth, canvasHeight); // Create an appropriately sized but empty canvas image data object.
      
      globals.staticZoomBoxWidth = STATIC_ZOOM_BOX_FACTOR * canvasWidth; // Maintains the original canvas width/height ratio.
      globals.staticZoomBoxHeight = STATIC_ZOOM_BOX_FACTOR * canvasHeight; // Maintains the original canvas width/height ratio.      
      
      globals.pointer = {};
      globals.pointer.down = false;  
                 
      window.addEventListener('hashchange', handleHashChange, false); // This event handler executes whenever the URL hash string changes.
      
      canvas.addEventListener('mousedown', handlePointer, false);
      canvas.addEventListener('mousemove', handlePointer, false);
      canvas.addEventListener('mouseup', handlePointer, false);    
            
      document.getElementById('resetButton').addEventListener('click', handleResetButton, false);
      document.getElementById('lightenButton').addEventListener('click', handleLightenButton, false);    
      document.getElementById('saveButton').addEventListener('click', handleSaveButton, false);        
      document.getElementById('filenameForm').addEventListener('submit', handleFormSubmit, false);    
      
      ctx.fillStyle = "rgba(255, 0, 0, 0.3)"; // The color and opacity of the zoom box. This is what gets saved when calling ctx.save().          
 
      handleHashChange();
    } // handleLoad
    
    /*----------------------------------------------------------------------------------------------------------------------------------------------------------*/    
    
    function handleHashChange() {
      var hashValues = getHashValues(); // This function examines window.location.hash but doesn't change it.
      
      if (hashValues) {
        globals.ReMax = hashValues.ReMax;
        globals.ReMin = hashValues.ReMin;
        globals.ImMax = hashValues.ImMax;
        globals.ImMin = hashValues.ImMin;
        globals.grayscaleFactor = hashValues.grayscaleFactor;
      }
      else {
        globals.ReMax = adjusted_RE_MAX();
        globals.ReMin = RE_MIN;
        globals.ImMax = IM_MAX;
        globals.ImMin = IM_MIN;     
        globals.grayscaleFactor = 1; // Multiplying any value by 1 has no effect.
      } // if-else
      
      drawMandelbrot(globals.ReMax, globals.ReMin, globals.ImMax, globals.ImMin, globals.grayscaleFactor);
    } // handelHashChange    

    /*----------------------------------------------------------------------------------------------------------------------------------------------------------*/        

    function getHashValues() {
      var dirtyComplexPlaneExtremaString = (window.location.hash).replace('#', ''); // Remove the leading "#" character from the string.
      var complexPlaneExtremaString = dirtyComplexPlaneExtremaString.split(','); // Returns an array. Assumes the following string form: "ReMax,ReMin,ImMax,ImMin,grayscaleFactor" (note that if grayscaleFactor is 1, the image's grayscale is not affected).
      
      var ReMax = parseFloat( complexPlaneExtremaString[0] ); 
      var ReMin = parseFloat( complexPlaneExtremaString[1] ); 
      var ImMax = parseFloat( complexPlaneExtremaString[2] ); 
      var ImMin = parseFloat( complexPlaneExtremaString[3] );
      var grayscaleFactor = parseFloat( complexPlaneExtremaString[4] );
      
      if ( isNaN(ReMax) || isNaN(ReMin) || isNaN(ImMax) || isNaN(ImMin) || isNaN(grayscaleFactor) ) { 
        return null;
      } // if 
      
      return {ReMax: ReMax, ReMin: ReMin, ImMax: ImMax, ImMin: ImMin, grayscaleFactor: grayscaleFactor};
    } // getHashValues
        
    /*----------------------------------------------------------------------------------------------------------------------------------------------------------*/        

    function adjusted_RE_MAX() {    
      var ReMax = globals.canvas.width * ( (IM_MAX - IM_MIN) / globals.canvas.height ) + RE_MIN;
      
      if (RE_MAX != ReMax) {
        alert("RE_MAX has been adjusted to: " + ReMax); // The user should never see this if RE_MAX is set correctly above.
      } // if

      return ReMax;
    } // adjusted_RE_MAX    
    
    /*----------------------------------------------------------------------------------------------------------------------------------------------------------*/    
    
    function drawMandelbrot(ReMax, ReMin, ImMax, ImMin, grayscaleFactor) {            
      document.getElementById('messageBox').innerHTML = "Calculating..."; // This isn't displayed until the drawMandelbrot function block exits. 
      document.getElementById('elapsedTime').innerHTML = ""; // Erase the prior run's statistics.           
      
      if (window.setImmediate) {
        window.setImmediate(calculateMandelbrot); // Allow the drawMandelbrot function to immediately terminate, thus printing "Calculating..." to the screen.       
      }
      else {
        window.setTimeout(calculateMandelbrot, 0); // Allow the drawMandelbrot function to immediately terminate, thus printing "Calculating..." to the screen.      
      }           
      
      function calculateMandelbrot() {
        var startTime = new Date(); // Report how long it takes to render this particular region of the Mandelbrot set.             
        
        var canvas = globals.canvas;
        var canvasWidth = canvas.width;
        var canvasHeight = canvas.height;
        var ctx = canvas.context;
        var imageDataObjectData = ctx.imageDataObject.data; // imageDataObjectData is a reference to, not a copy of, ctx.imageDataObject.data
        
        var maxPixelGrayscaleValue = 0; // This will contain the lightest shade of gray in the drawn Mandelbrot image.
        
        var x_coefficient = (ReMax - ReMin) / canvasWidth; // Keep the below loops as computation-free as possible.
        var y_coefficient = (ImMin - ImMax) / canvasHeight; // Keep the below loops as computation-free as possible.
  
        var iterationSum = 0;
        var currentPixel = 0;          
        for (var y = 0; y < canvasHeight; y++) {
          var c_Im = (y * y_coefficient) + ImMax; // Note that c = c_Re + c_Im*i
          
          for (var x = 0; x < canvasWidth; x++) {
            var c_Re = (x * x_coefficient) + ReMin // Convert the canvas x-coordinate to a complex plane Re-coordinate. c_Re represents the real part of a c value.
            
            var z_Re = 0; // The first z value (Zo) must be 0.
            var z_Im = 0; // The first z value (Zo) must be 0. Note that z = z_Re + z_Im*i
            
            var c_belongsToMandelbrotSet = true; // Assume that the c associated with Zn belongs to the Mandelbrot set (i.e., Zn remains bounded under iteration of Zn+1 = (Zn)^2 + c).
            var exponentialSmoothingSum = 0;
            for (var iterationCount = 1; iterationCount <= MAX_ITERATIONS; iterationCount++) {
              iterationSum++; // Keep track of how many iterations were performed in total so we can report this to the user.
            
              var z_Re_squared = z_Re * z_Re; // A small speed optimization.
              var z_Im_squared = z_Im * z_Im; // A small speed optimization.
              
              exponentialSmoothingSum += Math.exp( -(z_Re_squared + z_Im_squared) ); // Technically, this should be e^(-|z|). However, avoiding the expensive square root operation doesn't really affect the resulting image.              
              if (exponentialSmoothingSum >= 255) { // Don't cycle through the gray colors.
                exponentialSmoothingSum = 255;
              }
      
              if (z_Re_squared + z_Im_squared > 4) { // Checks if |z^2| is greater than 2. This approach avoids the expensive square root operation.
                c_belongsToMandelbrotSet = false; // This complex c value is not part of the Mandelbrot set (because it will always tend towards infinity under iteration).
                break; // Immediately check the next c value to see if it belongs to the Mandelbrot set or not.
              } // if
              
              // The next two lines perform Zn+1 = (Zn)^2 + c (recall that (x + yi)^2 = x^2 - y^2 + 2xyi, thus the real part is x^2 - y^2 and the imaginary part is 2xyi).
              z_Im = (2 * z_Re * z_Im) + c_Im; // We must calculate the next value of z_Im first because it depends on the current value of z_Re (not the next value of z_Re).
              z_Re = z_Re_squared - z_Im_squared + c_Re; // Calculate the next value of z_Re.
            } // for   
            
            if (c_belongsToMandelbrotSet) { // This complex c value is probably part of the Mandelbrot set because Zn did not tend toward infinity within MAX_ITERATIONS iterations.
              imageDataObjectData[currentPixel++] = 0; // Red. Note that there are 255 possible shades of red, green, blue, and alpha (i.e., opacity).
              imageDataObjectData[currentPixel++] = 0; // Green.
              imageDataObjectData[currentPixel++] = 0; // Blue.
              imageDataObjectData[currentPixel++] = 255; // Alpha (i.e., 0% transparency).
            } 
            else { // This complex c value is definitely not part of the Mandelbrot set because Zn would tend toward infinity under iteration (i.e., |Zn| > 2).
              var pixelGrayscaleValue = 255 - exponentialSmoothingSum % 256; // Force the value of exponentialSmoothingSum to be between 0 and 255 inclusively. Note that all values for red, green, and blue are identical when using a grayscale.
              var adjustedPixelGrayscaleValue = pixelGrayscaleValue * grayscaleFactor; // Avoids doing this more than once.
              
              imageDataObjectData[currentPixel++] = adjustedPixelGrayscaleValue; // Because we mod by 256, the value of exponentialSmoothingSum will always be between 0 and 255.
              imageDataObjectData[currentPixel++] = adjustedPixelGrayscaleValue; // If exponentialSmoothingSum is 255 (it's maximum possible value), then 255 % 256 = 255.
              imageDataObjectData[currentPixel++] = adjustedPixelGrayscaleValue; // When exponentialSmoothingSum is 255, we have 255 - 255 = 0, so the shade values for RGB are all set to 0 (that is, the c-value pixel is rendered black - indicating that this particular c-value very slowly tends towards infinity).
              imageDataObjectData[currentPixel++] = 255; // Always draw the c-value pixels with no transparency.
              
              if (pixelGrayscaleValue > maxPixelGrayscaleValue) {
                maxPixelGrayscaleValue = pixelGrayscaleValue; // Determine the lightest shade of gray in case the user clicks the Lighten button.
              } // if
            } // if-else
          } // for
        } // for        
        
        globals.maxPixelGrayscaleValue = maxPixelGrayscaleValue; // Store the lightest shade of gray in case the user clicks the Lighten button.      
        ctx.putImageData(ctx.imageDataObject, 0, 0); // Render our carefully constructed canvas image data array to the canvas.
            
        var elapsedMilliseconds = (new Date()) - startTime;
        document.getElementById('elapsedTime').innerHTML = iterationSum.format() + " iterations in " + (elapsedMilliseconds / 1000).toFixed(2) + " seconds"; // Note that the UI element is not updated until after this block terminates (which is the desired behavior).            
        document.getElementById('messageBox').innerHTML = DEFAULT_MESSAGE; // Erase the "Calculating..." message and replace it with the default message.        
      } // calculateMandelbrot
    } // drawMandelbrot
    
    /*----------------------------------------------------------------------------------------------------------------------------------------------------------*/
    
    function xToRe(x) {
      var x_coefficient = (globals.ReMax - globals.ReMin) / globals.canvas.width; 
      
      return (x * x_coefficient) + globals.ReMin; // Converts a canvas x-coordinate value to the associated complex plane Re-coordinate.
    } // xToRe
    
    /*----------------------------------------------------------------------------------------------------------------------------------------------------------*/    

    function yToIm(y) {
      var y_coefficient = (globals.ImMin - globals.ImMax) / globals.canvas.height; 
      
      return (y * y_coefficient) + globals.ImMax; // Converts a canvas y-coordinate value to the associated complex plane Im-coordinate.
    } // yToIm
    
    /*----------------------------------------------------------------------------------------------------------------------------------------------------------*/

    function handlePointer(evt) {
      var canvasWidthHeightRatio = globals.canvas.width / globals.canvas.height;
      var ctx = globals.canvas.context;
      
      var canvasX;
      var canvasY;      
      
      if (evt.offsetX && evt.offsetY) {
        canvasX = evt.offsetX; // Not supported in Firefox.
        canvasY = evt.offsetY; // Does not assume that the canvas element is a direct descendent of the body element.
      } else {
        canvasX = evt.clientX - evt.target.offsetLeft; // Supported in Firefox.
        canvasY = evt.clientY - evt.target.offsetTop; // Assumes that the canvas element is a direct descendent of the body element.
      } // if-else
      
      var zoomBoxWidth;
      var zoomBoxHeight;
      
      var ReMax;
      var ReMin;
      var ImMax;
      var ImMin;
      
      var staticZoomBoxWidth = globals.staticZoomBoxWidth;
      var staticZoomBoxHeight = globals.staticZoomBoxHeight;
      var halfStaticZoomBoxWidth = staticZoomBoxWidth / 2;xx
      var halfStaticZoomBoxHeight = staticZoomBoxHeight / 2;
      
      switch (evt.type) {
        case 'mousedown':
          globals.pointer.down = true;      
          globals.pointer.x1 = canvasX;
          globals.pointer.y1 = canvasY;
          break;
        case 'mousemove':
          if (globals.pointer.down) {
            zoomBoxHeight = Math.abs(canvasY - globals.pointer.y1);  
            zoomBoxWidth = zoomBoxHeight * canvasWidthHeightRatio; // We must keep the zoom box dimensions proportional to the canvas dimensions in order to ensure that the resulting zoomed Mandelbrot image does not become skewed.
            ctx.putImageData(ctx.imageDataObject, 0, 0); // Assumes that an initial image of the Mandelbrot set is drawn before we get to this point in the code. The purpose of this line is to erase the prior zoom box rectangle before drawing the next zoom box rectangle.
            ctx.fillRect(globals.pointer.x1, globals.pointer.y1, zoomBoxWidth, zoomBoxHeight); // With a freshly painted image of the current Mandelbrot set in place (see prior line), draw a new zoom box rectangle.
          }
          break;
        case 'mouseup':
          globals.pointer.down = false;          
          
          zoomBoxHeight = Math.abs(canvasY - globals.pointer.y1); // Only allow the zoom box to be drawn from an upper-left corner position down to a lower-right corner position.
          zoomBoxWidth = zoomBoxHeight * canvasWidthHeightRatio; // Again, ensure that the width/height ratio of the zoom box is proportional to the canvas's (this simplifies the algorithm).          
          
          if (zoomBoxHeight == 0) { // No zoom box has been drawn, so honor the fixed sized zoom box.          
            ctx.fillRect(canvasX - halfStaticZoomBoxWidth, canvasY - halfStaticZoomBoxHeight, staticZoomBoxWidth, staticZoomBoxHeight); // Just leave this on the screen.
                         
            ReMin = xToRe(canvasX - halfStaticZoomBoxWidth); // Center the static zoom box about the point (evt.offsetX, evt.offsetY).
            ImMax = yToIm(canvasY - halfStaticZoomBoxHeight); 
            
            ReMax = xToRe(canvasX + halfStaticZoomBoxWidth);
            ImMin = yToIm(canvasY + halfStaticZoomBoxHeight);
          } 
          else { // A (possibly tiny) zoom box has been drawn, so honor it.
            ReMin = xToRe(globals.pointer.x1); // Convert the mouse's x-coordinate value (on the canvas) to the associated Re-coordinate value in the complex plane.
            ImMax = yToIm(globals.pointer.y1); // Convert the mouse's y-coordinate value (on the canvas) to the associated Im-coordinate value in the complex plane.
                                      
            ReMax = xToRe(zoomBoxWidth + globals.pointer.x1); // Convert the zoom box's final x-coordinate value to the associated Re-coordinate value in the complex plane.  
            ImMin = yToIm(zoomBoxHeight + globals.pointer.y1);  // Convert the zoom box's final y-coordinate value to the associated Re-coordinate value in the complex plane.            
          } // if-else        
        
          window.location.hash = ReMax + "," + ReMin + "," + ImMax + "," + ImMin + "," + globals.grayscaleFactor; // This triggers the handleHashChange event handler which, among other things, is responsible for drawing the Mandelbrot set.
          break; 
        default:
          alert("Error in switch statement."); // Although unnecessary, defensive programming techniques such as this are highly recommended.
      } // switch              
    } // handlePointer    
    
    /*----------------------------------------------------------------------------------------------------------------------------------------------------------*/
    
    function handleResetButton() {
      window.location.hash = adjusted_RE_MAX() + "," + RE_MIN + "," + IM_MAX + "," + IM_MIN + "," + 1; // // This triggers the handleHashChange event handler which, among other things, is responsible for drawing the Mandelbrot set.
    } // handleResetButton
    
    /*----------------------------------------------------------------------------------------------------------------------------------------------------------*/
    
    function handleLightenButton() {
    /* 
      This multiplies by a value (factor) such that black (0) stays black and the lightest gray value in the image becomes white (255). Thus, clicking the 
      Lighten button removes much of the mathematical meaning of the (proper) grayscale but can make "dark" images more visible.
    */
      var grayscaleFactor = 255 / globals.maxPixelGrayscaleValue; // For the canvas element, 255 is white, 0 is black.

      window.location.hash = globals.ReMax + "," + globals.ReMin + "," + globals.ImMax + "," + globals.ImMin + "," + grayscaleFactor; // This invokes handleHashChange which, among other things, is responsibile for drawing the Mandelbrot set.
    } // handleResetButton
    
    /*----------------------------------------------------------------------------------------------------------------------------------------------------------*/

    function handleSaveButton() {
      document.getElementById('filenameForm').style.visibility = "visible";
      document.getElementById('filename').focus(); // Place the cursor in the filename text input box.
    } // handleResetButton 
 
    /*----------------------------------------------------------------------------------------------------------------------------------------------------------*/

    function handleFormSubmit(evt) {
      alert("handleFormSubmit fired.");    
      evt.preventDefault(); // Do not refresh the page when the submit button is clicked.
      document.getElementById('filenameForm').style.visibility = "hidden";
    } // handleFormSubmit
  </script>
</body>

</html>

La principale différence entre Mandelbrot 4 et Mandelbrot 5 est que le gestionnaire d’événements handleHashChange (qui est appelé chaque fois que l’URL de la page change) déclenche le dessin de l’ensemble de Mandelbrot :


function handleHashChange() {
  var hashValues = getHashValues(); // This function examines window.location.hash but doesn't change it.
  
  if (hashValues) {
    globals.ReMax = hashValues.ReMax;
    globals.ReMin = hashValues.ReMin;
    globals.ImMax = hashValues.ImMax;
    globals.ImMin = hashValues.ImMin;
    globals.grayscaleFactor = hashValues.grayscaleFactor;
  }
  else {
    globals.ReMax = adjusted_RE_MAX();
    globals.ReMin = RE_MIN;
    globals.ImMax = IM_MAX;
    globals.ImMin = IM_MIN;     
    globals.grayscaleFactor = 1; // Multiplying any value by 1 has no effect.
  } // if-else
  
  drawMandelbrot(globals.ReMax, globals.ReMin, globals.ImMax, globals.ImMin, globals.grayscaleFactor);
} // handelHashChange

Ainsi, pour afficher une nouvelle image de l’ensemble de Mandelbrot, il nous suffit de modifier la chaîne de hachage de l’URL de la page en mettant à jour window.location.hash. Ceci se produit initialement quand le gestionnaire d’événements handleLoad appelle directement le gestionnaire d’événements handleHashChange (voir la dernière ligne) :


function handleLoad() {          
  var canvas = document.getElementsByTagName('canvas')[0];
  var canvasWidth = canvas.width;
  var canvasHeight = canvas.height;      
  var ctx = canvas.getContext('2d');
  
  document.getElementsByTagName('table')[0].width = canvasWidth;
  document.getElementById('messageBox').innerHTML = DEFAULT_MESSAGE;            

  globals.canvas = canvas;
  globals.canvas.context = ctx;
  globals.canvas.context.imageDataObject = ctx.createImageData(canvasWidth, canvasHeight);
  
  globals.staticZoomBoxWidth = STATIC_ZOOM_BOX_FACTOR * canvasWidth; 
  globals.staticZoomBoxHeight = STATIC_ZOOM_BOX_FACTOR * canvasHeight; 
  
  globals.pointer = {};
  globals.pointer.down = false;  
             
  window.addEventListener('hashchange', handleHashChange, false); // This event handler executes whenever the URL hash string changes.
  
  canvas.addEventListener('mousedown', handlePointer, false);
  canvas.addEventListener('mousemove', handlePointer, false);
  canvas.addEventListener('mouseup', handlePointer, false);    
        
  document.getElementById('resetButton').addEventListener('click', handleResetButton, false);
  document.getElementById('lightenButton').addEventListener('click', handleLightenButton, false);    
  document.getElementById('saveButton').addEventListener('click', handleSaveButton, false);        
  document.getElementById('filenameForm').addEventListener('submit', handleFormSubmit, false);    
  
  ctx.fillStyle = "rgba(255, 0, 0, 0.3)";

  handleHashChange(); // On page load, simulate a page URL change to draw the initial Mandelbrot set.
} // handleLoad

La fonction getHashValues est utilisée pour convertir la chaîne de hachage actuelle en valeurs numériques utilisables :


function getHashValues() {
  var dirtyComplexPlaneExtremaString = (window.location.hash).replace('#', ''); // Remove the leading "#" character from the string.
  var complexPlaneExtremaString = dirtyComplexPlaneExtremaString.split(','); // Returns an array. Assumes the following string form: "ReMax,ReMin,ImMax,ImMin,grayscaleFactor" (note that if grayscaleFactor is 1, the image's grayscale is not effected).
  
  var ReMax = parseFloat( complexPlaneExtremaString[0] ); 
  var ReMin = parseFloat( complexPlaneExtremaString[1] ); 
  var ImMax = parseFloat( complexPlaneExtremaString[2] ); 
  var ImMin = parseFloat( complexPlaneExtremaString[3] );
  var grayscaleFactor = parseFloat( complexPlaneExtremaString[4] );
  
  if ( isNaN(ReMax) || isNaN(ReMin) || isNaN(ImMax) || isNaN(ImMin) || isNaN(grayscaleFactor) ) { 
    return null;
  } // if 
  
  return {ReMax: ReMax, ReMin: ReMin, ImMax: ImMax, ImMin: ImMin, grayscaleFactor: grayscaleFactor};
} // getHashValues

La première étape consiste à supprimer le caractère de tête « # » de la chaîne de hachage : Ensuite, en supposant que les extrêmes du plan complexe sont de la forme « ReMax,ReMin,ImMax,ImMin,grayscaleFactor », nous les fractionnons en un tableau et les convertissons en valeurs numériques à l’aide de parseFloat.

Si l’une des valeurs attendues est manquante ou mal formée, la valeur null est renvoyée. Sinon, un littéral d’objet contenant les extrêmes du plan complexe est renvoyé.

Le gestionnaire d’événements handlePointer est presque identique au précédent, hormis que :


setExtrema(ReMax, ReMin, ImMax, ImMin); // Must set these globals prior to calling drawMandelbort because drawMandelbort accesses them.
if (window.setImmediate) {
  window.setImmediate(drawMandelbrot);
}
else {
  window.setTimeout(drawMandelbrot, 0);
}

a été remplacé par :


window.location.hash = ReMax + "," + ReMin + "," + ImMax + "," + ImMin + "," + globals.grayscaleFactor;

Comme vous l’aurez peut-être deviné, les méthodes setImmediate/setTimeout ont été déplacées vers la fonction drawMandelbrot :


function drawMandelbrot(ReMax, ReMin, ImMax, ImMin, grayscaleFactor) {            
  document.getElementById('messageBox').innerHTML = "Calculating..."; // This isn't displayed until the drawMandelbrot function block exits. 
  document.getElementById('elapsedTime').innerHTML = ""; // Erase the prior run's statistics.           
  
  if (window.setImmediate) {
    window.setImmediate(calculateMandelbrot); // Allow the drawMandelbrot function to immediately terminate, thus printing "Calculating..." to the screen.       
  }
  else {
    window.setTimeout(calculateMandelbrot, 0); // Allow the drawMandelbrot function to immediately terminate, thus printing "Calculating..." to the screen.      
  }           
  
  function calculateMandelbrot() {
    var startTime = new Date(); // Report how long it takes to render this particular region of the Mandelbrot set.             
    
    var canvas = globals.canvas;
    var canvasWidth = canvas.width;
    var canvasHeight = canvas.height;
    var ctx = canvas.context;
    var imageDataObjectData = ctx.imageDataObject.data; // imageDataObjectData is a reference to, not a copy of, ctx.imageDataObject.data
    
    var maxPixelGrayscaleValue = 0; // This will contain the lightest shade of gray in the drawn Mandelbrot image.
    
    var x_coefficient = (ReMax - ReMin) / canvasWidth; // Keep the below loops as computation-free as possible.
    var y_coefficient = (ImMin - ImMax) / canvasHeight; // Keep the below loops as computation-free as possible.

    var iterationSum = 0;
    var currentPixel = 0;          
    for (var y = 0; y < canvasHeight; y++) {
      var c_Im = (y * y_coefficient) + ImMax; // Note that c = c_Re + c_Im*i
      
      for (var x = 0; x < canvasWidth; x++) {
        var c_Re = (x * x_coefficient) + ReMin // Convert the canvas x-coordinate to a complex plane Re-coordinate. c_Re represents the real part of a c value.
        
        var z_Re = 0; // The first z value (Zo) must be 0.
        var z_Im = 0; // The first z value (Zo) must be 0. Note that z = z_Re + z_Im*i
        
        var c_belongsToMandelbrotSet = true; // Assume that the c associated with Zn belongs to the Mandelbrot set (i.e., Zn remains bounded under iteration of Zn+1 = (Zn)^2 + c).
        var exponentialSmoothingSum = 0;
        for (var iterationCount = 1; iterationCount <= MAX_ITERATIONS; iterationCount++) {
          iterationSum++; // Keep track of how many iterations were performed in total so we can report this to the user.
        
          var z_Re_squared = z_Re * z_Re; // A small speed optimization.
          var z_Im_squared = z_Im * z_Im; // A small speed optimization.
          
          exponentialSmoothingSum += Math.exp( -(z_Re_squared + z_Im_squared) ); // Technically, this should be e^(-|z|). However, avoiding the expensive square root operation doesn't really affect the resulting image.              
          if (exponentialSmoothingSum >= 255) { // Don't cycle through the gray colors.
            exponentialSmoothingSum = 255;
          }
  
          if (z_Re_squared + z_Im_squared > 4) { // Checks if |z^2| is greater than 2. This approach avoids the expensive square root operation.
            c_belongsToMandelbrotSet = false; // This complex c value is not part of the Mandelbrot set (because it will always tend towards infinity under iteration).
            break; // Immediately check the next c value to see if it belongs to the Mandelbrot set or not.
          } // if
          
          // The next two lines perform Zn+1 = (Zn)^2 + c (recall that (x + yi)^2 = x^2 - y^2 + 2xyi, thus the real part is x^2 - y^2 and the imaginary part is 2xyi).
          z_Im = (2 * z_Re * z_Im) + c_Im; // We must calculate the next value of z_Im first because it depends on the current value of z_Re (not the next value of z_Re).
          z_Re = z_Re_squared - z_Im_squared + c_Re; // Calculate the next value of z_Re.
        } // for   
        
        if (c_belongsToMandelbrotSet) { // This complex c value is probably part of the Mandelbrot set because Zn did not tend toward infinity within MAX_ITERATIONS iterations.
          imageDataObjectData[currentPixel++] = 0; // Red. Note that there are 255 possible shades of red, green, blue, and alpha (i.e., opacity).
          imageDataObjectData[currentPixel++] = 0; // Green.
          imageDataObjectData[currentPixel++] = 0; // Blue.
          imageDataObjectData[currentPixel++] = 255; // Alpha (i.e., 0% transparency).
        } 
        else { // This complex c value is definitely not part of the Mandelbrot set because Zn would tend toward infinity under iteration (i.e., |Zn| > 2).
          var pixelGrayscaleValue = 255 - exponentialSmoothingSum % 256; // Force the value of exponentialSmoothingSum to be between 0 and 255 inclusively. Note that all values for red, green, and blue are identical when using a grayscale.
          var adjustedPixelGrayscaleValue = pixelGrayscaleValue * grayscaleFactor; // Avoids doing this more than once.
          
          imageDataObjectData[currentPixel++] = adjustedPixelGrayscaleValue; // Because we mod by 256, the value of exponentialSmoothingSum will always be between 0 and 255.
          imageDataObjectData[currentPixel++] = adjustedPixelGrayscaleValue; // If exponentialSmoothingSum is 255 (its maximum possible value), then 255 % 256 = 255.
          imageDataObjectData[currentPixel++] = adjustedPixelGrayscaleValue; // When exponentialSmoothingSum is 255, we have 255 - 255 = 0, so the shade values for RGB are all set to 0 (that is, the c-value pixel is rendered black - indicating that this particular c-value very slowly tends towards infinity).
          imageDataObjectData[currentPixel++] = 255; // Always draw the c-value pixels with no transparency.
          
          if (pixelGrayscaleValue > maxPixelGrayscaleValue) {
            maxPixelGrayscaleValue = pixelGrayscaleValue; // Determine the lightest shade of gray in case the user clicks the Lighten button.
          } // if
        } // if-else
      } // for
    } // for        
    
    globals.maxPixelGrayscaleValue = maxPixelGrayscaleValue; // Store the lightest shade of gray in case the user clicks the Lighten button.      
    ctx.putImageData(ctx.imageDataObject, 0, 0); // Render our carefully constructed canvas image data array to the canvas.
        
    var elapsedMilliseconds = (new Date()) - startTime;
    document.getElementById('elapsedTime').innerHTML = iterationSum.format() + " iterations in " + (elapsedMilliseconds / 1000).toFixed(2) + " seconds"; // Note that the UI element is not updated until after this block terminates (which is the desired behavior).            
    document.getElementById('messageBox').innerHTML = DEFAULT_MESSAGE; // Erase the "Calculating..." message and replace it with the default message.        
  } // calculateMandelbrot
} // drawMandelbrot

Le principal changement apporté à la fonction drawMandelbrot est sa capacité à éclaircir une image en fonction de la valeur de son paramètre grayscaleFactor :


function drawMandelbrot(ReMax, ReMin, ImMax, ImMin, grayscaleFactor) {
  .
  .
  .        
        if (c_belongsToMandelbrotSet) {
          imageDataObjectData[currentPixel++] = 0;
          imageDataObjectData[currentPixel++] = 0;
          imageDataObjectData[currentPixel++] = 0;
          imageDataObjectData[currentPixel++] = 255;
        } 
        else {
          var pixelGrayscaleValue = 255 - exponentialSmoothingSum % 256;green, and blue are identical when using a grayscale.
          var adjustedPixelGrayscaleValue = pixelGrayscaleValue * grayscaleFactor; 
          
          imageDataObjectData[currentPixel++] = adjustedPixelGrayscaleValue; // Because we mod by 256, the value of exponentialSmoothingSum will always be between 0 and 255.
          imageDataObjectData[currentPixel++] = adjustedPixelGrayscaleValue; // If exponentialSmoothingSum is 255 (its maximum possible value), then 255 % 256 = 255.
          imageDataObjectData[currentPixel++] = adjustedPixelGrayscaleValue; // When exponentialSmoothingSum is 255, we have 255 - 255 = 0, so the shade values for RGB are all set to 0 (that is, the c-value pixel is rendered black - indicating that this particular c-value very slowly tends towards infinity).
          imageDataObjectData[currentPixel++] = 255;
          
          if (pixelGrayscaleValue > maxPixelGrayscaleValue) {
            maxPixelGrayscaleValue = pixelGrayscaleValue; // Determine the lightest shade of gray in case the user clicks the Lighten button.
          }
  .
  .
  . 
      
    globals.maxPixelGrayscaleValue = maxPixelGrayscaleValue; // Store the lightest shade of gray in case the user clicks the Lighten button.      
    ctx.putImageData(ctx.imageDataObject, 0, 0); // Render our carefully constructed canvas image data array to the canvas.
  .
  .
  . 


Comme vous pouvez le constater sur la ligne var adjustedPixelGrayscaleValue = pixelGrayscaleValue * grayscaleFactor, le paramètre grayscaleFactor est multiplié par la valeur de nuance de gris du pixel actuel (pixelGrayscaleValue). Cette valeur de nuance de gris ajustée (adjustedPixelGrayscaleValue) est ensuite utilisée pour définir le tableau imageDataObjectData comme illustré dans l’exemple de code précédent.

Lorsqu’une image est calculée, la valeur de nuance de gris la plus claire (maximale) est déterminée et enregistrée dans une variable globale :


globals.maxPixelGrayscaleValue = maxPixelGrayscaleValue;

Quand l’utilisateur clique sur le bouton Lighten, la nuance de gris la plus claire pour l’image actuelle est déjà connue et une version plus claire de l’image est dessinée comme suit :


function handleLightenButton() {
  var grayscaleFactor = 255 / globals.maxPixelGrayscaleValue; // For the canvas element, 255 is white, 0 is black.

  window.location.hash = globals.ReMax + "," + globals.ReMin + "," + globals.ImMax + "," + globals.ImMin + "," + grayscaleFactor; // This invokes handleHashChange which, among other things, is responsibile for drawing the Mandelbrot set.
}

Autrement dit, lorsque handleLightenButton exécute la ligne :


window.location.hash = globals.ReMax + "," + globals.ReMin + "," + globals.ImMax + "," + globals.ImMin + "," + grayscaleFactor

la valeur (grayscaleFactor) passée à la fonction drawMandelbrot (via la chaîne de hachage d’URL) est telle que noir (0) reste noir et que la valeur de nuance de gris la plus claire (maximale) dans l’image devient blanche (255).

Considérez l’image sombre suivante et son URL :

Une zone sombre de l’ensemble de Mandelbrot (avant une pression sur le bouton Lighten)

http://samples.msdn.microsoft.com/Workshop/samples/mandelbrot/mandelbrotExplorer.html#-0.7521294801871914,-0.7521614447995544,0.03795943464882932,0.037938124907254026,1

Le caractère de fin « 1 » dans l’URL est le grayscaleFactor pour cette image (une valeur de 1 n’a aucun effet d’éclaircissement, car la multiplication par 1 d’une valeur réelle n’a aucun effet).

Quand l’utilisateur clique sur le bouton Lighten, la valeur de nuance de gris la plus claire est utilisée pour produire un grayscaleFactor d’environ 3,0386 :

La zone sombre de l’ensemble de Mandelbrot après une pression sur le bouton Lighten

http://samples.msdn.microsoft.com/Workshop/samples/mandelbrot/mandelbrotExplorer.html#-0.7521294801871914,-0.7521614447995544,0.03795943464882932,0.037938124907254026,3.03862433470554

Cette valeur (3,0386) est multipliée par la valeur de nuance de gris de chaque pixel de la première image, ce qui génère la seconde image éclaircie.

Soit dit en passant, comme grayscaleFactor = 255 / globals.maxPixelGrayscaleValue, il en résulte que la valeur de nuance de gris la plus claire (maximale) dans l’image sombre est d’environ 84 :

L’équation grayScaleFactor

Ainsi, la valeur de nuance de gris la plus claire devient blanche dans l’image éclaircie, comme suit :

Équation de 84 fois 3,0386 (ce qui correspond à environ 255)

Sachez que les pixels noirs (0) restent noirs car zéro multiplié par un nombre réel est toujours égal à zéro.

Maintenant que nous sommes en mesure de générer des images de qualité de l’ensemble de Mandelbrot, la fonctionnalité logique suivante à ajouter est la capacité à enregistrer des images localement. Cet aspect est discuté dans Enregistrement d’images de la zone de dessin localement.

Rubriques connexes

Enregistrement d’images de la zone de dessin localement

 

 

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