Drawing Color Spectrum with Waveform

i've come across this ActionScript sample, which demonstrates drawing of the color spectrum, one line at a time via a loop, using waveforms.

however, the waveform location of each RGB channel create a color spectrum that is missing colors (pure yellow, cyan and magenta) and therefore the spectrum is incomplete.

how can i remedy this problem so that the drawn color spectrum will exhibit all colors?

// Loop through all of the pixels from '0' to the specified width.
for(var i:int = 0; i < nWidth; i++)
    {
    // Calculate the color percentage based on the current pixel.
    nColorPercent = i / nWidth;

    // Calculate the radians of the angle to use for rotating color values.
    nRadians = (-360 * nColorPercent) * (Math.PI / 180);

    // Calculate the RGB channels based on the angle.
    nR = Math.cos(nRadians)                   * 127 + 128 << 16;
    nG = Math.cos(nRadians + 2 * Math.PI / 3) * 127 + 128 << 8;
    nB = Math.cos(nRadians + 4 * Math.PI / 3) * 127 + 128;

    // OR the individual color channels together.
    nColor  = nR | nG | nB;
    }

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UPDATED SOLUTION

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for anyone interested, below is the solution i wrote to address the above problem. RGB waveforms are not used to create the full color spectrum. also, the code is flexible so you can assign your own size and color variables for the produced开发者_StackOverflow sprite. the color variables in this example are red, yellow, green, cyan, blue, magenta, red to produce the complete color spectrum

/*
//SpectrumGradient Object Call

var spectrum:SpectrumGradient = new SpectrumGradient(stage.stageWidth, stage.stageHeight, 0xFF0000, 0xFFFF00, 0x00FF00, 0x00FFFF, 0x0000FF, 0xFF00FF, 0xFF0000);
this.addChild(spectrum);
*/


package
{
    import flash.display.BitmapData;
    import flash.display.CapsStyle;
    import flash.display.GradientType;
    import flash.display.LineScaleMode;
    import flash.display.Sprite;
    import flash.geom.Matrix;

    public class SpectrumGradient extends Sprite
        {
        public function SpectrumGradient(spriteWidth:Number, spriteHeight:Number, ...spriteColors)
            {
            //Setup spectrum sprite
            var spectrum:Sprite = new Sprite();
            var spectrumAlphas:Array = new Array();
            var spectrumRatios:Array = new Array();
            var spectrumPartition:Number = 255 / (spriteColors.length - 1);

            for (var pushLoop:int = 0; pushLoop < spriteColors.length; pushLoop++)
                {
                spectrumAlphas.push(1);
                spectrumRatios.push(pushLoop * spectrumPartition);
                }

            //Create spectrum sprite as evenly distributed linear gradient using supplied spriteColors
            var spectrumMatrix:Matrix = new Matrix();
            spectrumMatrix.createGradientBox(spriteWidth, spriteHeight);
            spectrum.graphics.lineStyle();
            spectrum.graphics.beginGradientFill(GradientType.LINEAR, spriteColors, spectrumAlphas, spectrumRatios, spectrumMatrix);
            spectrum.graphics.drawRect(0, 0, spriteWidth, 1);
            spectrum.graphics.endFill();

            //Assign bitmapData to the spectrum sprite
            var bitmapData:BitmapData = new BitmapData(spectrum.width, spectrum.height, true, 0);
            bitmapData.draw(spectrum);

            var pixelColor:Number;

            for (var i:int = 0; i < spriteWidth; i++)
                {
                //Retrieve the color number for each pixel of the spectrum sprite
                pixelColor = bitmapData.getPixel(i, 0);

                //Create new matrices for the white and black gradient lines
                var matrixWhite:Matrix = new Matrix();
                matrixWhite.createGradientBox(1, spriteHeight / 2, Math.PI * 0.5, 0, 0);
                var matrixBlack = new Matrix();
                matrixBlack.createGradientBox(1, spriteHeight / 2, Math.PI * 0.5, 0, spriteHeight / 2);

                //Each slice of the sprite is composed of two vertical lines:  the first fades from white to the pixelColor, the second fades from pixelColor to black
                graphics.lineStyle(1, 0, 1, false, LineScaleMode.NONE, CapsStyle.NONE);
                graphics.lineGradientStyle(GradientType.LINEAR, [0xFFFFFF, pixelColor], [100, 100], [0, 255], matrixWhite);
                graphics.moveTo(i, 0);
                graphics.lineTo(i, spriteHeight / 2);
                graphics.lineGradientStyle(GradientType.LINEAR, [pixelColor, 0], [100, 100], [0, 255], matrixBlack);
                graphics.moveTo(i, spriteHeight / 2);
                graphics.lineTo(i, spriteHeight);
                }

            }
        }
}

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you can't have all colors at once. all RGB colors, that's 256 x 256 x 256, so you'd need 4096 x 4096 pixels for showing all of them.

Also, there is no "natural"/sensible way of displaying them all. At least until now, nobody has come up with a 2 dimensional color space that really makes sense. For displaying colors, you'll always have to pick 2. That's why common color choosers either use a hue slider and a lightness/saturation plane or a hue/saturation plane and a lightness slider.

please also note that the first (rectangular) spectrum can be easily drawn with 2 superposed gradients. a horizontal one for the hue, and a vertical (semitransparent) for lightness. its faster and completely smooth (if you zoom you don't see the individual lines).

edit: here's a working example of how this can be achieved with a single gradient, which is preferable for obvious reasons:

package  {
    import flash.display.*;
    import flash.events.Event;
    import flash.events.MouseEvent;
    import flash.geom.Matrix;

    public class GradientTest extends Sprite {

        public function GradientTest() {
            var colors:Array = [0xFF0000, 0xFFFF00, 0x00FF00, 0x00FFFF, 0x0000FF, 0xFF00FF, 0xFF0000];
            var part:Number = 0xFF / (colors.length-1);
            var ratios:Array = [], alphas:Array = [];
            var m:Matrix = new Matrix();
            m.createGradientBox(500, 20);
            for (var i:int = 0; i < colors.length; i++) {
                ratios.push(part * i);
                alphas.push(100);
            }

            this.graphics.beginGradientFill(GradientType.LINEAR, colors, alphas, ratios, m);
            this.graphics.drawRect(0, 0, 500, 20);

            //just to get the RGB values under the mouse:
            var b:BitmapData = new BitmapData(this.width, this.height, true, 0);
            b.draw(this);
            stage.addEventListener(MouseEvent.MOUSE_MOVE, function (e:Event):void {
                if (hitTestPoint(mouseX, mouseY)) {
                    var s:String = b.getPixel(mouseX, mouseY).toString(16);
                    while (s.length < 6) s = "0" + s;
                    trace("#" + s);                 
                }
            });
        }   
    }
}

the approach using waveforms is a bit like a hammer in search of a nail. just because bit operations and trigonometry are great tools, doesn't mean you should prefer them to a solution that is much simpler.