Algorithm to trend towards a given number after n iterations

Question

I'm trying to find a good algorithm to accomplish the following:

I have two RGB colors. I start off with one color (say, red = 255, 0, 0) and after a number of iterations, I want it to turn blue (0, 0, 255).

My current algorithm simply takes the sum of each component of the color and divides by two, which does the trick but much too quickly. At each iteration, I want the the numbers to change by only 1 tenth of their original value. So iteration 1 might return the color (230, 0, 25) and so on. Keep in mind, the destination color can also change. so suddenly instead of blue, I want green.

Does anyone know of a good way to accomplish this? I can't seem to figure out the math.

Thank you!

Answer 1

There have been two posts about other color spaces and a linear approach already.

But if you are really looking for an algorithm that does exactly what you're asking for, check this out:

static class ColorChanger {
    static private final int    APPROACH_STEPS  = 10;

    private final Color         mStartColor;
    private final Color         mTargetColor;

    private int                 mApproachStep   = 0;
    private Color               mCurrentColor;

    public ColorChanger(final Color pStartColor, final Color pTargetColor) {
        mStartColor = pStartColor;
        mTargetColor = pTargetColor;
        System.out.println("\nStarting color is: " + mStartColor);
        System.out.println("Approaching target 1: " + mTargetColor);
    }

    public Color approach() {
        ++mApproachStep;
        if (mApproachStep <= APPROACH_STEPS) { // dont overshoot target color. could throw an exception here too
            final int newRedCode = nextColorCode(mStartColor.getRed(), mTargetColor.getRed());
            final int newGreenCode = nextColorCode(mStartColor.getGreen(), mTargetColor.getGreen());
            final int newBlueCode = nextColorCode(mStartColor.getBlue(), mTargetColor.getBlue());
            mCurrentColor = new Color(newRedCode, newGreenCode, newBlueCode);
        }
        System.out.println("\tNew step color is: " + mCurrentColor);
        return mCurrentColor;
    }

    private int nextColorCode(final int pCurrentCode, final int pTargetCode) {
        final int diff = pTargetCode - pCurrentCode;
        final int newCode = pCurrentCode + diff * mApproachStep / APPROACH_STEPS;
        return newCode;
    }

    public Color getCurrentColor() {
        return mCurrentColor;
    }

    public boolean isTargetColor() {
        return mApproachStep == APPROACH_STEPS;
    }
}

public static void main(final String[] args) {
    final Color startColor = Color.RED;
    final Color targetColor1 = Color.GREEN;
    final Color targetColor2 = Color.BLUE;
    final Color targetColor3 = Color.RED;

    // approach in only 5 steps, will by far not reach target color
    final ColorChanger cc1 = new ColorChanger(startColor, targetColor1);
    for (int i = 0; i < 5; i++) {
        cc1.approach();
    }

    // full approach #1
    final ColorChanger cc2 = new ColorChanger(cc1.getCurrentColor(), targetColor2);
    while (!cc2.isTargetColor()) {
        cc2.approach();
    }

    // full approach #2
    final ColorChanger cc3 = new ColorChanger(cc2.getCurrentColor(), targetColor3);
    for (int i = 0; i < ColorChanger.APPROACH_STEPS; i++) {
        cc3.approach();
    }

    System.out.println("Program ends");
}