我的对数螺旋函数无法正确计算

Question

I wasn't so sure where to ask this question (between math and here)

I try to draw Logarithmic Spiral using this formula

It works (well it show a spiral on screen) , but when i change the pitch (a) the spiral does not change his pitch , only rotation and size (and setting a to 1 should make a circle but it does not)

i tried thoses :

double step = (end - start) / sample;
        for (int i = 1;i <= sample;i++) {
            double t = start+i*step;
            coordinates[i-1][0] =  a * Math.pow(Math.E,b*t) * Math.cos(t);
            coordinates[i-1][1] = a * Math.pow(Math.E,b*t) * Math.sin(t);
}

(a and b are constant , start = -4*PI , end = 4*PI)

and

    double step = (end - start) / sample;
        for (int i = 1;i <= sample;i++) {
            double r = start+i*step;
        double t = (1/b)*Math.log(r/a);
            coordinates[i-1][0] = r* Math.cos(t);
            coordinates[i-1][1] = r* Math.sin(t);
}

(a and b are constant , start = 0 , end = 10)

I guessing I have made a big error in the formula but I don't see wich one. I can provide an output picture if that can help , but I don't see how

Edit: I did succed to make it work using r = a exp(θ cot b)

    double r = Math.pow(a,t*(1/Math.tan(b)));

But i still don't get why the other formula didn't work out , that's why i edited this question rather than answering it.

Answer 1

My guess would be that there's a rounding issue going on. I am assuming both 'a' and 'b' are doubles... I have to ask as it's not written in the code but assume this is the case. If not that'll be the problem :)

Next I'd look at i*step and ensure this is what you're expecting... I would have thought this is ok but you're not casting the int 'i' to a double so asking for problems if you reshuffle parts.

Ahhh, actually I'd want to look at is 'sample'. If this is an int as I'd expect this will give you the wrong result for step since you're dividing by an int which I expect will give an int return value... actually my 1p's bet is on it's sample declared as an int.

If that doesn't fix it, you can print out the step value and ensure it's what you're expecting, also check 't' is calculating correctly if it isn't this sample issue.