polynomial change of LED brightness arduino

Question

I try to change the brightness of an LED following the formular in out1. I'm pretty sure that something is going wrong because it doesn't really change its brightness and it never stops lightening. Can pleas somebody help me. It should basically do the same than a sin wave but instead of the sin I try to use my equation!

const int LED = 11;
const int LED1 = 10;
const int LED2 = 9;

void setup()
{
}

void loop()
{
float in1, out1, out2, out3;

for (in1 = 0; in1 < 10; in1++)
{
out1 = 8.8 * pow(10,-4) * pow(in1,4) - 0.0034 * pow(in1,3) +0.37* pow(in1,2) -6.7 *in1 +1.7 *pow(10,2);
//out2 = 1.207*pow(in1,4)-0.0011*pow(in1,3)+0.16*pow(in1,2)-5.5*in1+2,0763;
//out3 = 4.829*pow(in1,4)-0.034*pow(in1,3)+0.37*pow(in1,2)-6.7*in1+2,076;

analogWrite(LED,out1);
delay(10);
//analogWrite(LED1,out2);
//analogWrite(LED2,out3);

}

analogWrite(LED,LOW);

/*analogWrite(LED,out1);
analogWrite(LED1,out2);
analogWrite(LED2,out3);
//analogWrite(LED1,LOW);*/
delay(500);

Answer 1

Here is the proper way to implement a polynomial function. It's a direct application of Horner's method:

// Polynomial function for output 1.
static float f1(float x)
{
    return (((8.8e-4 * x - 0.0034) * x + 0.37) * x - 6.7) * x + 1.7e2;
}

You would use it like this:

void loop()
{
    for (int x = 0; x < 10; x++) {
        analogWrite(LED, f1(x));
        delay(10);
    }
    digitalWrite(LED, LOW);
    delay(500);
}

Answer 2

You should make sure that your code works with known good values for out1.

After dthat, try to make sure that your formula produce values in a valid range - check analogWrite to see what values it expects.

Then you should make sure that your code formula is what you want. Aka the code reflects your intent correctly.

edit: here is what I use to calculate polynomial functions.

//return poly functions
//x: independent variable
//degree: degree of the polynomial function
//p[]: array for the coefficients
double poly(double x, int degree, double p[]) {
  double tmp=0;  //temp variable

  while (degree--) tmp = tmp * x + p[degree];

  return tmp;
}

by providing different "degree" and "p[]/coef", you can calculate any polynomial function with one call to poly().

I generally use a set of macros to further simplify the calling to that function.