I put together some code for Bilinear interpolation.
The formula gave me a bit of a hard time, but eventually I got it to work. First I tried the formula from Wiki (link below) but it didn’t work for me. Then I tried to use the map() function, it was close but i want perfect. My issue with the map() function was that it seems to round down a little and i used it like this
int r1;
int r2;
int p;
r1=map(x, x1, x2, q11, q12)
r2=map(x, x1, x2, q21, q22)
p=map(y, y1, y2, r1, r2)
The idea is to sample 4 cell and and give the Quadrant names relative to their X Y values
q12 = Quadrant (1,2)
then you interpolate between them horizontally to get vitural points
r1 and r2
then you interpolate vertically along the y axis
Eventually I just broke the Wiki formula down into three bits like i did with the map function and it proved more accurate. Floating point values help also to prevent truncation (i believe this was my issue)
This is what the map function page says the math behind the map function is
long map(long x, long in_min, long in_max, long out_min, long out_max)
{
return (x - in_min) * (out_max - out_min) / (in_max - in_min) + out_min;
}
So here is my current issue that I am having a hard time overcoming. I want to compress my code a but and as always i would like to optimize it as much as possible. Custom functions are a nice neat way to make your code more readable to colleagues. I work with a team of 3 other people. Whats going on is how do i get the array into my custom function from the main loop. I tried a few times but just cant sort it out. I also google it and came to this web page which describes 3 methods. But they dont seem to work for me. Probably because i do not fully understand the description.
http://www.cplusplus.com/forum/articles/20881/
Here is my Code
/*Biliner Interpolation
*
*Code testing to search a table, find 4 cells that should be interpolated
*and actually interpolate them. Intended use is for a Electric boost control
*system to control the Waste Gate Duty of a solenoid.
*
* No Circuit
*
* Created 2/16/2017
* by George Katslas
*
*/
const byte a = 8; //The Size of the X axis
const byte b = 8; //The size of the Y axis
int xax [a] = {0, 500, 1000, 2000, 3000, 4000, 5000, 7000}; //X axis Data for testing
int yax [b] = {0, 10, 15, 20, 30, 35, 40, 45}; //Y axis Data for testing
int zdat [a] [b] = { //Z Data for testing
{70, 71, 72, 73, 74, 75, 76, 77},
{60, 61, 62, 63, 64, 65, 66, 67},
{50, 51, 52, 53, 54, 55, 56, 57},
{40, 41, 42, 43, 44, 45, 46, 47},
{30, 31, 32, 33, 34, 35, 36, 37},
{20, 21, 22, 23, 24, 25, 26, 27},
{10, 11, 12, 13, 14, 15, 16, 17},
{00, 01, 02, 03, 04, 05, 06, 07}
};
byte xmin = 0; //container for the X min
byte xmax = 0; //container for the X max
byte ymin = 0; //container for the Y min
byte ymax = 0; //container for the Y Max
void setup() {
Serial.begin(250000); //Open Serial Com
}
void loop() {
for (byte i = 0; i < a; i++) { //Prints the X axis
Serial.print(F("\t")); //Tab
Serial.print(xax[i]);
}
for (byte i = 0; i < b; i++) { //for the length of the y axis
Serial.println(); //print return
Serial.print(yax[i]); //print the Y Value
Serial.print(F("\t")); //Tab
for(byte j = 0; j < a; j++){ //For the legnth of the X axis
Serial.print(zdat[i] [j]); //Print the data
Serial.print(F("\t")); //Tab
}
}
Serial.println(); //Print a return
Serial.println(F("enter X val")); //Ask for X val
int input = getInput(); //Call custom function to read serial
int xin = input; //Store the input as X input
Serial.println(F("enter Y val")); //Ask for Y val
input = getInput(); //Call custom function to read serial input
int yin = input; //Store the input as Y input
//axis crawler I want to make this a custom function as its called twice
byte axisCell = 0; //variable to store the Cell Number 0 indexed!!
while(axisCell < a) { //wile the cell number is less than size of axis
if(xin > xax[axisCell]) axisCell++; //if X input is less than the value store in current cell then increment the cell number
else { //else
axisCell--;
if(axisCell < 0){ //if the cell number less than 0
xmin=0; //Xmin set 0
xmax=1; //Xmax set 1
}
else { //else
xmin=axisCell; //Xmin is Cell number
xmax=(axisCell+1); //Xmax is Cell number + 1
}
axisCell = 0; //Set the cell number to its default value
break; //break loop min max found
}
}
//axis crawler for the Y axis
while(axisCell < b) {
if(yin > yax[axisCell]) axisCell++;
else {
axisCell--;
if(axisCell < 0){
ymin=0;
ymax=1;
}
else {
ymin=axisCell;
ymax=(axisCell+1);
}
axisCell=0;
break;
}
}
int q11 = zdat [ymin] [xmin]; //store the data for each corresoinding quadrant
int q12 = zdat [ymin] [xmax];
int q21 = zdat [ymax] [xmin];
int q22 = zdat [ymax] [xmax];
Serial.print(F("Bilinear Interpolation "));
Serial.println(bilinIntrp(xin, xax[xmin], xax[xmax], yin, yax[ymin], yax[ymax], q11, q12, q21, q22)); //ohh baby
}
/* This Doesnt work :(
int findMax(int val, int axis[]) {
int axisCell = 0;
while(axisCell < a) {
if(val < axis[axisCell]) axisCell++;
else return axisCell;
}
}
*/
int bilinIntrp(float x, float x1, float x2, float y, float y1, float y2, float q11, float q12, float q21, float q22) {
float r1 = 0;
float r2 = 0;
float p = 0;
r1 = ((x2-x)/(x2-x1)*q11)+((x-x1)/(x2-x1)*q12); //linear interpolation between the lower two quadrants along the X axis
r2 = ((x2-x)/(x2-x1)*q21)+((x-x1)/(x2-x1)*q22); //linear interpolation between the upper two quadrants along the X axis
p = ((y2-y)/(y2-y1)*r1)+((y-y1)/(y2-y1)*r2); //linear interpolation between the two virtual points r1 and r2 along the Y axis
return p; //return the Magic number P value of our point
}
int getInput(){
int result;
while(Serial.available()==0); //Wait For Serial Data
while(Serial.available() > 0) { //Data is available
result = Serial.parseInt(); //Parse The Input
}
return result; //Return The Result
}
