Angle from X,Y

[Astronouth7303]

How do you find the angle from (X, Y)?

And how do you optimize this for realtime on the FRC?

And One Of Astronouth's Rare Contensts: Why would I care?

[Yan Wang]

Angle from (x,y) (I'm assuming on a normal Cartesian Plane) to what in relation to what as a vertex?

ie. angle between (x,y) and x-axis with origin as vertex.

[Astronouth7303]

The angle between (0,0) and (x,y) in relation to the x axis (A horizantal line, y=0)

[FotoPlasma]

The inverse tangent function (arctan) will give you the angle from the origin to a point. For example: given (x,y), arctan(y/x) = the angle from the origin to the point (x,y).

If you search CD for something like "arctan" or "trig" or "trigonometry", you should get a fair amount of results already covering implementation of trigonometric functions on the FRC controller.

I don't have any experience using these, myself, but I've heard that a few teams have had success with using an arbitrary degree Taylor series approximation of trig functions.

[Astronouth7303]

Doesn't arc tangent return an angle for a given slope? As in: -90 to 90.
I'm talking about 360 degrees. Like a Rectangular to Polar converter thing.

[Joe Ross]

Originally Posted by Astronouth7303

Doesn't arc tangent return an angle for a given slope? As in: -90 to 90.
I'm talking about 360 degrees. Like a Rectangular to Polar converter thing.

You then look at the signs of X and Y to see if what quadrant the angle is in.

[Astronouth7303]

:WHAP: Duh

unsigned int GetAngle(signed int X, signed int Y)
{
   signed int Angle = arctan(Y/abs(X));
 unsigned char OtherSide = IsNegetive(X);
 unsigned int Value = 0;
 
 if (OtherSide)
  Value = 180 - Angle + 360;
 else
  Value = Angle + 360;
 
 Value %= 360;
 return Value;
}

Unfortunately, you have to use a float for Angle because angles between -45 and 45 are as important as the others. I suppose I could flip X and Y around for that.

[Changed that tan to arctan]

[michael_obrien]

I don't know much about programming, but I screwed around with winamp AVS for a while, and on that there was a function known as "atan2(x,y)" which was the same as atan but it automatically corrected for quadrants... isn't there anything simular in C? I mean, C is much more powerful than that AVS junk from what I understand, it should at least have the same capabilities.

[The Lucas]

Originally Posted by Astronouth7303

:WHAP: Duh

Unfortunately, you have to use a float for Angle because angles between -45 and 45 are as important as the others. I suppose I could flip X and Y around for that.

[Changed that tan to arctan]

You don't need a float to represent (Y/X). Just try ((Y*100)/X) and scale your arctangent function to reflect this. This works well if you are using a lookup table. However, I would use a float if I was using a McLaurin series. Otherwise you are likely to overload a long the when you start getting into the higher powers (100^5 is way too big). Also you might want to check to make sure X is not zero before dividing by it.

Originally Posted by michael_obrien

I don't know much about programming, but I screwed around with winamp AVS for a while, and on that there was a function known as "atan2(x,y)" which was the same as atan but it automatically corrected for quadrants... isn't there anything simular in C? I mean, C is much more powerful than that AVS junk from what I understand, it should at least have the same capabilities.

IFI doen not provide us with libraries of functions like this, but C certainly has them. The standard atan function requires more prcessing and floating point math than most FIRST programmers want to put in thier RC

[Matt Reiland]

This is the formula that LeoM posted a while back to get the angle from rectangular coordinates. Worked extremely well back in 2002

Temp1 was the positive distance in X direction
Temp2 was the positive distance in Y direction
temp3 = (temp2*127) / SQR((temp1*temp1)+(temp2*temp2)) 'Make values on a 127 unit circle

ss_degrees = ((1-(temp3/118))*(((temp3+181)*temp3+744)/769))+((temp3/118)*(((((3*temp3-707)*temp3+42611)/20))+((temp3-115)/3)))

ss_degrees = (ss_degrees*180)/128 'Convert to Degrees

[Astronouth7303]

Ay. The problem is I don't get what it's doing.

[Astronouth7303]

My current code is like this:

#define abs(Num) ( ((Num) < 0) ? (0 - (Num)) : (Num) )
#define IsNegetive(Num) ( ((Num) < 0) ? 255 : 0 )
#define IsPositive(Num) ( ((Num) > 0) ? 255 : 0 )



/* 360 degrees = 256
  0 =   0 (0x00)
 45 =  32 (0x20)
 90 =  64 (0x40)
135 =  96 (0x60)
180 = 128 (0x80)
225 = 160 (0xA0)
270 = 192 (0xC0)
315 = 224 (0xE0) */

unsigned char GetAngle(signed char X, signed char Y)
{
   signed int  Angle = 0;
 unsigned char OtherSide = (X < 0) ? 255 : 0;
 unsigned char Value = 0;
 unsigned char Simple = (X == 0) | (Y == 0) | (X == Y);
 
 //Perform Simple tests
 if (Simple)
 {
  if (X == 0)
   if (Y < 0)
    Angle = 192; // Down
   else if (Y > 0)
    Angle = 64; //Up
   else // Y == 0
    Angle = 0; //None, default
  
  if (Y == 0)
   if (X < 0)
    Angle = 128; // Left
   else if (X > 0)
    Angle = 0; //Right
   else // X == 0
    Angle = 0; //None, default
  
  if (X == Y)
  {
   switch( (IsNegetive(X) & 2) | (IsNegetive(Y) & 1) )
   {
    case 0: //++
     Angle = 32;
     break;
    case 2: //-+
     Angle = 96;
     break;
    case 3: //--
     Angle = 160;
     break;
    case 1: //+-
     Angle = 224;
     break;
   }
  }
 }

 //Again for goto, no braces
 if (Simple) goto Done; //I hope that's right
 
 if (X > Y) //Preserve accuracy
  Angle = 64 - atan(abs(X)/Y);
 else
  Angle = atan(abs(X)/Y);
 
 Angle = OtherSide ? (127 - Angle) : Angle;
 Value = (unsigned char)((Angle + 255) % 255);
 
Done:
 return Value;
}

Nobody's answered the last question!

[Greg Ross]

Originally Posted by Astronouth7303

Nobody's answered the last question! [regarding optimization]

Jamie,

The best advice I've ever heard about optimization is "Don't -- until you need to." You generally want to get your code working, and only then worry about optimizing -- if necessary.

[Astronouth7303]

I was refeing to post 1:

Originally Posted by Astronouth7303

And One Of Astronouth's Rare Contensts: Why would I care?

[Greg Ross]

Originally Posted by Astronouth7303

I was refeing to post 1:

OK. And now I'm confused. I don't understand "And One Of Astronouth's Rare Contensts", so I don't know how to answer "Why would I care?" (I originally thought that line was part of your signature, so I just ignored it.)