Angle between vectors

[sai`ke]

Function to compute the smallest angle between vectors.

Consider two vectors v1 and v2, each with an x and y component, then this function will return the smallest angle between them in degrees.



All in- and output parameters are single floating point values.
Returns -1 when a zero length vector is given.

Code: [Select]

function angle( v1x, v1y, v2x, v2y: single ): single;
var
  cosangle: single;
  dist: single;
begin
  dist := ( distance( 0, 0, v1x, v1y ) * distance( 0, 0, v2x, v2y ) );
  if dist = 0 then
  begin
    Result := -1;
    exit;
  end

  cosangle := ( v1x * v2x + v1y * v2y ) / dist;
  Result := 90 - 720 * ( arctan( cosangle / ( 1 + sqrt( 1 - cosangle * cosangle ) ) ) ) / (2 * pi);

  if FloatToStr(Result) = 'NAN' then
    Result := 0.0;

end;


[rainrider]

atan2

[EnEsCe]

I think this should be in general scripting chat or something...

[sai`ke]

Okay, whatever floats your boat . I can't move it there so an admin should do that then.

Atan2?

[Kavukamari]

what is arctan()?

P.S. I made a slope script, it finds the slope between two coords, should I post it?

[urraka]

The inverse function of tan. It's trigonometry.

[sai`ke]

The arctan formula mess in there is actually a way to calculate the inverse cosine since it isn't available in the scriptcore nor in regular pascal.

[urraka]

I modified a bit your function. First, your are checking if dist equals 0 after making a division by dist. So I moved that line. And second, sometimes the function returns NAN if the points are very close to each other. So I made it return 0 in that case.

Code: [Select]

function angle( v1x, v1y, v2x, v2y: single ): single;
var
cosangle: single;
dist: single;
begin
dist := ( distance( 0, 0, v1x, v1y ) * distance( 0, 0, v2x, v2y ) );
if dist = 0 then
begin
Result := -1;
exit;
end

cosangle := ( v1x * v2x + v1y * v2y ) / dist;
Result := 90 - 720 * ( arctan( cosangle / ( 1 + sqrt( 1 - cosangle * cosangle ) ) ) ) / (2 * pi);

if FloatToStr(Result) = 'NAN' then
Result := 0.0;
end;

Btw, thanks for this script. Checking for angle >= 90 between the current and the last position (relative to the checkpoint) seems to be working almost perfectly in PerroRACE

[sai`ke]

Haha, yea oops. I'll also edit the script in the initial post then. Well I only tested it for a specific number of angles for which the NAN thing did not occur. They probably arise from numerical problems.

[Kavukamari]

Here is my SlopeCalc script if you want it, is pretty useless...

Code: [Select]

function SlopeCalc(const X1, X2, Y1, Y2: single):single;
begin
  Result:=RoundTo(((Y2-Y1)/(X2-X1)),2);
end;

ps it rounds to hundredths place

[poutch]

instead of   720 * (...) / (2 * pi);
u can do     360 * (...) / pi    which would use less cpu operations

and you could also use acos which is more direct :

Code: [Select]

function angle( v1x, v1y, v2x, v2y: single ): single;
begin
    Result := 180 / pi * acos( (v1x*v2x + v1y*v2y) / sqrt( (v1x*v1x + v1y*v1y) * (v2x*v2x + v2y*v2y) ) );
end;

*edit* ok you don't have arccos on the scriptcore so you can keep arctan ^^

[Kavukamari]

you could probably code arccos, but the computer would still be doing the same math (if my thinking is correct...)