Incorrect Formulae

Orkie · 10-30-2005, 04:47 AM

Please can somebody check the formulae that I'm using for my Logo interpreter. I just can't seem to get them right! This is my FORWARD code:

Code:

if(command[0] == "FORWARD")
     {
                   // Setup variables
                   point temp;
                   int distance = atoi(command[1].c_str());
                   
                   // If angle is within the x quadrant's boundries, use correct formula
                   if(angle >= 0 && angle < 90)
                   {
                            int tempAngle = angle;
                            
                            int opp = (int) ROUND(sin(tempAngle) * distance);
                            int adj = (int) ROUND(cos(tempAngle) * distance);
                            
                            temp.x = currentLocation.x + opp;
                            temp.y = currentLocation.y - adj;
                   }
                   else if(angle >= 90 && angle < 180)
                   {
                            int tempAngle = angle - 90;
                            
                            int opp = (int) ROUND(sin(tempAngle) * distance);
                            int adj = (int) ROUND(cos(tempAngle) * distance);
                            
                            temp.x = currentLocation.x + adj;
                            temp.y = currentLocation.y + opp;
                   }
                   else if(angle >= 180 && angle < 270)
                   {
                            int tempAngle = angle - 180;
                            
                            int opp = (int) ROUND(sin(tempAngle) * distance);
                            int adj = (int) ROUND(cos(tempAngle) * distance);
                            
                            temp.x = currentLocation.x - opp;
                            temp.y = currentLocation.y + adj;
                   }
                   else if(angle >= 270 && angle < 360)
                   {
                            int tempAngle = angle - 270;
                            
                            int opp = (int) ROUND(sin(tempAngle) * distance);
                            int adj = (int) ROUND(cos(tempAngle) * distance);
                            
                            temp.x = currentLocation.x - adj;
                            temp.y = currentLocation.y - opp;
                   }
                   else
                   {
                       error("Angle falls outside of allowed range");
                       return false;
                   }
                   
                   // Draw the line
                   aalineRGBA(screen, currentLocation.x, currentLocation.y, temp.x, temp.y, penColour.r, penColour.g, penColour.b, 255);
                   
                   // Make the new coordinates active
                   currentLocation = temp;
     }

It works out the new co-ordinates for after moving and stores them in temp.{x,y}. It then draws a line from the old location to the newly calculated one then sets the new location to be the current one for the next time that the function runs.

When I run the following program, I get a strange shape:

Code:

FORWARD 50 ;
RIGHT 10 ;
FORWARD 50 ;

And here is what is drawn:
[img=http://img474.imageshack.us/img474/8837/shape6dj.jpg]

I have used many different FORWARD functions, such this (tempx and tempy are equivalent to opp and adj):

Code:

int tempx = (int) ROUND(sin(angle) * distance);
int tempy = (int) ROUND(cos(angle) * distance);

Could this be a bug in SDL_gfx? Or is it my code? Thanks

naf · 10-30-2005, 09:43 AM

The picture does not come up for me.

Which direction is angle 0 at again? I'll assume straight up (12-O'Clock) because the adjustment is trivial (just add an offset and modulo).

Perhaps the problem is that you expect the trig functions to use degrees and not radians.

double trueangle = ( PI * angle / 180.0 );

Then, for all angles (no quadrants):
temp.x = oldposition.x + sin( trueangle ) * distance;
temp.y = oldposition.y + cos( trueangle ) * distance;

This little Maple script should help emphasize it.

Code:

for angle from 0 to 360 by 15 do     
 (angle,round(sin(Pi*angle/180)*distance),round(cos(Pi*angle/180)*distance)) 
end do;
                              0, 0, 100
                              15, 26, 97
                              30, 50, 87
                              45, 71, 71
                              60, 87, 50
                              75, 97, 26
                              90, 100, 0
                             105, 97, -26
                             120, 87, -50
                             135, 71, -71
                             150, 50, -87
                             165, 26, -97
                             180, 0, -100
                            195, -26, -97
                            210, -50, -87
                            225, -71, -71
                            240, -87, -50
                            255, -97, -26
                             270, -100, 0
                             285, -97, 26
                             300, -87, 50
                             315, -71, 71
                             330, -50, 87
                             345, -26, 97
                             360, 0, 100

Orkie · 10-30-2005, 10:13 AM

Thanks for that, I've got it working now. Clearly we haven't done enough trigonometry in school

Here is what I have now:

Code:

if(command[0] == "FORWARD")
     {
                   // Setup variables
                   point temp;
                   int distance = atoi(command[1].c_str());
                   
                   // Calculate new position and store in 'temp'
                   int realAngle = angle + 90;
                   long double degRad = M_PI / 180.0;
                   
                   int tempx = (int) ROUND(cos((realAngle * degRad)) * distance);
                   int tempy = (int) ROUND(sin((realAngle * degRad)) * distance);
                   
                   temp.x = currentLocation.x - tempx;
                   temp.y = currentLocation.y - tempy;
                   
                   // Draw the line
                   aalineRGBA(screen, currentLocation.x, currentLocation.y, temp.x, temp.y, penColour.r, penColour.g, penColour.b, 255);
                   
                   // Make the new coordinates active
                   currentLocation = temp;
     }