OpenEuphoria

Trig and the Infamous

• Posted by Larry Gregg <lgregg at BIG12.METROBBS.COM> May 05, 1998
• 655 views

=

> speed = sqrt((xv*xv)+(yv*yv))
> if speed > maxspeed then
>   xv = xv * maxspeed / speed
>   yv = yv * maxspeed / speed
> end if

Let us find the speed using the new xv and yv, call them xv2 and yv2.
 speed2 = sqrt(xv2*xv2 + yv2*yv2)
        = sqrt(xv*maxspeed/speed * xv*maxspeed/speed +
               yv*maxspeed/speed * yv*maxspeed/speed)
        = sqrt((maxspeed/speed)**2 * (xv**2 + yv**2))
        = (maxspeed / speed) * sqrt(xv**2 + yv**2)

 but sqrt(xv**2 + yv**2) is speed as defined above, so

 speed2 = (maxspeed / speed) * speed
        = maxspeed

 In your if statement above, try replacing xv and yv with:
    theta = arctan(yv / xv)
    xv = maxspeed * cos(theta)
    yv = maxspeed * sin(theta)

 The nice thing here is that this will work for arbitrary angle
 and speed.  So, if you are traveling at some speed s, and
 say angle = pi / 4 radians, and change the angle to pi / 8 radians,
 but your speed remains constant, you can just find xv and yv as:

    xv = s * cos(pi / 8)
    yv = s * sin(pi / 8)


Good stuff.  Hope I did this all correctly.  It has been a while.

------------------------------------------------------------------
Larry Gregg