1. Trig and the Infamous
- Posted by Larry Gregg <lgregg at BIG12.METROBBS.COM>
May 05, 1998
-
Last edited May 06, 1998
=
> 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
