arcctg function
function actg($arg){
return acos($arg/(sqrt(1 + $arg * $arg)));
}
(PHP 4, PHP 5, PHP 7, PHP 8)
atan — 反正切
$arg
) : float
返回 arg 的反正切值，单位是弧度。atan() 是
tan() 的反函数，它的意思是在
atan() 范围里的每个值都是
a==tan(atan(a))。
arg要处理的参数
arg 的反正切弧度。
arcctg function
function actg($arg){
return acos($arg/(sqrt(1 + $arg * $arg)));
}
Contrary to the current description, it should hold y == tan(atan(y)) for ALL y.
However, x == atan(tan(x)) only holds for those x which are in the range of atan, which are those x with -pi/2 < x < pi/2.
Of course, those equalities are limited by precision. On my machine
tan(atan(1000)) returns 1000.0000000001.
atan(tan(0)) returns 0 (correct).
atan(tan(M_PI)) returns -1.2246467991474E-16 instead of 0.
to obtain the direction of the line, you are better to use the <? atan2((y2-y1)/(x2-x1)) ?> function, since the regular atan function will only return arguments in the half-plane, ie. if y2-y1 and x2-x1 are negative, atan will give you an angle measurement less than 90 degrees, while it really should be between 180 and 270
Arc Tan curve manipulation.
I used this formula to help with increasing and then diminishing return for y given an increasing x for a game.
Ie: Food production (output) is y. Food research is x.
The more research you put into x the more you produce, however after a certain point you get less reward.
y = atan(x - pi()) + pi()/2;
The + pi()/2 moves it up the y axis so you'd add more if you want it to start higher.
The x - pi() moves it to the right so you'd minus more to move it more.
If you want stretched along the y axis change it to 2 * atan( ...... )
Dunno how useful it is... but it's there.
Daz