Question

What is the fastest way to calculate angle between a line and the x-axis?

I need to define a function, which is Injective at the PI:2PI interval (I have to angle between point which is the uppermost point and any point below).

PointType * top = UPPERMOST_POINT;
PointType * targ = TARGET_POINT;

double targetVectorX = targ->x - top->x;
double targetVectorY = targ->y - top->y;

first try

//#1
double magnitudeTarVec = sqrt(targetVectorX*targetVectorX + targetVectorY*targetVectorY);
angle = tarX / magTar;

second try

//#2 slower
angle = atan2(targetVectorY, targetVectorX);

I do not need the angle directly (radians or degrees), just any value is fine as far as by comparing these values of this kind from 2 points I can tell which angle is bigger. (for example angle in example one is between -1 and 1 (it is cosine argument))

Answer 1

Check for y being zero as atan2 does; then The quotient x/y will be plenty fine. (assuming I understand you correctly).