calculate angle from vector to coord

Question

I am breaking my head trying to find an appropriate formula to calculate a what sounds to be an easy task but in practice is a big mathematical headache.

I want to find out the offset it needs to turn my vector's angle (X, Y, Angle) to face a coord ( X, Y )

My vector won't always be facing 360 degrees, so i need that as a variable as well.. Hoping an answer before i'm breaking my pc screen. Thank you.

Answer 1

input

• p1 = (x1,y1) point1 (vector origin)
• p2 = (x2,y2) point2
• a1 = 360 deg direction of vector
• assuming your coodinate system is: X+ is right Y+ is up ang+ is CCW
• your image suggest that you have X,Y mixed up (angle usually start from X axis not Y)
• da=? change of a1 to match direction of p2-p1

solution 1:

• da=a1-a2=a1-atanxy(x2-x1,y1-y1)
• atanxy(dx,dy) is also called atan2 on some libs just make sure the order of operands is the right one
• you can also use mine atanxy in C++
• it is 4 quadrant arctangens

solution 2:

• v1=(cos(a1),sin(a1))
• v2=(x2-x1,y2-y1)
• da=acos(dot(v1,v2)/(|v1|*|v2|))

or the same slightly different

• v1=(cos(a1),sin(a1))
• v2=(x2-x1,y2-y1)
• v2/=|v2| // makes v2 unit vector, v1 is already unit
• da=acos(dot(v1,v2))

so:

da=acos((cos(a1)*(x2-x1)+sin(a1)*(y2-y1)/sqrt((x2-x1)*(x2-x1)+(y2-y1)*(y2-y1)));

[notes]

• just change it to match your coordinate system (which you did not specify)
• use radians or degrees according to your sin,cos,atan dependencies ...

Answer 2

The difference between the vectors is also a vector.

Then calculate the tangens (y part / x part) and invert it to an angle.

Of course use the sign of y if x = 0.

Answer 3

if the coord to face is (x2 ,y2)

deltaY = y2 - y1

deltaX = x2 - x1

You have the angle in degrees between the two points using this formula...

angleInDegrees = arctan(deltaY / deltaX) * 180 / PI

subtract the original angle of your vector and you will get the correct offset!