Calculate direction angle from two vectors?

Question

Say I have two 2D vectors, one for an objects current position and one for that objects previous position. How can I work out the angular direction of travel?

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Answer 1

Be careful to use atan2 to avoid quadrant issues and division by zero. That's what it's there for.

float getAngle(CGPoint ptA, CGPoint ptOrigin, CGPoint ptB)
{
    CGPoint A = makeVec(ptOrigin, ptA);
    CGPoint B = makeVec(ptOrigin, ptB);

    // angle with +ve x-axis, in the range (−π, π]
    float thetaA = atan2(A.x, A.y);  
    float thetaB = atan2(B.x, B.y);

    float thetaAB = thetaB - thetaA;

    // get in range (−π, π]
    while (thetaAB <= - M_PI)
        thetaAB += 2 * M_PI;

    while (thetaAB > M_PI)
        thetaAB -= 2 * M_PI;

    return thetaAB;
}

However, if you don't care about whether it's a +ve or -ve angle, just use the dot product rule (less CPU load):

float dotProduct(CGPoint p1, CGPoint p2) { return p1.x * p2.x + p1.y * p2.y; }

float getAngle(CGPoint A, CGPoint O, CGPoint B)
{
    CGPoint U = makeVec(O, A);
    CGPoint V = makeVec(O, B);

    float magU = vecGetMag(U);
    float magV = vecGetMag(V);
    float magUmagV = magU * magV;   assert (ABS(magUmagV) > 0.00001);

    // U.V = |U| |V| cos t
    float cosT = dotProduct(U, V) / magUmagV;
    float theta = acos(cosT);
    return theta;
}

Note that in either code section above, if one ( or both ) vectors are close to 0 length this is going to fail. So you might want to trap that somehow.