Calculate angle of rotation

0
votes

I have a rectangle on the scene and I want to rotate it with mouse. The rectangle has his own origin point. Clicking on the scene represents start of rotation and mouse moving represent angle of rotation.

enter image description here

where:

  • O - origin of rotation point
  • A - anchor point (saved in OnMousePress event)
  • C - current point (from OnMouseMove event)

so I calculate the angle in next steps:

Fistly, I get lengths of triangle sides:

AO = sqrt( (O.x - A.x)^2 + (O.y - A.y)^2 )

CO = sqrt( (O.x - C.x)^2 + (O.y - C.y)^2 )

AC = sqrt( (C.x - A.x)^2 + (C.y - A.y)^2 )

and then I calculate the angle (a):

a = arccos ( (AO^2 + CO^2 - AC^2) / (2 * AO * CO) )

it works, but this calculation look too complicated taking into account that I need to repeat on it all OnMouseMove call.

So my question - is there another way to calculate the angle? I write it in c++ so some code snippet will be apprecated.

2
c++rotationgeometry

2 Answers

2
votes

You can find angle between vectors OA and OC through their scalar product and cross product:

OA = (OA.X, OA.Y) = (A.X-O.X, A.Y-O.Y)
OC = (OC.X, OC.Y) = (C.X-O.X, C.Y-O.Y)
SP = OA * OC = OA.X*OC.X+OA.Y*OC.Y
CP = OA x OC = OA.X*OC.Y-OA.Y*OC.X
Angle = atan2(CP, SP)

Example: O = (0,0), A = (-1, 0), C = (-2, 1) SP = 2, CP = -1, Angle = -0.463

This method allows to avoid sqrt calculations, and determines rotation direction (unlike arccos)

1
votes

You use a dot product of vectors OA and OC divided by their magnitude to calculate cosine of the angle and then use acos() function to find the angle.

float cosAngle = (x1 * x2 + y1 * y2) / sqrt(x1*x1 + y1*y1) * sqrt(x2*x2 + y2*y2);
float angle = acos(cosAngle);