问题
Do either of the below approaches use the correct mathematics for rotating a point? If so, which one is correct?
POINT rotate_point(float cx,float cy,float angle,POINT p) { float s = sin(angle); float c = cos(angle); // translate point back to origin: p.x -= cx; p.y -= cy; // Which One Is Correct: // This? float xnew = p.x * c - p.y * s; float ynew = p.x * s + p.y * c; // Or This? float xnew = p.x * c + p.y * s; float ynew = -p.x * s + p.y * c; // translate point back: p.x = xnew + cx; p.y = ynew + cy; } 回答1:
It depends on how you define angle. If it is measured counterclockwise (which is the mathematical convention) then the correct rotation is your first one:
// This? float xnew = p.x * c - p.y * s; float ynew = p.x * s + p.y * c; But if it is measured clockwise, then the second is correct:
// Or This? float xnew = p.x * c + p.y * s; float ynew = -p.x * s + p.y * c; 回答2:
From Wikipedia
To carry out a rotation using matrices the point (x, y) to be rotated is written as a vector, then multiplied by a matrix calculated from the angle, θ, like so:
where (x′, y′) are the co-ordinates of the point after rotation, and the formulae for x′ and y′ can be seen to be
回答3:
This is extracted from my own vector library..
//---------------------------------------------------------------------------------- // Returns clockwise-rotated vector, using given angle and centered at vector //---------------------------------------------------------------------------------- CVector2D CVector2D::RotateVector(float fThetaRadian, const CVector2D& vector) const { // Basically still similar operation with rotation on origin // except we treat given rotation center (vector) as our origin now float fNewX = this->X - vector.X; float fNewY = this->Y - vector.Y; CVector2D vectorRes( cosf(fThetaRadian)* fNewX - sinf(fThetaRadian)* fNewY, sinf(fThetaRadian)* fNewX + cosf(fThetaRadian)* fNewY); vectorRes += vector; return vectorRes; } 来源：https://stackoverflow.com/questions/3162643/proper-trigonometry-for-rotating-a-point-around-the-origin