和差公式
sin(a+b) = sin(a)*cos(b)+cos(a)*sin(b)
sin(a-b) = sin(a)*cos(b)-cos(a)*sin(b)
cos(a+b) = cos(a)*cos(b)-sin(a)*sin(b)
cos(a-b) = cos(a)*cos(b)+sin(a)*sin(b)
旋转矩阵
点P.X=角度*cos*P的模长
点P.Y=角度*sin*P的模长
P角度=a
P1和P的夹角=b
即
P.X=r*cos(a)
P.Y=r*sin(a)
r=1
则P1的X点 = r*Cos(a+b)
根据和差公式得 = r*Cos(a)*Cos(b)-r*Sin(a)*Sin(b)
化简后得 = P.X*Cos(b)-P.Y*Sin(b)
P1的Y点 = r*Sin(a+b)
根据和差公式得 = r*Sin(a)*Cos(b)+r*Cos(a)*Sin(b)
化简后得 = P.Y*Cos(b)+P.X*Sin(b)
整理得
P1.X = P.X*Cos(b)-P.Y*Sin(b)
P1.Y = P.X*Sin(b)+P.Y*Cos(b)
矩阵写法
[x1,y1]=[cos(b),-sin(b),sin(b),cos(b)]*[x,y]
