I must've missed the reasoning in class or forgotten, sorry -- but why is rotation by an angle theta = cos(theta)v+sin(theta)(Nxu)?

keenan

@merc In the plane, the functions cos(theta) and sin(theta) literally mean nothing more than, "the x-coordinate on the unit circle after traveling a distance theta and "the y-coordinate on the unit circle after traveling a distance theta." This fact is easily forgotten when you study trigonometry, and instead you start to think about it as "some weird function." But it will help you enormously to always think of this picture:

In fact, if the inventors of this function had been thinking more carefully, they would have just called these functions CircleX(theta) and CircleY(theta), at which point nobody would be confused. (Which is a good reminder about the importance of variable names in your code! ;-))

Does it make sense from here why the expression you asked about gives you a rotation by an arbitrary angle theta?

I must've missed the reasoning in class or forgotten, sorry -- but why is rotation by an angle theta = cos(theta)v+sin(theta)(Nxu)?

@merc In the plane, the functions cos(theta) and sin(theta) literally mean nothing more than,

"the x-coordinate on the unit circle after traveling a distance thetaand"the y-coordinate on the unit circle after traveling a distance theta."This fact is easily forgotten when you study trigonometry, and instead you start to think about it as "some weird function." But it will help you enormously to always think of this picture:In fact, if the inventors of this function had been thinking more carefully, they would have just called these functions CircleX(theta) and CircleY(theta), at which point nobody would be confused. (Which is a good reminder about the importance of variable names in your code! ;-))

Does it make sense from here why the expression you asked about gives you a rotation by an arbitrary angle theta?