Rotation matrix derivation

Transferred from: http://www.cnblogs.com/luweimy/p/4121789.html

Pre-knowledge matrix multiplication

Introduction, go online check it

Two-angle and (differential) formulas

Derivation

Rotation Transformation is generally according to a certain center point, with a certain radius r rotation α of a certain angle, for the sake of simplicity we give the following scenario

False fixed point A (x, y) want to go through the rotation transformation to reach B (X ', α y '), known rotation angle and point a coordinate, calculate point B

To calculate point B, calculate his x ' and Y ' components, respectively.

Results:

According to the rule of matrix multiplication, we can introduce

The first row of the left matrix is multiplied by the first column of the right matrix and then added to the first column of the first row of the result matrix.

The second row of the left matrix is multiplied by the first column of the right matrix and then added, which is the element of the first column in the second row of the result matrix

As long as the rotation angle is given, the matrix can be computed, and then the point coordinates can be computed by using the matrix to the left by each point, so that we can transform the coordinates by the matrix.

If it is three-dimensional words also have to add a Z axis, more than one component, the matrix has become a 3x3, but probably the same principle, here only to do a simple principle analysis, if you want to calculate the coordinates of three-dimensional points to transform their own manual bar!!

(turn) rotation matrix derivation