理解transformation Matrix

1.Every matrix M is associated with a coordinate system. This coordinate system has origin (t0, t1, t2) and vectors (a00,a110,a20), (a01,a11,a21), and (a02,a12,a22) as axes. Matrix M maps the standard coordinate system to the coordinate system with the origin (0, 0, 0) and axes (1, 0, 0), (0, 1, 0), and (0, 0, 1).
直接paste一段关于AcgeMatrix3D的解释：

 

Class AcGeMatrix3d represents an affine transformation of 3D space, including translation. Each matrix M has the form:  

a00 a01 a02 t0
 a10 a11 a12 t1
 a20 a21 a22 t2

where the matrix A:  

a00 a01 a02
 a10 a11 a12 
a20 a21 a22

is called the linear part of M. 

Column T:  

t0
 t1
 t2

is called a translational part of M. 

To get AcGePoint3dpnt transformed by corresponding transformation one has to take the product M x P of the matrix M and point-column P = ( pnt.x, pnt.y, pnt.z, 1.0 ) to the power of T . To get AcGeVector3dvec transformed by corresponding transformation one has to take the product M x V of the matrix M and vector-column V = (vec.x, vec.y, vec.z, 0.0) to the power of T. 

Every matrix M is associated with a coordinate system. This coordinate system has origin (t0, t1, t2) and vectors (a00,a110,a20), (a01,a11,a21), and (a02,a12,a22) as axes. Matrix M maps the standard coordinate system to the coordinate system with the origin (0, 0, 0) and axes (1, 0, 0), (0, 1, 0), and (0, 0, 1).
2. 一些note关于3D数学基础：图形与游戏开发

1) 世界坐标系（translation）->惯性坐标系（rotation）->物体坐标系。还有camera坐标系。
2） 矩阵：矩阵是3D数学的重要基础，它主要用来描述两个坐标系之间的关系，通过定义一种运算而将一个坐标系的向量转换到另一个坐标系中
3） 用基向量（1,0,0）,(0,1,0),(0,0,1)乘任意矩阵M，得：矩阵M的每一行都可以理解为转换后的基向量。
4） 旋转坐标系相当于以相反的量旋转物体。
5） 使用4*4矩阵的一个原因就是它能包含平移（translation）。
6） 包含平移的仿射变换，基本思想：将变换的中心点平移到原点，进行线性变换，然后再将中心点平移到原来的位置。 TRT-1

 

posted @ 2011-03-31 18:08  能巴  阅读(2960)  评论(1)  编辑  收藏  举报