如何转换一个3x3的旋转矩阵为4x4矩阵？ [英] How to convert a 3x3 rotation matrix into 4x4 matrix?

问题描述

我目前使用一个3x3的旋转矩阵与3D点工作。

I'm currently using a 3x3 rotation matrix to work with 3D points.

请问这个矩阵从4x4矩阵有什么区别？

How does this matrix differ from a 4x4 Matrix?

和我怎么转换3x3矩阵成一个4x4？

And how do I convert a 3x3 matrix into a 4x4?

推荐答案

一个4x4矩阵可以用来做旋转和平移一个矩阵。

A 4x4 matrix can be used to do both rotation and translation in a single matrix.

在 TX ， TY 值时按下右侧的矩阵将被添加到X，Y， ž你正在改变顶点。

The tx, ty values down the right side of your matrix would be added to the x, y, z of the vertex you are transforming.

所以到3x3矩阵转换为四轮驱动，只需在值复制为3×3左上块，像这样：

So to convert a 3x3 matrix to a 4x4, you simply copy in the values for the 3x3 upper left block, like so:

[ a11  a12  a13 ]
[ a21  a22  a23 ]
[ a31  a32  a33 ]

这是3×3成为该4×4

That 3x3 becomes this 4x4

[ a11  a12  a13  0 ]
[ a21  a22  a23  0 ]
[ a31  a32  a33  0 ]
[   0    0    0  1 ]

请注意，在4×4的左上块得到直复制和0被输入为其他新的，额外的条目（表示我不希望被添加任何译本）。

Notice in the 4x4 the upper left block got straight copied, and 0's were entered for the other new, extra entries (indicating I don't want any translation to be added).

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