如何将 3x3 旋转矩阵转换为 4x4 矩阵? [英] How to convert a 3x3 rotation matrix into 4x4 matrix?

问题描述

我目前使用 3x3 旋转矩阵来处理 3D 点.

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

这个矩阵与 4x4 矩阵有何不同?

How does this matrix differ from a 4x4 Matrix?

如何将 3x3 矩阵转换为 4x4 矩阵?

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

推荐答案

一个 4x4 矩阵可用于在单个矩阵中进行旋转和平移.

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

矩阵右侧的 tx、ty 值将添加到您要变换的顶点的 x、y、z.

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.

因此要将 3x3 矩阵转换为 4x4，您只需复制 3x3 左上块的值，如下所示:

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 ]

那个 3x3 变成了这个 4x4

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 4x4 中，左上角的块被直接复制了，并且为其他新的额外条目输入了 0(表明我不想添加任何翻译).

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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