计算机图形学中的纯旋转
计算机图形学中什么叫纯旋转？这是否意味着应用于任何矩阵的变换都只是旋转？ 如果是这样，那么相交线之间的角度如何通过纯旋转来保留？
What is called a pure rotation in computer graphics? Does it mean the transformation applied on any matrix is only rotation?
If so, then how the angles between intersecting lines are preserved by pure rotation?
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从几何角度来看，角度当然是保留的。
从数学角度来看，您可以证明长度和点积在旋转下都保持不变。这意味着，如果有三个点 A、B 和 C，并让 Ax、Bx、Cx 为这些点旋转后的位置：
从 A 到 B 的距离与从 Ax 到 Bx 的距离相同.
如果设 V 为从 A 到 C 的向量，W 为从 B 到 C 的向量，则 V·W 与 Vx·Wx 相同。
这只是痛苦的数学。
由于两个向量的点积是它们之间角度的余弦乘以两个向量中每个向量的长度，因此旋转是保角的。
From a geometric perspective, angles are of course preserved.
From a mathematical prospective, you can show both length and dot product are unchanged under rotation. This means that if you have three points A, B, and C and let Ax, Bx, Cx be the location of these points after a rotation:
The distance from A to B is the same as the distance from Ax to Bx.
If you let V be the vector from A to C and and W be the vector from B to C, then V·W is the same as Vx·Wx.
This is just painful math.
Since the dot product of two vectors is the cosine of the angle between them times the length of each of the two vectors, you have that rotations are angle preserving.