旋转矩阵，使 Up 向量等于另一个向量

发布于 2024-10-16 01:23:09 字数 269 浏览 1 评论 0原文

我想调整矩阵的方向，使向上向量与另一个向量面向相同的方向。向前和向右向量的方向并不重要。

例如：

matrix4 m; // m.Up = 0, 1, 0
vector3 v = V3(1,0,0);

// Then I think I have to get the rotation from m.Up and v
// And then rotate the matrix accordingly

但我不知道该怎么做，我可能是错的。

原文

I want to orient my matrix so that the Up vector it facing the same direction as another vector. The orientation of the Forward and Right vectors do not matter.

For example:

matrix4 m; // m.Up = 0, 1, 0
vector3 v = V3(1,0,0);

// Then I think I have to get the rotation from m.Up and v
// And then rotate the matrix accordingly

But I don't know how todo this and I may be wrong.

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ぽ尐不点ル 2024-10-23 01:23:09

这是矩阵特别有用的旋转问题之一

。首先，将矩阵拆分为三个分量向量（向上、向前和向右）。

将您的向上向量设置为您想要的值。然后，调整前向和右向向量，使它们成直角，一个简单的方法是使用叉积。

例如：

//Gets a perpendicular vector
V3 V3::Perp() {
    V3 perp = v.Cross(NewV3(-1, 0, 0));
    if(perp.Length() == 0) {
        // If v is too close to -x try -y
        perp = v.Cross(NewV3(0, -1, 0));
    }
    return perp.Unit();
}
//up = Whatever you need
forward = up.Perp()
right = cross(up, forward);

之后，将向量插回到矩阵中，瞧：D。

This is one of the rotation problems that matricies are particularly useful for

First, split your matrix into the three component vectors (up, forward, and right).

Set your up vector to what you want it to be. Then, adjust your forward and right vectors so that they are at right angles, an easy way to do this would be through the use of cross products.

For example:

//Gets a perpendicular vector
V3 V3::Perp() {
    V3 perp = v.Cross(NewV3(-1, 0, 0));
    if(perp.Length() == 0) {
        // If v is too close to -x try -y
        perp = v.Cross(NewV3(0, -1, 0));
    }
    return perp.Unit();
}
//up = Whatever you need
forward = up.Perp()
right = cross(up, forward);

After that, plug your vectors back into the matrix and voila :D.

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