仅仅调用Pitch()和Yaw()怎么会导致摄像机最终Roll()? [英] How could simply calling Pitch() and Yaw() cause the camera to eventually Roll()?

问题描述

我正在编写一个基本的OpenGL游戏，并且我有一些可以在移动相机方面处理鼠标的代码.

I'm coding a basic OpenGL game and I've got some code that handles the mouse in terms of moving the camera.

我正在使用以下方法:

int windowWidth = 640;
int windowHeight = 480;

int oldMouseX = -1;
int oldMouseY = -1;

void mousePassiveHandler(int x, int y)
{
    int snapThreshold = 50;

    if (oldMouseX != -1 && oldMouseY != -1)
    {
        cam.yaw((x - oldMouseX)/10.0);
        cam.pitch((y - oldMouseY)/10.0);


        oldMouseX = x;
        oldMouseY = y;

        if ((fabs(x - (windowWidth / 2)) > snapThreshold) || (fabs(y - (windowHeight / 2)) > snapThreshold))
        {
            oldMouseX = windowWidth / 2;
            oldMouseY = windowHeight / 2;
            glutWarpPointer(windowWidth / 2, windowHeight / 2);
        }
    }
    else
    {
        oldMouseX = windowWidth / 2;
        oldMouseY = windowHeight / 2;
        glutWarpPointer(windowWidth / 2, windowHeight / 2);
    }


    glutPostRedisplay();

}

但是，环顾四周后，您会发现相机开始滚动"(旋转).由于我只打电话给Pitch和Yaw，所以我不知道这怎么可能.

However, after looking around in circles you'll find the camera starts to "roll" (rotate). Since I'm only calling Pitch and Yaw, I don't see how this is possible.

这是我用于我的Camera类的代码: http://pastebin.com/m20d2b01e

Here is the code I'm using for my Camera class: http://pastebin.com/m20d2b01e

据我所知，我的相机不会滚动".它应该简单地上下倾斜或左右偏航.不滚动.

As far as I know, my camera "rolling" shouldn't happen. It should simply pitch up and down or yaw left and right. NOT roll.

这可能是什么原因造成的?

What could be causing this?

推荐答案

祝贺您-您已经发现了李群理论！

Congratulations -- you have discovered Lie group theory!

是的，有可能.一系列转型的结果 取决于执行顺序.推销 其次是偏航与进行偏航不一样，其次 间距.实际上，在无限偏航的范围内 和音高，差异等于纯滚动；一般 情况要复杂一些.

Yes, it's possible. The outcome of a series of transformations depends on the order in which they're executed. Doing a pitch followed by a yaw is not the same as a doing a yaw, followed by a pitch. In fact, in the limit of infinitesimally small yaws and pitches, the difference amounts to a pure roll; the general case is a little more complicated.

(物理学家称之为 旋转组".

(Physicists call this the "commutation relationships of the rotational group".)

如果您熟悉旋转矩阵，则可以解决 很容易

If you're familiar with rotation matrices, you can work it out quite easily.

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