将 2D 屏幕坐标取消投影到 3D 坐标 [英] Unprojecting 2D Screen Coordinates to 3D Coordinates

问题描述

我想知道如何将 2D 屏幕坐标映射到 3D 世界(特别是 xz 平面):

I was wondering how I would go about mapping 2D screen coordinates to a 3D world (specifically the xz plane) knowing:

-相机位置

-屏幕平面方程

-xz 平面方程

当我将鼠标悬停在 xz 平面上时，我想要做的就是点亮它.

All I want to do is have the land on the xz plane light up when I hover the mouse over it.

非常感谢任何帮助！

谢谢！

推荐答案

如果你的世界被旋转和移动，使得相机位于 x=y=z=0(世界坐标)，world z 坐标远离观察者(进入屏幕)增加，投影平面平行于屏幕，位于z=d(世界坐标；d > 0)，然后您可以通过以下方式根据世界坐标确定屏幕坐标:

If your world is rotated and shifted such that the camera is at x=y=z=0 (world coordinates), the world z coordinate increases away from the viewer (into the screen), and the projection plane is parallel to the screen and is at z=d (world coordinate; d > 0), then you determine screen coordinates from world coordinates this way:

xs = d * xw/zw
ys = d * yw/zw

这很直观:物体离观察者/投影平面越远，它的 zw 越大，xs 和 ys 越小，更接近 xw=yw=0 和 zw=+infinity 的消失点，投影到投影平面的中心 xs=ys=0.

And that's pretty intuitive: the farther the object from the viewer/projection plane, the bigger its zw and the smaller xs and ys, closer to the vanishing point of xw=yw=0 and zw=+infinity, which projects onto the center of the projection plane xs=ys=0.

通过重新排列上面的每一个你得到 xw 和 zw:

By rearranging each of the above you get xw and zw back:

xw = xs * zw/d
zw = d * yw/ys

现在，如果你的物体(土地)是在某个 yw 处的一个平面，那么，那个 yw 是已知的，所以你可以替换它并得到zw:

Now, if your object (the land) is a plane at a certain yw, then, well, that yw is known, so you can substitute it and get zw:

zw = d * yw/ys

找到zw，你现在可以再次通过替换得到xw:

Having found zw, you can now get xw by, again, substitution:

xw = xs * zw/d = xs * (d * yw/ys)/d = xs * yw/ys

因此，鉴于鼠标指针的开始和屏幕坐标 xs 和 ys 中描述的设置(0,0 是屏幕/窗口中心)，相机和投影平面之间的距离 d 和陆地平面的 yw 你得到鼠标指向的陆地点的位置:

So, there, given the setup described in the beginning and screen coordinates xs and ys of the mouse pointer (0,0 being the screen/window center), the distance between the camera and the projection plane d, and the land plane's yw you get the location of the land spot the mouse points at:

xw = xs * yw/ys
zw = d * yw/ys

当然，这些 xw 和 zw 是在旋转和移动的世界坐标中，如果你想要土地地图"中的原始绝对坐标，你不旋转和不移动它们.

Of course, these xw and zw are in the rotated and shifted world coordinates and if you want the original absolute coordinates in the "map" of the land, you un-rotate and un-shift them.

这就是它的要点.

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