Unprojecting 2D屏幕坐标的三维坐标 [英] Unprojecting 2D Screen Coordinates to 3D Coordinates

问题描述

我想知道我怎么会去映射2D屏幕坐标转换为三维世界（特别是XZ平面）了解：

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

相机的 - 位

在屏幕平面 - 方程

在XZ平面的 - 方程

-equation of the xz plane

我想要做的是有在XZ平面上亮起的土地时，我悬停鼠标。

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

任何帮助是极大AP preciated！

Any help is greatly appreciated!

谢谢！

推荐答案

如果你的世界是旋转移位，使得相机在 X = Y = Z = 0 （世界坐标），世界以Z 协调增加远离观察者（到屏幕），和投影平面平行于屏幕，是以Z = D （世界坐标; D＆GT; 0 ），然后确定从世界屏幕坐标坐标系是这样的：

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

这就是pretty的直观：从浏览器/投影平面更远的目标，更大的 ZW 和较小的 XS 和 YS ，接近 XW = YW = 0 和 ZW = +无限，其投影到中央的投影平面 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.

通过以上你重新安排各获得 XW 和 ZW 回：

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

XW = XS * ZW / D
ZW = D * YW / YS

现在，如果你的对象（土地）是平面上一定 YW ，然后，嗯，那 YW 是已知的，这样你就可以代替它，并获得 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

已经找到 ZW ，你现在可以得到 XW 通过再次替换：

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​​，有鉴于在鼠标指针的开始和屏幕坐标 XS 和 YS 描述的设置（0,0是屏幕/窗口中心），相机和投影平面 D ，和之间的距离地平面的 YW 你拿到土地点的位置，鼠标点：

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 在旋转和移动世界坐标，如果你想在原来的在地图土地的绝对坐标，您取消旋转和未转移他们。

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.

这是它的精神。

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