3D到2D投影 [英] 3D to 2D projection

问题描述

我正在尝试使用Java（具有处理，实际上是）的游戏编写一些具有酷炫的3D效果。

I'm trying to write a game in Java (Processing, actually) with some cool 3D effects.

我可以选择两个3D渲染器，但是都没有默认渲染器的质量或灵活性。我当时在想，如果我能得到一个能投影的函数

I have a choice of two 3D renderers, but neither have the quality or flexibility of the default renderer. I was thinking that if I could get a function to proje

所以说我有一组在3D空间中漂浮的坐标（x，y，z）。我如何在2D屏幕上找到应该绘制点的位置（视角）？

So say I have a set of coordinates (x, y, z) floating in 3D space. How would I get where on the 2D screen that point should be drawn (perspective)?

为了澄清，我只需要最低裸线 （不考虑摄像机的位置，我可以通过偏移点数来获得效果）-我不是在重新编写OpenGL。

Just to clarify, I need only the bare minimum (not taking the position of the camera into account, I can get that effect just by offsetting the points) - I'm not re-writing OpenGL.

是的，我看到有关此问题还有很多其他问题，但似乎没有一个确切的答案。

And yes, I see that there are many other questions on this - but none of them seem to really have a definitive answer.

推荐答案

您的最低要求。

column = X*focal/Z + width/2
row = -Y*focal/Z  + height/2

符号为：

X，Y，Z 是3D坐标，以毫米或米为单位；

X, Y, Z are 3D coordinates in distance units such as mm or meters;

焦距是摄像机的焦距，以像素为单位（对于VGA分辨率，焦距= 500是一个合理的选择，因为它将产生一个查看约60度；如果图像尺寸较大，请按比例缩放焦距）；注意，物理焦点〜1cm ＜＜ Z，从而简化了上一个答案中给出的公式。

focal is a focal length of the camera in pixels (focal= 500 for VGA resolution is a reasonable choice since it will generate a field of view about 60 deg; if you have a larger image size scale your focal length proportionally); note that physically focal~1cm << Z, which simplifies formulas presented in the previous answer.

高度和宽度是图像或传感器的尺寸（以像素为单位）；

height and width are the dimensions of the image or sensor in pixels;

行，列-是图像像素坐标（注意：行从顶部开始并向下移动，而Y向上）。这是一组标准的坐标系，其中心位于相机中心（对于X，Y，Z）和图像的左上角（对于行，列，请参见绿线）。

row, column - are image pixels coordinates (note: row starts on top and goes down, while Y goes up). This is a standard set of coordinate systems centered on camera center (for X, Y, Z) and on the upper-left image corner (for row, column, see green lines).

您不确实不需要使用OpenGL，因为这些公式易于实现。但是会有一些副作用，例如，当您的对象具有多个曲面时，它们将无法正确显示，因为您无法模拟遮挡。因此，您可以添加一个深度缓冲区，该深度缓冲区是一个简单的2D数组，具有浮点Z值，可以跟踪哪些像素更近，哪些像素更远；如果尝试在同一投影位置进行多次写入，则较近的像素将始终获胜。祝你好运。

You don't need to use OpenGL indeed since these formulas are easy to implement. But there will be some side-effects such as whenever your object has several surfaces they won't display correctly since you have no way to simulate occlusions. Thus you can add a depth buffer which is a simple 2D array with float Z values that keeps track which pixels are closer and which are further; if there is an attempt to write more than once at the same projected location, the closer pixel always wins. Good luck.

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