2d - 屏幕坐标到等距坐标

Question

我正在努力将鼠标/屏幕坐标转换为等距图 block 索引。我已经尝试了所有可以在这里或在互联网上找到的公式，但它们似乎都不起作用，或者我遗漏了一些东西。

这是一张图片，原点在左上角，一个图 block 的尺寸是 128x64px。

如果有任何帮助，我将不胜感激。

Answer 1

基本上，您需要应用一个带有其他一些位的旋转矩阵。下面是一些用 AWK 编写的示例代码，应该很容易移植到任何其他语言:

END {
   PI = 3.1415;
   x = 878.0;
   y = 158.0;

   # Translate one origin to the other 
   x1 = x - 128*5;
   # Stretch the height so that it's the same as the width in the isometric
   # This makes the rotation easier
   # Invert the sign because y is upwards in math but downwards in graphics
   y1 = y * -2;

   # Apply a counter-clockwise rotation of 45 degrees
   xr = cos(PI/4)*x1 - sin(PI/4)*y1;
   yr = sin(PI/4)*x1 + cos(PI/4)*y1;

   # The side of each isometric tile (which is now a square after the stretch) 
   diag = 64 * sqrt(2);
   # Calculate which tile the coordinate belongs to
   x2 = int(xr / diag);
   # Don't forget to invert the sign again
   y2 = int(yr * -1 / diag);

   # See the final result
   print x2, y2;
}

我用几个不同的坐标对其进行了测试，结果似乎是正确的。