如何网状成-1正常化为1，然后从归一目到原来还原？ [英] How to normalize a mesh into -1 to 1, then revert from normalized mesh to original one?

问题描述

我有在X，Y，Z格式的网格模型。让说。

I have a mesh model in X, Y, Z format. Lets say.

Points *P;

在第一步骤中，我想这个目成正常化（-1，-1，-1）（1，1,1）。
这里正常化的手段本网格放入一箱（-1，-1，-1）（1，1,1）。

In first step, I want to normalize this mesh into (-1, -1, -1) to (1, 1, 1). Here normalize means to fit this mesh into a box of (-1, -1, -1) to (1, 1, 1).

在那之后我做一些处理，以规范化的网格，最后我希望恢复尺寸类似的与原来的网格。

then after that I do some processing to normalized mesh, finally i want to revert the dimensions to similar with the original mesh.

STEP-1：
    P =原始网格尺寸;

step-1: P = Original Mesh dimensions;

步2：
    NP =正常化（P）; //从（-1，-1，-1）（1，1,1）

step-2: nP = Normalize(P); // from (-1, -1, -1) to (1, 1, 1)

步3：
    CNP =做点什么（NP），顶点数量有所增加或减少。

step-3: cnP = do something with (nP), number of vertices has increased or decreased.

步4：
    原始网格尺寸=恢复（CNP）; //尺寸应该是相同的与原网

step-4: Original Mesh dimensions = Revert(cnP); // dimension should be same with the original mesh

我该怎么办呢？

推荐答案

我知道它是多么容易迷失在编程和彻底无缘基础数学的简单性。但请相信我，这真的很简单。

I know how easy it can be to get lost in programming and completely miss the simplicity of the underlying math. But trust me, it really is simple.

最直观的方式去了解你的问题大概是这样的：

The most intuitive way to go about your problem is probably this:

1. 确定所有三个坐标轴的最小值和最大值（即 X ，是和以Z ）。此信息由您的立方体的八个角的顶点遏制。在六个变量（例如， min_x ， max_x ，等等）。

1. determine the minimum and maximum value for all three coordinate axes (i.e., x, y and z). This information is contained by the eight corner vertices of your cube. Save these six values in six variables (e.g., min_x, max_x, etc.).

有关网格中所有点 P =（X，Y，Z），计算

For all points p = (x,y,z) in the mesh, compute

q =  ( 2.0*(x-min_x)/(max_x-min_x) - 1.0
       2.0*(y-min_y)/(max_y-min_y) - 1.0
       2.0*(z-min_z)/(max_z-min_z) - 1.0 )

现在①等于 P 转换为间隔（ - 1，-1， -1） - （+ 1，+ 1，+ 1）的。

now q equals p translated to the interval (-1,-1,-1) -- (+1,+1,+1).

做任何你需要在这个中间网格做。

Do whatever you need to do on this intermediate grid.

转换所有坐标 Q =（XX，YY，ZZ）通过执行逆运算回原来的网格：

Convert all coordinates q = (xx, yy, zz) back to the original grid by doing the inverse operation:

p =  ( (xx+1.0)*(max_x-min_x)/2.0 + min_x
       (yy+1.0)*(max_y-min_y)/2.0 + min_y
       (zz+1.0)*(max_z-min_z)/2.0 + min_z )

清理你所做的任何混乱，并继续与你的程序的其余部分。

Clean up any mess you've made and continue with the rest of your program.

这是那么容易，它可能要做更多的工作，以找出库中包含这些功能是不是比他们自己写的。

This is so easy, it's probably a lot more work to find out which library contains these functions than it is to write them yourself.

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