移动数字范围的中点(Shift Middle Point of Number Range)

 我有一个功能，可以将任何数字范围标准化为新范围。 
 
 如 
 [123,456]至[0,10] 
 要么 
 [-50,50]至[-1,1] 
 
 我需要帮助改变新范围的中间点。 
 
 我正在使用它作为GUI滑块，其范围为[-100,100]但控制值为[-2,2] 。 
 GUI Slider默认值为0但默认值为1 （无）。 
 我的程序是CLI的GUI，我无法将该程序的默认值更改为0 。 
 
  
 
Slider
-100 --------------||-------------- 100
                    0
Value
-2 |  |  | -1 |  |  0|  |  | 1  |  |  2

Shifted Value
-2 |  | -1 |  | 0 | 1|  |  |  |  |  | 2
 
 
 规范化 
 
 https://dotnetfiddle.net/42jHvM 
 
// Normalize Function
public static double Normalize(double val, double valmin, double valmax, double min, double max, double midpoint) 
{
    return (((val - valmin) / (valmax - valmin)) * (max - min)) + min;
}
 
 
double output = Normalize(  0, // slider input
                         -100, // input min
                          100, // input max
                           -2, // normalize min
                            2, // normalize max
                            1  // middle point
                         );
 
 
 转移中点 
 
 在我的例子中，我使用[-100,100]转换为[-2,2] 。 
 
 input [-100,100]的中间点为0 。 
 但我需要output [-2,2]的中间点为1而不是0 。 
 
 所以它会倾斜，朝-2慢，朝2快。 
 
 示例 I在photoshop中制作以使用渐变可视化中点移位。 
 
  
 
 缓解 
 
 我尝试使用Ease Out Tween来移动中间点，但我不知道要使用什么值。 
 示例输出需要为Min: -2 ， Mid: 1 ， Max: 2 。 
 
 https://dotnetfiddle.net/nfNlBC 
 
 它用： 
 
//t: current time
//b: start value
//c: change in value
//d: duration
 
 
 中间点移动后： 
 
 输入-100应输出-2 。 
 输入-50应输出-0.50 ？ 
 输入0应输出1 。 
 输入50应输出1.75 ？ 
 输入100应输出2 。 
 
 之前 
 
-100 | -50 | -25  |  0  |  25 |  50 | 100

 -2  | -1  | -0.5 |  0  | 0.5 |  1  |  2
 
 approximated 
 
-100 | -50  | -25  |  0  |  25  |  50  | 100

 -2  |-0.50 | 0.25 |  1  | 1.25 | 1.75 |  2
 
 
 题 
 
 如何修改Normalize函数，或通过新的Shift / Easing函数运行它的输出来设置范围的新中点并重新调整数字？ 

I have a function that Normalizes any number range to a new range.
 
Such as
 [123,456] to [0,10]
 or
 [-50,50] to [-1,1]
 
I need help shifting the middle point of the new range.
 
I'm using this for a GUI Slider that has a range of [-100,100] but controls a value of [-2,2].
 The GUI Slider default is 0 but the value default is 1 (none).
 My program is a GUI for a CLI and I'm not able to change that program's value default to 0.
 
 
Slider
-100 --------------||-------------- 100
                    0
Value
-2 |  |  | -1 |  |  0|  |  | 1  |  |  2

Shifted Value
-2 |  | -1 |  | 0 | 1|  |  |  |  |  | 2
 
 
Normalize
 
https://dotnetfiddle.net/42jHvM
 
// Normalize Function
public static double Normalize(double val, double valmin, double valmax, double min, double max, double midpoint) 
{
    return (((val - valmin) / (valmax - valmin)) * (max - min)) + min;
}
 
 
double output = Normalize(  0, // slider input
                         -100, // input min
                          100, // input max
                           -2, // normalize min
                            2, // normalize max
                            1  // middle point
                         );
 
 
Shift Middle Point
 
In my example I use [-100,100] converted to [-2,2].
 
The middle point of the input [-100,100] is 0.
 But I need the output [-2,2] to have a middle point of 1 instead of 0.
 
So it will be skewed, slower towards -2, faster towards 2.
 
Example I made in photoshop to visualize the middle point shift using a gradient.
 
 
Easing
 
I tried using an Ease Out Tween to shift the middle point, but I don't know what values to use.
 The example output needs to be Min: -2, Mid: 1, Max: 2.
 
https://dotnetfiddle.net/nfNlBC
 
It uses:
 
//t: current time
//b: start value
//c: change in value
//d: duration
 
 
After the middle point has been shifted:
 
Input of -100 should output -2.
 Input of -50 should output -0.50?
 Input of 0 should output 1.
 Input of 50 should output 1.75?
 Input of 100 should output 2. 
 
Before
 
-100 | -50 | -25  |  0  |  25 |  50 | 100

 -2  | -1  | -0.5 |  0  | 0.5 |  1  |  2
 
After approximated
 
-100 | -50  | -25  |  0  |  25  |  50  | 100

 -2  |-0.50 | 0.25 |  1  | 1.25 | 1.75 |  2
 
 
Question
 
How can I modify the Normalize function, or run it's output through a new Shift/Easing function to set the new middle point of the range and readjust the numbers?

原文：https://stackoverflow.com/questions/51177865