Numerical remapping method (remap)

Although numerical remapping does not belong to the system api, But it is indispensable in our daily work .

0~1 It's actually very simple

-1,1 -> 0,1 when , Namely  x * 0.5 + 0.5 = y
0,1 -> -1,1 when , Namely  y * 2 - 1 = x

x and y Is reversible

In addition to certain values like the above , For example, if my scope is not fixed, what should I do ？
Don't panic. , There is also a formula to use , Or the world of mathematics is magical ~

float Remap(float x, float t1, float t2, float s1, float s2)
{
    return (s2 - s1) / (t2 - t1) * (x - t1) + s1;
    return (x - t1) / (t2 - t1) * (s2 - s1) + s1;
}

The above 2 This formula is equivalent , How to use it , It depends on how you organize .

among x = The input values , t1 = The minimum value of the input value , t2 = The maximum value of the input value , s1 = Minimum value of output value , s2 = The maximum value of the output value

Take up a ：

set up t1=0, t2=1, s1=-1, s2=1 when ,

When x=0 when , Function output value =-1

When x=1 when , Function output value =1

When x=0.5 when , Function output value =0

What about? , Smart, you should understand how to use it

The above is generally written in the logic script , If you change to shader here , for example hlsl Words , Because of the blessing of vector register , It's written like this

void Remap(float4 In, float2 InMinMax, float2 OutMinMax, out float4 Out)
{
    Out = (In - InMinMax.x) * (OutMinMax.y - OutMinMax.x) / (InMinMax.y - InMinMax.x) + OutMinMax.x;
}

image unity If you want to c# If you can write that in the , It needs a new database com.unity.mathematics Talent , It has  SIMD The blessing of function , Of course, there are a lot of people who don't really adapt hlsl It's written in this way ~