Basic Mathf question?

Questions & Answers
1

After looking through the Mathf class in the maunal, I cannot find the method I’m looking for.

Basically I have two ranges of floats:

floatA = 5; floatB = 10;

floatC = 50; floatD = 100;

How can I return a number between floatC and floatD depending on what numbers floatA and floatB are?

For example lets say I’m creating a speedometer:

floatA = 0; (lowest speed) and floatB = 90; (max speed).

Depending on the speed of the vehicle, it should produce a float between floatC and floatD …how can achieve this?

4

Think of it as two calculations.

First, you want to find out what proportion of the distance your number is between A and B.

Second, you want to apply that proportion to the interval (C, D).

These 2 calculations can be performed using Mathf.InverseLerp and Mathf.Lerp respectively.

Assuming a dial-type speedometer, where what you’re looking for is the angle for a given speed, you want something like this…

float minSpeed = 0; float maxSpeed = 100;
float minAngle = 50; float maxAngle = 170;

float AngleForSpeed(float speed)
{
     float t = Mathf.InverseLerp( minSpeed, maxSpeed, speed);
     return Mathf.Lerp(minAngle, maxAngle, t);
}
2

What you are looking for is a method which is usually called “map” in other languages. However Mathf doesn’t have such a method. Though what map does is actually the chained result of Mathf.InverseLerp and Mathf.Lerp.

So a reference implementation would be

public static class MapFunctionExtension
{
    public static float Map(this float aValue, float aFromMin, float aFromMax, float aToMin, float aToMax)
    {
        return Mathf.Lerp(aToMin, aToMax, Mathf.InverseLerp(aFromMin, aFromMax, aValue);
    }
}

With this extension you can simply do

float speed = 10;
float mapped = speed.Map(0, 90, 5, 25);

This will map the value speed from the range 0 - 90 to the range 5 - 25. So in the case of the value 10 we get back a value of 7.2222

Of course this is just an example implementation. A better solution is to implement the whole mapping in one function since method calls are not for free.

public static class MapFunctionExtension
{
    public static float Map(this float aValue, float aFromMin, float aFromMax, float aToMin, float aToMax)
    {
         // value between 0 and 1
        float t = (aValue - aFromMin) / (aFromMax - aFromMin);
        
        // clamp t to the 0-1 range
        if (t < 0f) t = 0f;
        else if (t > 1f) t = 1f;
        
        // lerp back to the new range
        return aToMin * (1-t) + aToMax * (t);
    }
}

This would do pretty much the same as the above method but more efficient. Note there are no safety checks when min and max have the same value. Though this should never be the case anyways. Just for reference, this is how Unity implemented InverseLerp, Lerp and Clamp01.

3

Example:
Speed Min/Max: 0, 90

Needle Angle Min/Max: 0, 180

If speed is 45 then needle angle would 90.

if speed is 22 then needle angel would be 45.

Just examples ty again