Math formula for changing number between two range [closed] - swift

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Here is my issue as an example:
I have two variables, minNumber = 12 & maxNumber = 24 and a maxLimit = 30
and I have a percentage between 1.0 - 0.0, I want the following result:
when the percentage decrease from 1.0 to 0.5, I want minNumber to increase to the maxLimit, and when the percentage decrease from 0.5 to 0.0, the maxLimit went down to maxNumber
so,
percentage = 1.0
var result = 0
while percentage >= 0 {
if percentage < 0.5 {
result = 12.1, 12.2, ..., 29.8, 29.9, 30 (what formula can produce this sequence)
} else {
result = 30, 29.9, ..., 24.1, 24.0 (what formula can produce this sequence)
}
percentage = percentage - 0.1
print("\(result)")
}

Answer 1

If I understand your question correctly, you want result value to "move" in an angle-like shape from minNumber via maxLimit to maxNumber. The basis behind this transformation is following formula. If you have a value X from a range Xmin to XMax and you want to map it to a range Ymin to Ymax then
Y = (Ymin * (Xmax - X) + Ymax * (X - Xmin)) / (Xmax - Xmin)
For you case you should apply this formula for two intervals:
mapping [0; 0.5] range to [minNumber; maxLimit]
mapping [0.5; 1.0] range to [maxLimit; maxNumber]
I think the code becomes more clear if you call:
leftNumber = minNumber
middleNumber = maxLimit
rightNumber = maxNumber
and use two while loops instead of one with inner if:
let leftNumber = 12.0 // minNumber
let middleNumber = 30.0 // maxLimit
let rightNumber = 23.0 // maxNumber
let leftPercentage = 0.0
let middlePercentage = 0.5
let rightPercentage = 1.0
let percentageStep = 0.1
var percentage = leftPercentage
var result = 0.0
while percentage <= middlePercentage {
result = ((percentage - leftPercentage) * middleNumber + (middlePercentage - percentage) * leftNumber)/(middlePercentage - leftPercentage)
percentage = percentage + percentageStep
print("\(result)")
}
while percentage <= rightPercentage {
result = ((rightPercentage - percentage) * middleNumber + (percentage - middlePercentage) * rightNumber)/(rightPercentage - middlePercentage)
percentage = percentage + percentageStep
print("\(result)")
}
You can see output of this code here
Update: Where the formula comes from?
When we say that "you have a value X from a range Xmin to XMax and you want to map it to a range Ymin to Ymax", what exactly do you mean by "map"? Usually what you want is that X splits the [Xmin, Xmax] range in the same proportion as Y splits the [Ymin, Ymax] range. Let's write that:
(X - Xmin)/(Xmax - Xmin) = (Y - Ymin)/(Ymax - Ymin)
If you try to solve it for Y you can see that:
(Y - Ymin) = (X - Xmin)/(Xmax - Xmin)*(Ymax - Ymin) =
= (Ymax * (X - Xmin) - Ymin * (X-Xmin))/(Xmax - Xmin)
so
Y = (Ymax * (X - Xmin) - Ymin * (X - Xmin))/(Xmax - Xmin) + Ymin =
= (Ymax * (X - Xmin) + Ymin * (Xmin - X) + Ymin * (Xmax - Xmin))/(Xmax - Xmin) =
= (Ymax * (X - Xmin) + Ymin * (Xmax - X))/(Xmax - Xmin)
which is exactly that formula.