kingdoms_game/mods/utils/transform.lua

--[[
Copyright (c) 2014, Robert 'Bobby' Zenz
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--- Various mathematical functions for transforming values.
transform = {}


--- Performs a linear transform on the given value to transform the value
-- from the range -10/10 to 0/1.
--
-- @param value The value to transform.
-- @param new_min Optional. The minimum value for the new range, defaults to 0.
-- @param new_max Optional. The maximum value for the new range, defaults to 1.
-- @return The transformed value.
function transform.big_linear(value, new_min, new_max)
	return transform.linear(value, -10, 10, new_min, new_max)
end

--- Performs the given transformation on the given value with the peak in center
-- of the min and max values.
--
-- @param value The value to transform.
-- @param transformation The transformation function, assumed to accept five
--                       values.
-- @param min Optional. The original minimum value, defaults to -1.
-- @param max Optional. The original maximum value, default to 1.
-- @param new_min Optional. The minimum value for the new range, defaults to 0.
-- @param new_max Optional. The maximum value for the new range, defaults to 1.
-- @return The transformed value.
function transform.centered(value, transformation, min, max, new_min, new_max)
	min = min or -1
	max = max or 1
	
	local center = (min + max) / 2
	
	if value < center then
		return transformation(value, min, center, new_min, new_max)
	else
		return transformation(value, max, center, new_min, new_max)
	end
end

--- Performs a cosine transformation on the given value with the peak in center
-- of the min and max values.
--
-- @param value The value to transform.
-- @param min Optional. The original minimum value, defaults to -1.
-- @param max Optional. The original maximum value, default to 1.
-- @param new_min Optional. The minimum value for the new range, defaults to 0.
-- @param new_max Optional. The maximum value for the new range, defaults to 1.
-- @return The transformed value.
function transform.centered_cosine(value, min, max, new_min, new_max)
	return transform.centered(value, transform.cosine, min, max, new_min, new_max)
end

--- Performs a linear transformation on the given value with the peak in center
-- of the min and max values.
--
-- @param value The value to transform.
-- @param min Optional. The original minimum value, defaults to -1.
-- @param max Optional. The original maximum value, default to 1.
-- @param new_min Optional. The minimum value for the new range, defaults to 0.
-- @param new_max Optional. The maximum value for the new range, defaults to 1.
function transform.centered_linear(value, min, max, new_min, new_max)
	return transform.centered(value, transform.linear, min, max, new_min, new_max)
end

--- Performs a cosine transform on the given value to transform the value
-- from one range to another.
--
-- @param value The value to transform.
-- @param min Optional. The original minimum value of the range, defaults to -1.
-- @param max Optional. The original maximum value of the range, defaults to 1.
-- @param new_min Optional. The minimum value for the new range, defaults to 0.
-- @param new_max Optional. The maximum value for the new range, defaults to 1.
-- @return The transformed value.
function transform.cosine(value, min, max, new_min, new_max)
	min = min or -1
	max = max or 1
	
	if new_min == nil or new_max == nil then
		return interpolate.cosine((value - min) / (max - min))
	else
		return interpolate.cosine((value - min) / (max - min)) * (new_max - new_min) + new_min
	end
end

--- Performs a linear transform on the given value to transform the value
-- from one range to another.
--
-- @param value The value to transform.
-- @param min Optional. The original minimum value of the range, defaults to -1.
-- @param max Optional. The original maximum value of the range, defaults to 1.
-- @param new_min Optional. The minimum value for the new range, defaults to 0.
-- @param new_max Optional. The maximum value for the new range, defaults to 1.
-- @return The transformed value.
function transform.linear(value, min, max, new_min, new_max)
	min = min or -1
	max = max or 1
	
	if new_min == nil or new_max == nil then
		return (value - min) / (max - min)
	else
		return (value - min) / (max - min) * (new_max - new_min) + new_min
	end
end

--- Performs a linear transform on the given value to transform the value
-- from the range -1/1 to 0/1.
--
-- @param value The value to transform.
-- @param new_min Optional. The minimum value for the new range, defaults to 0.
-- @param new_max Optional. The maximum value for the new range, defaults to 1.
-- @return The transformed value.
function transform.small_linear(value, new_min, new_max)
	return transform.linear(value, -1, 1, new_min, new_max)
end