minetest-australopithecus-utils/utils/mathutil.lua

--[[
Copyright (c) 2014, Robert 'Bobby' Zenz
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--- Various mathemtical functions.
mathutil = {}


--- 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 mathutil.big_linear(value, new_min, new_max)
	return mathutil.linear(value, -10, 10, 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 mathutil.centered_linear(value, min, max, new_min, new_max)
	min = min or -1
	max = max or 1
	
	local center = (min + max) / 2
	
	if value < center then
		return mathutil.linear(value, min, center, new_min, new_max)
	else
		return mathutil.linear(value, max, center, new_min, new_max)
	end
end

--- Performs a cosine interpolation with the given offset between the given
-- min and max values.
--
-- @param offset The offset to get, should be between 0 and 1.
-- @param min Optional. The minimum value of the range, defaults to 0.
-- @param max Optional. The maximum value of the range, defaults to 1.
-- @return The interpolated value at the given offset.
function mathutil.cosine(offset, min, max)
	local value = (1 - math.cos(offset * math.pi)) / 2
	
	if min ~= nil and max ~= nil then
		return min * (1 - value) + max * value
	else
		return value
	end
end

--- Clamps one value to the given minimum/maximum values. Defaults to
-- 0 to 1 if min/max are omitted.
--
-- @param value The value to clamp.
-- @param min Optional. The minimum value, defaults to 0.
-- @param max Optional. The masximum value, defaults to 1.
-- @return The value clamped to the given range.
function mathutil.clamp(value, min, max)
	if min == nil or max == nil then
		return math.min(math.max(value, -1), 1)
	else
		return math.min(math.max(value, min), max)
	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 mathutil.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

--- Gets the next lower prime from the given number.
--
-- @param number The number.
-- @return The next lower prime.
function mathutil.next_lower_prime(number)
	for lower = number, 0, -1 do
		if (lower <= 2 or math.fmod(lower, 2) ~= 0)
			and (lower <= 3 or math.fmod(lower, 3) ~= 0)
			and (lower <= 5 or math.fmod(lower, 5) ~= 0)
			and (lower <= 7 or math.fmod(lower, 7) ~= 0) then
			
			return lower
		end	
	end
	
	return 0
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 mathutil.small_linear(value, new_min, new_max)
	return mathutil.linear(value, -1, 1, new_min, new_max)
end