kingdoms_game/mods/utils/mathutil.lua

--[[
Copyright (c) 2014, Robert 'Bobby' Zenz
All rights reserved.

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:

* Redistributions of source code must retain the above copyright notice, this
  list of conditions and the following disclaimer.

* Redistributions in binary form must reproduce the above copyright notice,
  this list of conditions and the following disclaimer in the documentation
  and/or other materials provided with the distribution.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
--]]


--- Various mathematical functions.
mathutil = {
	--- The maximum value a signed 8bit integer can have.
	SIGNED_8BIT_MAX = 2^7 - 1,
	
	--- The minimum value a signed 8bit integer can have.
	SIGNED_8BIT_MIN = -2^7,
	
	--- The maximum value a signed 16bit integer can have.
	SIGNED_16BIT_MAX = 2^15 - 1,
	
	--- The minimum value a signed 16bit integer can have.
	SIGNED_16BIT_MIN = -2^15,
	
	--- The maximum value a signed 32bit integer can have.
	SIGNED_32BIT_MAX = 2^31 - 1,
	
	--- The minimum value a signed 32bit integer can have.
	SIGNED_32BIT_MIN = -2^31,
	
	--- The maximum value an unsigned 8bit integer can have.
	UNSIGNED_8BIT_MAX = 2^8 - 1,
	
	--- The minimum value an unsigned 8bit integer can have.
	UNSIGNED_8BIT_MIN = 0,
	
	--- The maximum value an unsigned 16bit integer can have.
	UNSIGNED_16BIT_MAX = 2^16 - 1,
	
	--- The minimum value an unsigned 16bit integer can have.
	UNSIGNED_16BIT_MIN = 0,
	
	--- The maximum value an unsigned 32bit integer can have.
	UNSIGNED_32BIT_MAX = 2^32 - 1,
	
	--- The minimum value an unsigned 32bit integer can have.
	UNSIGNED_32BIT_MIN = 0
}


--- Uses the Cantor Pairing function on the two given values and returns
-- a unique integer for the given numbers.
--
-- @param a The first value.
-- @param b The second value.
-- @return A unique value for the two given values.
function mathutil.cantor_pairing(a, b)
	return ((a + b) * (a + b + 1)) / 2 + b
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

--- Gets the distance between the two given points or objects.
--
-- @param a The first object. Either a position or an ObjectRef.
-- @param b The second object. Either a position or an ObjectRef.
-- @return The distance between the two given points or objects.
function mathutil.distance(a, b)
	if type(a.getpos) == "function" then
		a = a:getpos()
	end
	
	if type(b.getpos) == "function" then
		b = b:getpos()
	end
	
	local distance_point = {
		x = math.abs(a.x - b.x),
		y = math.abs(a.y - b.y),
		z = math.abs(a.z - b.z)
	}
	
	local distance2d = math.sqrt(math.pow(distance_point.x, 2) + math.pow(distance_point.z, 2))
	local distance3d = math.sqrt(math.pow(distance2d, 2) + math.pow(distance_point.y, 2))
	
	return distance3d
end

--- Returns a vector indicating the general direction from a to b.
--
-- @param source_pos The source point, a vector.
-- @param target_pos The target point, a vector.
-- @return The vector containing the direction, either 1 for the positive
--         direction or -1 for the negative one.
function mathutil.direction(source_pos, target_pos)
	return {
		x = mathutil.sign(target_pos.x - source_pos.x),
		y = mathutil.sign(target_pos.y - source_pos.y),
		z = mathutil.sign(target_pos.z - source_pos.z)
	}
end

--- Gets the distance between two given points in the x/z plane.
--
-- @param a The first object. Either a position or an ObjectRef.
-- @param b The first object. Either a position or an ObjectRef.
-- @return The distance between the two given points or objects in
--         the x/z plane.
function mathutil.distance2d(a, b)
	if type(a.getpos) == "function" then
		a = a:getpos()
	end
	
	if type(b.getpos) == "function" then
		b = b:getpos()
	end
	
	local distance_point = {
		x = math.abs(a.x - b.x),
		z = math.abs(a.z - b.z)
	}
	
	return math.sqrt(math.pow(distance_point.x, 2) + math.pow(distance_point.z, 2))
end

--- Tests if the given value is within the given range.
--
-- @param value The value to test.
-- @param min The minimum value. It can also be a table with either two values,
--            the first being the minimum and the second being the maximum, or
--            with two named values, min and max.
-- @param max The maximum value. Not used if min is a table.
function mathutil.in_range(value, min, max)
	if type(min) == "table" then
		if min.min == nil then
			max = min[2]
			min = min[1]
		else
			max = min.max
			min = min.min
		end
	end
	
	if min > max then
		local temp = min
		min = max
		max = temp
	end
	
	return value >= min and value <= max
end

--- Checks if the given first two values intersect with the other given values.
--
-- @param min_a The first minimum value.
-- @param max_a The first maximum value.
-- @param min_b The second minimum value.
-- @param max_b The second maximum value.
-- @return true if the first values intersect with the second.
function mathutil.intersects(min_a, max_a, min_b, max_b)
	return mathutil.in_range(min_a, min_b, max_b)
		or mathutil.in_range(max_a, min_b, max_b)
		or (min_a < min_b
			and max_a > max_b)
end

--- Checks if the given first two positions intersect with the other given
-- positions.
--
-- @param min_a The first minimum value.
-- @param max_a The first maximum value.
-- @param min_b The second minimum value.
-- @param max_b The second maximum value.
-- @return true if the first positions intersect with the second.
function mathutil.intersects3d(min_a, max_a, min_b, max_b)
	return mathutil.intersects(min_a.x, min_b.x)
		and mathutil.intersects(min_a.z, min_b.z)
		and mathutil.intersects(min_a.y, min_b.y)
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

--- Rounds to the nearest number with the given decimal places.
--
-- @param value The value to round.
-- @param decimal_places Optional. The number of decimal places to round to,
--                       defaults to 0.
-- @return The rounded value.
function mathutil.round(value, decimal_places)
	decimal_places = decimal_places or 0
	
	local multiplicator = 10 ^ decimal_places
	return math.floor(value * multiplicator + 0.5) / multiplicator
end

--- Gets the sign of the given number.
--
-- @param number The number of which to get the sign.
-- @return 1 for a positive number, -1 for a negative one. Zero is considered
--         a positive number for this function, there for returns 1.
function mathutil.sign(number)
	if number >= 0 then
		return 1
	else
		return -1
	end
end