mirror of https://gitea.it/1414codeforge/gear
[spec/*,*] Split library in submodules.
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--- General stateless utility algorithms
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--
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-- @module gear.algo
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-- @copyright 2022 The DoubleFourteen Code Forge
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-- @author Lorenzo Cogotti
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local floor = math.floor
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local min, max = math.min, math.max
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local algo = {}
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--- Clamp x within range [a,b] (where b >= a).
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--
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-- @param x (number) value to clamp.
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-- @param a (number) interval lower bound (inclusive).
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-- @param b (number) interval upper bound (includive).
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-- @return (number) clamped value.
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function algo.clamp(x, a, b) return min(max(x, a), b) end
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--- Fast remove from array.
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--
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-- Replace 'array[i]' with last array's element and
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-- discard array's tail.
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function algo.removefast(array, i)
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local n = #array
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array[i] = array[n] -- NOP if i == n
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array[n] = nil
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end
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local function lt(a, b) return a < b end
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--- Sort array using Insertion Sort - O(n^2).
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--
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-- Provides the most basic sorting algorithm around.
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-- Performs better than regular table.sort() for small arrays
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-- (~100 elements).
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--
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-- @param array (table) array to be sorted.
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-- @param less (function|nil) comparison function, takes 2 arguments,
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-- returns true if its first argument is less than its second argument, false otherwise.
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-- Defaults to operator <.
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function algo.insertionsort(array, less)
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less = less or lt
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for i = 2,#array do
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local val = array[i]
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local j = i
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while j > 1 and less(val, array[j-1]) do
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array[j] = array[j-1]
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j = j - 1
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end
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array[j] = val
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end
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end
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--- Binary search last element where
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-- what <= array[i] - also known as lower bound.
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--
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-- @param array (table) an array sorted according to the less function.
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-- @param what the comparison argument.
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-- @param less (function|nil) sorting criterium, a function taking 2 arguments,
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-- returns true if the first argument is less than the second argument,
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-- false otherwise. Defaults to using the < operator.
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--
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-- @return (number) the greatest index i, where what <= array[i].
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-- If no such element exists, it returns an out of bounds index
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-- such that array[i] == nil.
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function algo.bsearchl(array, what, less)
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less = less or lt
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local lo, hi = 1, #array
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local ofs, mid = -1, hi
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while mid > 0 do
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mid = floor(hi / 2)
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-- array[lo+mid] <= what <-> what >= array[lo+mid]
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-- <-> not what < array[lo+mid]
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if not less(what, array[lo+mid]) then
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lo = lo + mid
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ofs = 0 -- at least one element where array[lo+mid] <= what
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end
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hi = hi - mid
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end
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return lo + ofs
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end
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--- Binary search first element where
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-- what >= array[i] - also known as upper bound.
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--
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-- @param array (array) an array sorted according to the less function.
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-- @param what the comparison argument.
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-- @param less (function|nil) sorting criterium, a function taking 2 arguments,
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-- returns true if the first argument is less than the second argument,
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-- false otherwise. Defaults to using the < operator.
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--
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-- @return (number) the smallest index i, where what >= array[i].
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-- If no such element exists, it returns an out of bounds index
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-- such that array[i] == nil.
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function algo.bsearchr(array, what, less)
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less = less or lt
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local lo, hi = 1, #array
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local ofs, mid = -1, hi
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while mid > 0 do
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mid = floor(hi / 2)
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-- array[lo+mid] >= what <-> not array[lo+mid] < what
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if not less(array[lo+mid], what) then
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ofs = 0
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else
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lo = lo + mid
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ofs = 1
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end
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hi = hi - mid
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end
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return lo + ofs
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end
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return algo
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@ -1,527 +1,21 @@
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--- LÖVE Utility Library
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--- LÖVE Utility Gear
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--
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-- Stateless general purpose functions and utilities.
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-- General purpose functions and utilities.
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-- Provides various basic functionality, including: general utility
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-- algorithms, linear algebra and simple bounds checking functions.
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-- Code is reasonably optimized for speed.
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--
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-- @module df-utils
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-- @module gear
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-- @copyright 2022 The DoubleFourteen Code Forge
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-- @author Lorenzo Cogotti
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local utils = {}
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local BASE = (...)..'.'
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local floor = math.floor
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local min, max = math.min, math.max
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local sin, cos = math.sin, math.cos
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local sqrt = math.sqrt
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--- Clamp x within range [a,b] (where b >= a).
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--
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-- @param x (number) value to clamp.
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-- @param a (number) interval lower bound (inclusive).
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-- @param b (number) interval upper bound (includive).
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-- @return (number) clamped value.
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function utils.clamp(x, a, b) return min(max(x, a), b) end
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--- Test whether a string starts with a prefix.
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function utils.startswith(s, prefix)
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return s:sub(1, #prefix) == prefix
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end
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--- Test whether a string ends with a trailing suffix.
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function utils.endswith(s, trailing)
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return trailing == "" or s:sub(-#trailing) == trailing
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end
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--- Merge table 'from' into table 'to'.
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--
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-- For every field in 'from', copy it to destination
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-- table 'to', whenever the same field is nil in that table.
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--
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-- The same process is applied recursively to sub-tables.
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function utils.mergetable(to, from)
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for k,v in pairs(from) do
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if to[k] == nil then
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to[k] = type(v) == 'table' and utils.mergetable({}, v) or v
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end
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end
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return to
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end
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--- Test whether 'obj' is an instance of a given class 'cls'.
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function utils.isinstance(obj, cls)
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repeat
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local m = getmetatable(obj)
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if m == cls then return true end
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obj = m
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until obj == nil
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return false
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end
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local function opless(a, b) return a < b end
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--- Sort array using Insertion Sort - O(n^2).
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--
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-- Provides the most basic sorting algorithm around.
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-- Performs better than regular table.sort() for small arrays
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-- (~100 elements).
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--
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-- @param array (table) array to be sorted.
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-- @param less (function|nil) comparison function, takes 2 arguments,
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-- returns true if its first argument is less than its second argument, false otherwise.
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-- Defaults to operator <.
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function utils.insertionsort(array, less)
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less = less or opless
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for i = 2,#array do
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local val = array[i]
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local j = i
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while j > 1 and less(val, array[j-1]) do
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array[j] = array[j-1]
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j = j - 1
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end
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array[j] = val
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end
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end
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--- Binary search last element where
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-- what <= array[i] - also known as lower bound.
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--
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-- @param array (table) an array sorted according to the less function.
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-- @param what the comparison argument.
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-- @param less (function|nil) sorting criterium, a function taking 2 arguments,
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-- returns true if the first argument is less than the second argument,
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-- false otherwise. Defaults to using the < operator.
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--
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-- @return (number) the greatest index i, where what <= array[i].
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-- If no such element exists, it returns an out of bounds index
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-- such that array[i] == nil.
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function utils.bsearchl(array, what, less)
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less = less or opless
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local lo, hi = 1, #array
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local ofs, mid = -1, hi
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while mid > 0 do
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mid = floor(hi / 2)
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-- array[lo+mid] <= what <-> what >= array[lo+mid]
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-- <-> not what < array[lo+mid]
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if not less(what, array[lo+mid]) then
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lo = lo + mid
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ofs = 0 -- at least one element where array[lo+mid] <= what
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end
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hi = hi - mid
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end
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return lo + ofs
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end
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--- Binary search first element where
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-- what >= array[i] - also known as upper bound.
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--
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-- @param array (array) an array sorted according to the less function.
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-- @param what the comparison argument.
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-- @param less (function|nil) sorting criterium, a function taking 2 arguments,
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-- returns true if the first argument is less than the second argument,
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-- false otherwise. Defaults to using the < operator.
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--
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-- @return (number) the smallest index i, where what >= array[i].
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-- If no such element exists, it returns an out of bounds index
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-- such that array[i] == nil.
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function utils.bsearchr(array, what, less)
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less = less or opless
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local lo, hi = 1, #array
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local ofs, mid = -1, hi
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while mid > 0 do
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mid = floor(hi / 2)
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-- array[lo+mid] >= what <-> not array[lo+mid] < what
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if not less(array[lo+mid], what) then
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ofs = 0
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else
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lo = lo + mid
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ofs = 1
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end
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hi = hi - mid
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end
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return lo + ofs
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end
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--- Fast remove from array.
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--
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-- Replace 'array[i]' with last array's element and
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-- discard array's tail.
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function utils.removefast(array, i)
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local n = #array
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array[i] = array[n] -- NOP if i == n
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array[n] = nil
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end
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--- Vector dot product.
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function utils.dot(x1,y1, x2,y2)
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return x1*x2 + y1*y2
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end
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--- utils.dot() equivalent for 3D vector.
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function utils.dot3(x1,y1,z1, x2,y2,z2)
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return x1*x2 + y1*y2 + z1*z2
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end
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--- Vector squared length.
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function utils.vecsqrlen(x,y)
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return x*x + y*y -- utils.dot(x,y, x,y)
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end
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--- utils.vecsqrlen() equivalent for 3D vectors.
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function utils.vecsqrlen3(x,y,z)
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return x*x + y*y + z*z
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end
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--- Vector length.
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function utils.veclen(x,y)
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return sqrt(x*x + y*y) -- sqrt(utils.vecsqrlen(x,y))
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end
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--- utils.veclen() equivalent for 3D vectors.
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function utils.veclen3(x,y,z)
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return sqrt(x*x + y*y + z*z)
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end
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--- Vector addition (inline this function when possible).
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function utils.vecadd(x1,y1, x2,y2)
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return x1+x2, y1+y2
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end
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--- utils.vecadd() equivalent for 3D vectors.
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function utils.vecadd3(x1,y1,z1, x2,y2,z2)
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return x1+x2, y1+y2, z1+z2
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end
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--- Vector subtraction (inline this function when possible).
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function utils.vecsub(x1,y1, x2,y2)
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return x1-x2, y1-y2
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end
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--- utils.vecsub() equivalent for 3D vectors.
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function utils.vecsub3(x1,y1,z1, x2,y2,z2)
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return x1-x2, y1-y2, z1-z2
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end
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--- Vector scale (inline this function when possible).
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function utils.vecscale(x,y, s)
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return x*s, y*s
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end
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--- utils.vecscale() equivalent for 3D vectors.
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function utils.vecscale3(x,y,z, s)
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return x*s, y*s, z*s
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end
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--- Vector division by scalar (inline this function when possible).
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function utils.vecdiv(x,y, s)
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return x/s, y/s
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end
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--- utils.vecdiv() equivalent for 3D vectors.
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function utils.vecdiv3(x,y,z, s)
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return x/s, y/s, z/s
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end
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--- Vector fused multiply add (inline this function when possible).
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--
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-- @return the first vector, added to the second vector scaled by a factor.
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function utils.vecma(x1,y1, s, x2,y2)
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return x1 + x2*s, y1 + y2*s
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end
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--- utils.vecma() equivalent for 3D vectors.
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function utils.vecma3(x1,y1,z1, s, x2,y2,z2)
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return x1 + x2*s, y1 + y2*s, z1 + z2*s
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end
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--- Test vectors for equality with optional epsilon.
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function utils.veceq(x1,y1, x2,y2, eps)
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local abs = math.abs
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eps = eps or 0.001
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return abs(x1-x2) < eps and abs(y1-y2) < eps
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end
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--- utils.veceq() equivalent for 3D vectors.
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function utils.veceq3(x1,y1,z1, x2,y2,z2, eps)
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local abs = math.abs
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eps = eps or 0.001
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return abs(x1-x2) < eps and
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abs(y1-y2) < eps and
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abs(z1-z2) < eps
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end
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--- Normalize vector.
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--
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-- @return (x,y, len) normalized components and vector's original length.
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function utils.normalize(x,y)
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local len = sqrt(x*x + y*y) -- utils.veclen(x,y)
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if len < 1.0e-4 then
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return x,y, 0
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end
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return x / len, y / len, len
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end
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--- utils.normalize() equivalent for 3D vectors.
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function utils.normalize3(x,y,z)
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local len = sqrt(x*x + y*y + z*z)
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if len < 1.0e-4 then
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return x,y,z, 0
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end
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return x / len, y / len, z / len, len
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end
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--- Calculate the squared distance between two vectors/points.
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function utils.sqrdist(x1,y1, x2,y2)
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local dx,dy = x2-x1, y2-y1
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return dx*dx, dy*dy -- utils.vecsqrlen(dx,dy)
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end
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--- utils.sqrdist() equivalent for 3D vectors.
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function utils.sqrdist3(x1,y1,z1, x2,y2,z2)
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local dx,dy,dz = x2-x1, y2-y1, z2-z1
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return dx*dx, dy*dy, dz*dz
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end
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--- Calculate the distance between two vectors/points.
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function utils.distance(x1,y1, x2,y2)
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local dx,dy = x2-x1, y2-y1
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return sqrt(dx*dx + dy*dy) -- sqrt(utils.sqrdist(x1,y1, x2,y2))
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end
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--- utils.distance() equivalent for 3D vectors/points.
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function utils.distance3(x1,y1,z1, x2,y2,z2)
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local dx,dy,dz = x2-x1, y2-y1, z2-z1
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return sqrt(dx*dx + dy*dy + dz*dz)
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end
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--- Calculate and return the union of two rectangles.
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function utils.rectunion(x1,y1,w1,h1, x2,y2,w2,h2)
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local xw1,yh1, xw2,yh2
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if w1 < 0 or h1 < 0 then
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local huge = math.huge
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x1,y1,xw1,yh1 = huge,huge,-huge,-huge
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else
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xw1,yh1 = x1 + w1,y1 + h1
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end
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if w2 < 0 or h2 < 0 then
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local huge = math.huge
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x2,y2,xw2,yh2 = huge,huge,-huge,-huge
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else
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xw2,yh2 = x2 + w2,y2 + h2
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end
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x1 = min(x1, x2)
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y1 = min(y1, y2)
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xw1 = max(xw1, xw2)
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xh1 = max(xh1, xh2)
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return x1, y1, xw1 - x1, yh1 - y1
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end
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--- Extend rectangle to include a point.
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function utils.rectexpand(x,y,w,h, px,py)
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if w < 0 or h < 0 then
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return px,py,0,0
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end
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local xw, yh
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x = min(x, px)
|
||||
y = min(y, py)
|
||||
xw = max(x+w, px)
|
||||
yh = max(y+h, py)
|
||||
|
||||
return x, y, xw-x, yh-y
|
||||
end
|
||||
|
||||
--- Calculate and return the intersection between two rectangles.
|
||||
function utils.rectintersection(x1,y1,w1,h1, x2,y2,w2,h2)
|
||||
if w1 < 0 or h1 < 0 then
|
||||
return x1,y1,w1,h1
|
||||
elseif w2 < 0 or h2 < 0 then
|
||||
return x2,y2,w2,h2
|
||||
end
|
||||
|
||||
local xw1,yh1 = x1+w1, y1+h1
|
||||
local xw2,yh2 = x2+w2, y2+h2
|
||||
|
||||
x1 = max(x1, x2)
|
||||
y1 = max(y1, y2)
|
||||
xw1 = min(xw1, xw2)
|
||||
yh1 = min(yh1, yh2)
|
||||
return x1,y1, xw1-x1,yh1-y1
|
||||
end
|
||||
|
||||
--- Test whether point (x,y) lies inside a rectangle.
|
||||
function utils.pointinrect(x,y, rx,ry,rw,rh)
|
||||
return x >= rx and y >= ry and x-rx <= rw and y-ry <= rh
|
||||
end
|
||||
|
||||
--- Test whether the first rectangle lies inside the second.
|
||||
function utils.rectinside(x1,y1,w1,h1, x2,y2,w2,h2)
|
||||
return (x1 >= x2 and y1 >= y2 and w1 <= w2 and h1 <= h2 and w2 >= 0 and h2 >= 0)
|
||||
or ((w1 < 0 or h1 < 0) and (w2 >= 0 and h2 >= 0))
|
||||
end
|
||||
|
||||
--- Test two rectangles for equality with optional epsilon.
|
||||
function utils.recteq(x1,y1,w1,h1, x2,y2,w2,h2, eps)
|
||||
local abs = math.abs
|
||||
|
||||
eps = eps or 0.007
|
||||
|
||||
return (abs(x1 - x2) <= eps and
|
||||
abs(y1 - y2) <= eps and
|
||||
abs(w1 - w2) <= eps and
|
||||
abs(h1 - h2) <= eps)
|
||||
or ((w1 < 0 or h1 < 0) and (w2 < 0 or h2 < 0))
|
||||
end
|
||||
|
||||
--- Test whether a rectangle is empty.
|
||||
function utils.rectempty(x,y,w,h)
|
||||
return w < 0 or h < 0
|
||||
end
|
||||
|
||||
local function rotatesincos(px,py, sina,cosa, ox,oy)
|
||||
return ox + cosa*px - sina*py,
|
||||
oy + sina*px + cosa*py
|
||||
end
|
||||
|
||||
--- Rotate point (px,py) around (ox,oy) about rot radians.
|
||||
function utils.rotatepoint(px,py, rot, ox,oy)
|
||||
ox = ox or 0
|
||||
oy = oy or 0
|
||||
|
||||
local sina,cosa = sin(rot), cos(rot)
|
||||
|
||||
return rotatesincos(px,py, sina,cosa, ox,oy)
|
||||
end
|
||||
|
||||
--- Rotate an axis-aligned rectangle around (ox,oy) about rot radians,
|
||||
-- and return the result's minimum enclosing
|
||||
-- axis-aligned rectangle.
|
||||
--
|
||||
-- NOTE: This causes precision loss, possibly generating
|
||||
-- larger bounds than needed for the rotated geometry
|
||||
-- Don't use this function repeatedly on the same bounds.
|
||||
function utils.rotatebounds(bx,by,bw,bh, rot, ox,oy)
|
||||
if bw < 0 or bh < 0 then
|
||||
return bx,by,bw,bh
|
||||
end
|
||||
|
||||
ox = ox or 0
|
||||
oy = oy or 0
|
||||
|
||||
local sina,cosa = sin(rot), cos(rot)
|
||||
|
||||
local x1,y1 = rotatesincos(bx, by, sina,cosa, ox,oy)
|
||||
local x2,y2 = rotatesincos(bx+bw, by, sina,cosa, ox,oy)
|
||||
local x3,y3 = rotatesincos(bx+bw, by+bh, sina,cosa, ox,oy)
|
||||
local x4,y4 = rotatesincos(bx, by+bh, sina,cosa, ox,oy)
|
||||
|
||||
local rx = min(min(min(x1, x2), x3), x4)
|
||||
local ry = min(min(min(y1, y2), y3), y4)
|
||||
local rxw = max(max(max(x1, x2), x3), x4)
|
||||
local ryh = max(max(max(y1, y2), y3), y4)
|
||||
|
||||
return rx,ry, rxw-rx,ryh-ry
|
||||
end
|
||||
|
||||
--- Transform world coordinates to screen coordinates.
|
||||
--
|
||||
-- @param x (number) World coordinate X.
|
||||
-- @param y (number) World coordinate Y.
|
||||
-- @param vx (number|nil) Point of view X coordinate, defaults to w/2.
|
||||
-- @param vy (number|nil) Point of view Y coordinate, defaults to h/2.
|
||||
-- @param rot (number|nil) View rotation in radians, defaults to 0.
|
||||
-- @param scale (number|nil) View scale (zoom), defaults to 1.
|
||||
-- @param left (number|nil) Viewport left corner, defaults to 0.
|
||||
-- @param top (number|nil) Viewport top corner, defaults to 0.
|
||||
-- @param w (number|nil) Viewport width, defaults to love.graphics.getWidth().
|
||||
-- @param h (number|nil) Viewport height, defaults to love.graphics.getHeight().
|
||||
--
|
||||
-- @return (x,y) Transformed to screen coordinates according to
|
||||
-- viewport and offset.
|
||||
function utils.toscreencoords(x,y, vx,vy, rot, scale, left,top, w,h)
|
||||
left,top = left or 0, top or 0
|
||||
w,h = w or love.graphics.getWidth(), h or love.graphics.getHeight()
|
||||
|
||||
local halfw,halfh = w/2, h/2
|
||||
|
||||
vx,vy = vx or halfw, vy or halfh
|
||||
rot = rot or 0
|
||||
scale = scale or 1
|
||||
|
||||
local sina,cosa = sin(rot), cos(rot)
|
||||
|
||||
x,y = x - vx, y - vy
|
||||
x,y = cosa*x - sina*y, sina*x + cosa*y
|
||||
return x*scale + halfw + left, y*scale + halfh + top
|
||||
end
|
||||
|
||||
--- Transform screen coordinates to world coordinates.
|
||||
--
|
||||
-- @param x (number) Screen coordinate X.
|
||||
-- @param y (number) Screen coordinate Y.
|
||||
-- @param vx (number|nil) Point of view X coordinate, defaults to w/2.
|
||||
-- @param vy (number|nil) Point of view Y coordinate, defaults to h/2.
|
||||
-- @param rot (number|nil) View rotation in radians, defaults to 0.
|
||||
-- @param scale (number|nil) View scale (zoom), defaults to 1.
|
||||
-- @param left (number|nil) Viewport left corner, defaults to 0.
|
||||
-- @param top (number|nil) Viewport top corner, defaults to 0.
|
||||
-- @param w (number|nil) Viewport width, defaults to love.graphics.getWidth().
|
||||
-- @param h (number|nil) Viewport height, defaults to love.graphics.getHeight().
|
||||
--
|
||||
-- @return (x,y) Transformed to world coordinates according to
|
||||
-- viewport and offset.
|
||||
function utils.toworldcoords(x,y, vx,vy, rot, scale, left,top,w,h)
|
||||
left, top = left or 0, top or 0
|
||||
w,h = w or love.graphics.getWidth(), h or love.graphics.getHeight()
|
||||
|
||||
local halfw,halfh = w/2, h/2
|
||||
|
||||
vx,vy = vx or halfw, vy or halfh
|
||||
rot = rot or 0
|
||||
scale = scale or 1
|
||||
|
||||
local sina,cosa = sin(-rot), cos(-rot)
|
||||
|
||||
x,y = (x - halfw - left) / scale, (y - halfh - top) / scale
|
||||
x,y = cosa*x - sina*y, sina*x + cosa*y
|
||||
return x+vx, y+vy
|
||||
end
|
||||
|
||||
|
||||
return utils
|
||||
return {
|
||||
algo = require(BASE..'algo'),
|
||||
meta = require(BASE..'meta'),
|
||||
rect = require(BASE..'rect'),
|
||||
strings = require(BASE..'strings'),
|
||||
vec = require(BASE..'vec')
|
||||
}
|
||||
|
||||
@ -0,0 +1,38 @@
|
||||
--- Functions dealing with metatables and tables merging.
|
||||
--
|
||||
-- @module gear.meta
|
||||
-- @copyright 2022 The DoubleFourteen Code Forge
|
||||
-- @author Lorenzo Cogotti
|
||||
|
||||
local meta = {}
|
||||
|
||||
|
||||
--- Test whether 'obj' is an instance of a given class 'cls'.
|
||||
function meta.isinstance(obj, cls)
|
||||
repeat
|
||||
local m = getmetatable(obj)
|
||||
if m == cls then return true end
|
||||
|
||||
obj = m
|
||||
until obj == nil
|
||||
|
||||
return false
|
||||
end
|
||||
|
||||
--- Merge table 'from' into table 'to'.
|
||||
--
|
||||
-- For every field in 'from', copy it to destination
|
||||
-- table 'to', whenever the same field is nil in that table.
|
||||
--
|
||||
-- The same process is applied recursively to sub-tables.
|
||||
function meta.mergetable(to, from)
|
||||
for k,v in pairs(from) do
|
||||
if to[k] == nil then
|
||||
to[k] = type(v) == 'table' and meta.mergetable({}, v) or v
|
||||
end
|
||||
end
|
||||
|
||||
return to
|
||||
end
|
||||
|
||||
return meta
|
||||
@ -0,0 +1,135 @@
|
||||
--- Axis-aligned rectangles.
|
||||
--
|
||||
-- Function for basic bounding rectangles building and testing.
|
||||
--
|
||||
-- @module gear.rect
|
||||
-- @copyright 2022 The DoubleFourteen Code Forge
|
||||
-- @author Lorenzo Cogotti
|
||||
|
||||
local rotatesincos = require((...):gsub('rect', '')..'vec').rotatesincos
|
||||
|
||||
local min, max = math.min, math.max
|
||||
local abs = math.abs
|
||||
|
||||
local rect = {}
|
||||
|
||||
|
||||
--- Extend rectangle to include a point.
|
||||
function rect.expand(x,y,w,h, px,py)
|
||||
if w < 0 or h < 0 then
|
||||
return px,py,0,0
|
||||
end
|
||||
|
||||
local xw, yh
|
||||
x = min(x, px)
|
||||
y = min(y, py)
|
||||
xw = max(x+w, px)
|
||||
yh = max(y+h, py)
|
||||
|
||||
return x, y, xw-x, yh-y
|
||||
end
|
||||
|
||||
--- Calculate and return the union of two rectangles.
|
||||
function rect.union(x1,y1,w1,h1, x2,y2,w2,h2)
|
||||
local xw1,yh1, xw2,yh2
|
||||
|
||||
if w1 < 0 or h1 < 0 then
|
||||
local huge = math.huge
|
||||
|
||||
x1,y1,xw1,yh1 = huge,huge,-huge,-huge
|
||||
else
|
||||
xw1,yh1 = x1 + w1,y1 + h1
|
||||
end
|
||||
if w2 < 0 or h2 < 0 then
|
||||
local huge = math.huge
|
||||
|
||||
x2,y2,xw2,yh2 = huge,huge,-huge,-huge
|
||||
else
|
||||
xw2,yh2 = x2 + w2,y2 + h2
|
||||
end
|
||||
|
||||
x1 = min(x1, x2)
|
||||
y1 = min(y1, y2)
|
||||
xw1 = max(xw1, xw2)
|
||||
xh1 = max(xh1, xh2)
|
||||
|
||||
return x1, y1, xw1 - x1, yh1 - y1
|
||||
end
|
||||
|
||||
--- Calculate and return the intersection between two rectangles.
|
||||
function rect.intersection(x1,y1,w1,h1, x2,y2,w2,h2)
|
||||
if w1 < 0 or h1 < 0 then
|
||||
return x1,y1,w1,h1
|
||||
elseif w2 < 0 or h2 < 0 then
|
||||
return x2,y2,w2,h2
|
||||
end
|
||||
|
||||
local xw1,yh1 = x1+w1, y1+h1
|
||||
local xw2,yh2 = x2+w2, y2+h2
|
||||
|
||||
x1 = max(x1, x2)
|
||||
y1 = max(y1, y2)
|
||||
xw1 = min(xw1, xw2)
|
||||
yh1 = min(yh1, yh2)
|
||||
return x1,y1, xw1-x1,yh1-y1
|
||||
end
|
||||
|
||||
--- Rotate rectangle around (ox,oy) about rot radians,
|
||||
-- and return the result's minimum enclosing
|
||||
-- axis-aligned rectangle.
|
||||
--
|
||||
-- NOTE: This causes precision loss, possibly generating
|
||||
-- larger bounds than needed for the rotated geometry
|
||||
-- Don't use this function repeatedly on the same bounds.
|
||||
function rect.rotate(rx,ry,rw,rh, rot, ox,oy)
|
||||
if rw < 0 or rh < 0 then
|
||||
return rx,ry,rw,rh
|
||||
end
|
||||
|
||||
ox = ox or 0
|
||||
oy = oy or 0
|
||||
|
||||
local sina,cosa = sin(rot),cos(rot)
|
||||
|
||||
local x1,y1 = rotatesincos(rx, ry, sina,cosa, ox,oy)
|
||||
local x2,y2 = rotatesincos(rx+rw, ry, sina,cosa, ox,oy)
|
||||
local x3,y3 = rotatesincos(rx+rw, ry+rh, sina,cosa, ox,oy)
|
||||
local x4,y4 = rotatesincos(rx, ry+rh, sina,cosa, ox,oy)
|
||||
|
||||
local rxw, rxh
|
||||
rx = min(min(min(x1, x2), x3), x4)
|
||||
ry = min(min(min(y1, y2), y3), y4)
|
||||
rxw = max(max(max(x1, x2), x3), x4)
|
||||
ryh = max(max(max(y1, y2), y3), y4)
|
||||
|
||||
return rx,ry, rxw-rx,ryh-ry
|
||||
end
|
||||
|
||||
--- Test whether point (x,y) lies inside a rectangle.
|
||||
function rect.pointinside(x,y, rx,ry,rw,rh)
|
||||
return x >= rx and y >= ry and x-rx <= rw and y-ry <= rh
|
||||
end
|
||||
|
||||
--- Test whether the first rectangle lies inside the second.
|
||||
function rect.rectinside(x1,y1,w1,h1, x2,y2,w2,h2)
|
||||
return (x1 >= x2 and y1 >= y2 and w1 <= w2 and h1 <= h2 and w2 >= 0 and h2 >= 0)
|
||||
or ((w1 < 0 or h1 < 0) and (w2 >= 0 and h2 >= 0))
|
||||
end
|
||||
|
||||
--- Test two rectangles for equality with optional epsilon.
|
||||
function rect.eq(x1,y1,w1,h1, x2,y2,w2,h2, eps)
|
||||
eps = eps or 0.007
|
||||
|
||||
return (abs(x1 - x2) <= eps and
|
||||
abs(y1 - y2) <= eps and
|
||||
abs(w1 - w2) <= eps and
|
||||
abs(h1 - h2) <= eps)
|
||||
or ((w1 < 0 or h1 < 0) and (w2 < 0 or h2 < 0))
|
||||
end
|
||||
|
||||
--- Test whether a rectangle is empty.
|
||||
function rect.isempty(x,y,w,h)
|
||||
return w < 0 or h < 0
|
||||
end
|
||||
|
||||
return rect
|
||||
@ -0,0 +1,216 @@
|
||||
require 'busted.runner'()
|
||||
|
||||
describe("gear", function()
|
||||
|
||||
setup(function()
|
||||
gear = require 'init'
|
||||
algo = gear.algo
|
||||
rect = gear.rect
|
||||
math = require 'math'
|
||||
end)
|
||||
|
||||
describe("insertion sort #sort", function()
|
||||
local insertionsort = algo.insertionsort
|
||||
|
||||
it("sorts arrays", function()
|
||||
local elems = {}
|
||||
local expect = {}
|
||||
|
||||
for n = 2,512 do
|
||||
for i = 1,n do
|
||||
elems[i] = math.random(-32768, 32767)
|
||||
expect[i] = elems[i]
|
||||
end
|
||||
|
||||
table.sort(expect)
|
||||
insertionsort(elems)
|
||||
|
||||
assert.are.same(expect, elems)
|
||||
end
|
||||
end)
|
||||
|
||||
it("has no effect on single element array", function()
|
||||
|
||||
for i = 1,10 do
|
||||
local val = (math.random() - 0.5) * 1024
|
||||
local expect = { val }
|
||||
local elems = { val }
|
||||
|
||||
insertionsort(elems)
|
||||
|
||||
assert.are.same(expect, elems)
|
||||
end
|
||||
end)
|
||||
|
||||
it("does nothing on empty array", function()
|
||||
local expect = {}
|
||||
local elems = {}
|
||||
|
||||
insertionsort(elems)
|
||||
|
||||
assert.are.same(expect, elems)
|
||||
end)
|
||||
end)
|
||||
|
||||
describe("binary search #bsearch", function()
|
||||
local bsearchl = algo.bsearchl
|
||||
local bsearchr = algo.bsearchr
|
||||
|
||||
it("behaves properly on empty arrays", function()
|
||||
local empty = {}
|
||||
|
||||
local idx = bsearchr(empty, 1)
|
||||
assert.is_true(empty[idx] == nil)
|
||||
|
||||
idx = bsearchl(empty, 1)
|
||||
assert.is_true(empty[idx] == nil)
|
||||
end)
|
||||
|
||||
it("finds elements within sorted arrays", function()
|
||||
local dims = { 1, 2, 64, 512, 1024 }
|
||||
|
||||
for _,n in ipairs(dims) do
|
||||
local elems = {}
|
||||
|
||||
for i = 1,n do
|
||||
elems[#elems+1] = ((math.random() - 0.5) * 4096)
|
||||
end
|
||||
|
||||
local mustfind = {}
|
||||
for i = 1,10 do
|
||||
mustfind[#mustfind+1] = elems[math.random(1,#elems)]
|
||||
end
|
||||
|
||||
local mustnotfind = {
|
||||
4097,
|
||||
-4097,
|
||||
-math.huge,
|
||||
math.huge,
|
||||
16386,
|
||||
-16386
|
||||
}
|
||||
|
||||
table.sort(elems)
|
||||
|
||||
for _,v in ipairs(mustfind) do
|
||||
local idx = bsearchl(elems, v)
|
||||
assert.equal(v, elems[idx])
|
||||
assert.is_false(elems[idx+1] ~= nil and elems[idx+1] <= v)
|
||||
|
||||
idx = bsearchr(elems, v)
|
||||
assert.equal(v, elems[idx])
|
||||
assert.is_false(elems[idx+1] ~= nil and elems[idx+1] <= v)
|
||||
end
|
||||
for _,v in ipairs(mustnotfind) do
|
||||
local idx = bsearchl(elems, v)
|
||||
assert.not_equal(v, elems[idx])
|
||||
if v < elems[1] then
|
||||
assert.is_true(elems[idx] == nil)
|
||||
else
|
||||
assert.is_true(elems[idx] <= v)
|
||||
end
|
||||
|
||||
idx = bsearchr(elems, v)
|
||||
assert.not_equal(v, elems[idx])
|
||||
if v > elems[#elems] then
|
||||
assert.is_true(elems[idx] == nil)
|
||||
else
|
||||
assert.is_true(elems[idx] >= v)
|
||||
end
|
||||
end
|
||||
end
|
||||
end)
|
||||
end)
|
||||
|
||||
describe("rect #bounds", function()
|
||||
local bigreal = 9999999.0
|
||||
local min,max = math.min, math.max
|
||||
local pointinrect = rect.pointinside
|
||||
local rectempty = rect.isempty
|
||||
local recteq = rect.eq
|
||||
local rectexpand = rect.expand
|
||||
local rectinside = rect.rectinside
|
||||
local rectintersection = rect.intersection
|
||||
local rectunion = rect.union
|
||||
|
||||
it("is empty if its dimensions are negative", function()
|
||||
assert.is_true(rectempty(0,0,-1,-1))
|
||||
assert.is_true(rectempty(bigreal,bigreal,-bigreal,-bigreal))
|
||||
assert.is_true(rectempty(-bigreal,-bigreal,-bigreal,-bigreal))
|
||||
assert.is_true(rectempty(0,0,bigreal,-1))
|
||||
assert.is_true(rectempty(0,0,0,-1))
|
||||
assert.is_true(rectempty(0,0,-1,bigreal))
|
||||
assert.is_true(rectempty(0,0,-1,0))
|
||||
|
||||
assert.is_false(rectempty(0,0,0,0))
|
||||
assert.is_false(rectempty(0,0,-0,0))
|
||||
assert.is_false(rectempty(bigreal,bigreal,bigreal,bigreal))
|
||||
end)
|
||||
it("doesn't contain anything if empty", function()
|
||||
local x,y,w,h = 0,0,-1,-1
|
||||
|
||||
assert.is_false(rectinside(0,0,0,0, x,y,w,h))
|
||||
assert.is_false(rectinside(x,y,w,h, x,y,w,h))
|
||||
assert.is_false(rectinside(0,0,bigreal,bigreal, x,y,w,h))
|
||||
assert.is_false(rectinside(0,0,-bigreal,-bigreal, x,y,w,h))
|
||||
end)
|
||||
it("always contains empty rect if non-empty", function()
|
||||
assert.is_true(rectinside(0,0,-1,-1, 0,0,0,0))
|
||||
assert.is_true(rectinside(bigreal,bigreal,-bigreal,-bigreal, 0,0,0,0))
|
||||
assert.is_true(rectinside(bigreal,bigreal,bigreal,-bigreal, 0,0,0,0))
|
||||
assert.is_true(rectinside(bigreal,bigreal,-bigreal,bigreal, 0,0,0,0))
|
||||
assert.is_true(rectinside(bigreal,bigreal,-1.0e-5,bigreal, 0,0,0,0))
|
||||
end)
|
||||
it("may contain a single point", function()
|
||||
for i,pt in ipairs({{0,0}, {bigreal,bigreal}, {-bigreal,-bigreal}}) do
|
||||
local px,py = pt[1], pt[2]
|
||||
local x,y,w,h = 0,0,-1,-1
|
||||
|
||||
x,y,w,h = rectexpand(x,y,w,h, px,py)
|
||||
assert.is_false(rectempty(x,y,w,h))
|
||||
assert.is_true(pointinrect(px,py, x,y,w,h))
|
||||
assert.is_true(recteq(x,y,w,h, px,py,0,0))
|
||||
end
|
||||
end)
|
||||
it("may expand arbitrarily to contain more points", function()
|
||||
local points = {}
|
||||
|
||||
local xmin,ymin = math.huge, math.huge
|
||||
local xmax,ymax = -math.huge,-math.huge
|
||||
for i = 1,16535 do
|
||||
local x = (math.random() - 0.5) * 50
|
||||
local y = (math.random() - 0.5) * 50
|
||||
|
||||
points[#points+1] = { x, y }
|
||||
xmin = min(xmin, x)
|
||||
ymin = min(ymin, y)
|
||||
xmax = max(xmax, x)
|
||||
ymax = max(ymax, y)
|
||||
end
|
||||
|
||||
local x,y,w,h = 0,0,-1,-1
|
||||
for i,pt in ipairs(points) do
|
||||
local px,py = pt[1], pt[2]
|
||||
x,y,w,h = rectexpand(x,y,w,h, px,py)
|
||||
|
||||
assert.is_true(pointinrect(px,py, x,y,w,h))
|
||||
end
|
||||
|
||||
local ex,ey,ew,eh = xmin,ymin, xmax-xmin,ymax-ymin
|
||||
assert.is_false(rectempty(x,y,w,h))
|
||||
assert.is_true(recteq(x,y,w,h, ex,ey,ew,eh, 0.1))
|
||||
end)
|
||||
it("may expand arbitrarily to contain more rects", function()
|
||||
pending("to be tested...")
|
||||
end)
|
||||
it("may be used to enclose arbitrary geometry", function()
|
||||
pending("to be tested...")
|
||||
end)
|
||||
it("may be tested against other rects", function()
|
||||
pending("to be tested...")
|
||||
end)
|
||||
it("may be intersected with other rects", function()
|
||||
pending("to be tested...")
|
||||
end)
|
||||
end)
|
||||
end)
|
||||
@ -0,0 +1,28 @@
|
||||
local strings = {}
|
||||
|
||||
|
||||
--- Test whether a string starts with a prefix.
|
||||
function strings.startswith(s, prefix)
|
||||
-- optimized version of: return s:sub(1, #prefix) == prefix
|
||||
for i = 1,#prefix do
|
||||
if s:byte(i) ~= prefix:byte(i) then
|
||||
return false
|
||||
end
|
||||
end
|
||||
return true
|
||||
end
|
||||
|
||||
--- Test whether a string ends with a trailing suffix.
|
||||
function strings.endswith(s, trailing)
|
||||
-- optimized version of: return trailing == "" or s:sub(-#trailing) == trailing
|
||||
local n1,n2 = #s,#trailing
|
||||
|
||||
for i = 0,n2-1 do
|
||||
if s:byte(n1-i) ~= trailing:byte(n2-i) then
|
||||
return false
|
||||
end
|
||||
end
|
||||
return true
|
||||
end
|
||||
|
||||
return strings
|
||||
@ -0,0 +1,254 @@
|
||||
--- Vector algebra.
|
||||
--
|
||||
-- Functions implementing basic 2D and 3D vector algebra.
|
||||
-- Code is reasonably optimized for speed.
|
||||
--
|
||||
-- @module gear.vec
|
||||
-- @copyright 2022 The DoubleFourteen Code Forge
|
||||
-- @author Lorenzo Cogotti
|
||||
|
||||
local min, max = math.min, math.max
|
||||
local sin, cos = math.sin, math.cos
|
||||
local abs = math.abs
|
||||
local sqrt = math.sqrt
|
||||
|
||||
local vec = {}
|
||||
|
||||
|
||||
--- Vector dot product.
|
||||
function vec.dot(x1,y1, x2,y2)
|
||||
return x1*x2 + y1*y2
|
||||
end
|
||||
|
||||
--- vec.dot() equivalent for 3D vector.
|
||||
function vec.dot3(x1,y1,z1, x2,y2,z2)
|
||||
return x1*x2 + y1*y2 + z1*z2
|
||||
end
|
||||
|
||||
--- Vector squared length.
|
||||
function vec.sqrlen(x,y)
|
||||
return x*x + y*y -- vec.dot(x,y, x,y)
|
||||
end
|
||||
|
||||
--- vec.sqrlen() equivalent for 3D vectors.
|
||||
function vec.sqrlen3(x,y,z)
|
||||
return x*x + y*y + z*z
|
||||
end
|
||||
|
||||
--- Vector length.
|
||||
function vec.len(x,y)
|
||||
return sqrt(x*x + y*y) -- sqrt(vec.sqrlen(x,y))
|
||||
end
|
||||
|
||||
--- vec.len() equivalent for 3D vectors.
|
||||
function vec.len3(x,y,z)
|
||||
return sqrt(x*x + y*y + z*z)
|
||||
end
|
||||
|
||||
--- Vector addition.
|
||||
function vec.add(x1,y1, x2,y2)
|
||||
return x1+x2, y1+y2
|
||||
end
|
||||
|
||||
--- vec.add() equivalent for 3D vectors.
|
||||
function vec.add3(x1,y1,z1, x2,y2,z2)
|
||||
return x1+x2, y1+y2, z1+z2
|
||||
end
|
||||
|
||||
--- Vector subtraction.
|
||||
function vec.sub(x1,y1, x2,y2)
|
||||
return x1-x2, y1-y2
|
||||
end
|
||||
|
||||
--- vec.sub() equivalent for 3D vectors.
|
||||
function vec.sub3(x1,y1,z1, x2,y2,z2)
|
||||
return x1-x2, y1-y2, z1-z2
|
||||
end
|
||||
|
||||
--- Vector scale.
|
||||
function vec.scale(x,y, s)
|
||||
return x*s, y*s
|
||||
end
|
||||
|
||||
--- vec.scale() equivalent for 3D vectors.
|
||||
function vec.scale3(x,y,z, s)
|
||||
return x*s, y*s, z*s
|
||||
end
|
||||
|
||||
--- Vector division by scalar.
|
||||
function vec.div(x,y, s)
|
||||
return x/s, y/s
|
||||
end
|
||||
|
||||
--- vec.div() equivalent for 3D vectors.
|
||||
function vec.div3(x,y,z, s)
|
||||
return x/s, y/s, z/s
|
||||
end
|
||||
|
||||
--- Vector multiply add.
|
||||
--
|
||||
-- @return the first vector, added to the second vector scaled by a factor.
|
||||
function vec.madd(x1,y1, s, x2,y2)
|
||||
return x1 + x2*s, y1 + y2*s
|
||||
end
|
||||
|
||||
--- vec.madd() equivalent for 3D vectors.
|
||||
function vec.madd3(x1,y1,z1, s, x2,y2,z2)
|
||||
return x1 + x2*s, y1 + y2*s, z1 + z2*s
|
||||
end
|
||||
|
||||
--- Test vectors for equality with optional epsilon.
|
||||
function vec.eq(x1,y1, x2,y2, eps)
|
||||
eps = eps or 0.001
|
||||
|
||||
return abs(x1-x2) < eps and abs(y1-y2) < eps
|
||||
end
|
||||
|
||||
--- vec.eq() equivalent for 3D vectors.
|
||||
function vec.eq3(x1,y1,z1, x2,y2,z2, eps)
|
||||
eps = eps or 0.001
|
||||
|
||||
return abs(x1-x2) < eps and
|
||||
abs(y1-y2) < eps and
|
||||
abs(z1-z2) < eps
|
||||
end
|
||||
|
||||
--- Normalize vector.
|
||||
--
|
||||
-- @return (x,y, len) normalized components and vector's original length.
|
||||
function vec.normalize(x,y)
|
||||
local len = sqrt(x*x + y*y) -- vec.len(x,y)
|
||||
|
||||
if len < 1.0e-4 then
|
||||
return x,y, 0
|
||||
end
|
||||
|
||||
return x / len, y / len, len
|
||||
end
|
||||
|
||||
--- vec.normalize() equivalent for 3D vectors.
|
||||
function vec.normalize3(x,y,z)
|
||||
local len = sqrt(x*x + y*y + z*z)
|
||||
|
||||
if len < 1.0e-4 then
|
||||
return x,y,z, 0
|
||||
end
|
||||
|
||||
return x / len, y / len, z / len, len
|
||||
end
|
||||
|
||||
--- Calculate the squared distance between two vectors/points.
|
||||
function vec.sqrdist(x1,y1, x2,y2)
|
||||
local dx,dy = x2-x1, y2-y1
|
||||
|
||||
return dx*dx, dy*dy -- vec.sqrlen(dx,dy)
|
||||
end
|
||||
|
||||
--- vec.sqrdist() equivalent for 3D vectors.
|
||||
function vec.sqrdist3(x1,y1,z1, x2,y2,z2)
|
||||
local dx,dy,dz = x2-x1, y2-y1, z2-z1
|
||||
|
||||
return dx*dx, dy*dy, dz*dz
|
||||
end
|
||||
|
||||
--- Calculate the distance between two vectors/points.
|
||||
function vec.dist(x1,y1, x2,y2)
|
||||
local dx,dy = x2-x1, y2-y1
|
||||
|
||||
return sqrt(dx*dx + dy*dy) -- sqrt(vec.sqrdist(x1,y1, x2,y2))
|
||||
end
|
||||
|
||||
--- vec.dist() equivalent for 3D vectors/points.
|
||||
function vec.dist3(x1,y1,z1, x2,y2,z2)
|
||||
local dx,dy,dz = x2-x1, y2-y1, z2-z1
|
||||
|
||||
return sqrt(dx*dx + dy*dy + dz*dz)
|
||||
end
|
||||
|
||||
--- Rotate point (px,py) around (ox,oy) by the provided
|
||||
-- sine and cosine.
|
||||
--
|
||||
-- This function should only be used for (valuable)
|
||||
-- optimization purposes.
|
||||
function vec.rotatesincos(px,py, sina,cosa, ox,oy)
|
||||
return ox + cosa*px - sina*py,
|
||||
oy + sina*px + cosa*py
|
||||
end
|
||||
|
||||
--- Rotate point (px,py) around (ox,oy) about rot radians.
|
||||
function vec.rotatepoint(px,py, rot, ox,oy)
|
||||
ox = ox or 0
|
||||
oy = oy or 0
|
||||
|
||||
local sina,cosa = sin(rot),cos(rot)
|
||||
|
||||
-- vec.rotatesincos(px,py, sina,cosa, ox,oy)
|
||||
return ox + cosa*px - sina*py,
|
||||
oy + sina*px + cosa*py
|
||||
end
|
||||
|
||||
--- Transform world coordinates to screen coordinates.
|
||||
--
|
||||
-- @param x (number) World coordinate X.
|
||||
-- @param y (number) World coordinate Y.
|
||||
-- @param vx (number|nil) Point of view X coordinate, defaults to w/2.
|
||||
-- @param vy (number|nil) Point of view Y coordinate, defaults to h/2.
|
||||
-- @param rot (number|nil) View rotation in radians, defaults to 0.
|
||||
-- @param scale (number|nil) View scale (zoom), defaults to 1.
|
||||
-- @param left (number|nil) Viewport left corner, defaults to 0.
|
||||
-- @param top (number|nil) Viewport top corner, defaults to 0.
|
||||
-- @param w (number|nil) Viewport width, defaults to love.graphics.getWidth().
|
||||
-- @param h (number|nil) Viewport height, defaults to love.graphics.getHeight().
|
||||
--
|
||||
-- @return (x,y) Transformed to screen coordinates according to
|
||||
-- viewport and offset.
|
||||
function vec.toscreencoords(x,y, vx,vy, rot, scale, left,top, w,h)
|
||||
left,top = left or 0, top or 0
|
||||
w,h = w or love.graphics.getWidth(), h or love.graphics.getHeight()
|
||||
|
||||
local halfw,halfh = w/2, h/2
|
||||
|
||||
vx,vy = vx or halfw, vy or halfh
|
||||
rot = rot or 0
|
||||
scale = scale or 1
|
||||
|
||||
local sina,cosa = sin(rot),cos(rot)
|
||||
|
||||
x,y = x - vx, y - vy
|
||||
x,y = cosa*x - sina*y, sina*x + cosa*y
|
||||
return x*scale + halfw + left, y*scale + halfh + top
|
||||
end
|
||||
|
||||
--- Transform screen coordinates to world coordinates.
|
||||
--
|
||||
-- @param x (number) Screen coordinate X.
|
||||
-- @param y (number) Screen coordinate Y.
|
||||
-- @param vx (number|nil) Point of view X coordinate, defaults to w/2.
|
||||
-- @param vy (number|nil) Point of view Y coordinate, defaults to h/2.
|
||||
-- @param rot (number|nil) View rotation in radians, defaults to 0.
|
||||
-- @param scale (number|nil) View scale (zoom), defaults to 1.
|
||||
-- @param left (number|nil) Viewport left corner, defaults to 0.
|
||||
-- @param top (number|nil) Viewport top corner, defaults to 0.
|
||||
-- @param w (number|nil) Viewport width, defaults to love.graphics.getWidth().
|
||||
-- @param h (number|nil) Viewport height, defaults to love.graphics.getHeight().
|
||||
--
|
||||
-- @return (x,y) Transformed to world coordinates according to
|
||||
-- viewport and offset.
|
||||
function vec.toworldcoords(x,y, vx,vy, rot, scale, left,top,w,h)
|
||||
left, top = left or 0, top or 0
|
||||
w,h = w or love.graphics.getWidth(), h or love.graphics.getHeight()
|
||||
|
||||
local halfw,halfh = w/2, h/2
|
||||
|
||||
vx,vy = vx or halfw, vy or halfh
|
||||
rot = rot or 0
|
||||
scale = scale or 1
|
||||
|
||||
local sina,cosa = sin(-rot),cos(-rot)
|
||||
|
||||
x,y = (x - halfw - left) / scale, (y - halfh - top) / scale
|
||||
x,y = cosa*x - sina*y, sina*x + cosa*y
|
||||
return x+vx, y+vy
|
||||
end
|
||||
|
||||
return vec
|
||||
Loading…
Reference in New Issue