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97 lines
2.3 KiB
Lua
97 lines
2.3 KiB
Lua
-- Geometry module for Lunatic.
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local ffi = require("ffi")
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local math = require("math")
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local type = type
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local assert = assert
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module(...)
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ffi.cdef[[
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typedef struct { double x, y; } dvec2_t;
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]]
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local vec2_
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local mt = {
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__add = function(a, b) return vec2_(a.x+b.x, a.y+b.y) end,
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__sub = function(a, b) return vec2_(a.x-b.x, a.y-b.y) end,
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__unm = function(a) return vec2_(-a.x, -b.x) end,
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__mul = function(a,b)
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if (type(a)=="number") then
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return vec2_(a*b.x, a*b.y)
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end
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assert(type(b)=="number")
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return vec2_(a.x*b, a.y*b)
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end,
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__div = function(a,b)
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assert(type(b)=="number")
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return vec2_(a.x/b, a.y/b)
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end,
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--[[
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-- NOTE: metamethods from metatype() are invoken on *any mix of types*
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-- This means that we can't check a "maybe-vec2" variable like "v ~= nil".
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__eq = function(a,b)
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return (a.x==b.x and a.y==b.y)
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end,
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--]]
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__len = function(a) return math.sqrt(a.x*a.x + a.y*a.y) end,
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__tostring = function(a) return "vec2("..a.x..", "..a.y..")" end,
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__index = {
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lensq = function(a) return a.x*a.x + a.y*a.y end,
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},
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}
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-- VEC2 user data constructor.
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-- * vec2(<table or ctype>), the arg should be indexable with "x" and "y"
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-- * vec2(x, y), assuming that x and y are numbers
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vec2_ = ffi.metatype("dvec2_t", mt)
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vec2 = vec2_
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-- Returns a vec2 from anything indexable with "x" and "y"
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-- (vec2(t) works if t is such a table, but not if it's a vec2)
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function tovec2(t)
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return vec2(t.x, t.y)
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end
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-- Two-element vector cross product.
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-- Anti-commutative, distributive.
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function cross2(v, w)
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return v.y*w.x - v.x*w.y
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end
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-- Finds the intersection point of two lines given by
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-- point a and vector v
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-- and
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-- point b and vector w
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--
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-- Returns:
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-- if <TODO>, nil
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-- if retpoint_p evaluates to a non-true value, coefficients cv and cw such that <TODO>
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-- else, the intersection point
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function intersect(a,v, b,w, retpoint_p)
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local vxw = cross2(v,w)
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if (vxw ~= 0) then
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local btoa = tovec2(a)-tovec2(b)
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local cv, cw = cross2(w, btoa)/vxw, cross2(v, btoa)/vxw
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if (retpoint_p) then
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return tovec2(a)+cv*tovec2(v)
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else
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return cv, cw
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end
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end
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-- return nil if v and w parallel (or either of them is a point), or if
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-- they contain NaNs
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end
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