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--[[
Copyright (c) 2012 Matthias Richter
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
Except as contained in this notice, the name(s) of the above copyright holders
shall not be used in advertising or otherwise to promote the sale, use or
other dealings in this Software without prior written authorization.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
]]--
local _PACKAGE = (...):match("^(.+)%.[^%.]+")
local vector = require(_PACKAGE .. '.vector-light')
local function support(shape_a, shape_b, dx, dy)
local x,y = shape_a:support(dx,dy)
return vector.sub(x,y, shape_b:support(-dx, -dy))
end
-- returns closest edge to the origin
local function closest_edge(simplex)
local e = {dist = math.huge}
local i = #simplex-1
for k = 1,#simplex-1,2 do
local ax,ay = simplex[i], simplex[i+1]
local bx,by = simplex[k], simplex[k+1]
i = k
local ex,ey = vector.perpendicular(bx-ax, by-ay)
local nx,ny = vector.normalize(ex,ey)
local d = vector.dot(ax,ay, nx,ny)
if d < e.dist then
e.dist = d
e.nx, e.ny = nx, ny
e.i = k
end
end
return e
end
local function EPA(shape_a, shape_b, simplex)
-- make sure simplex is oriented counter clockwise
local cx,cy, bx,by, ax,ay = unpack(simplex)
if vector.dot(ax-bx,ay-by, cx-bx,cy-by) < 0 then
simplex[1],simplex[2] = ax,ay
simplex[5],simplex[6] = cx,cy
end
-- the expanding polytype algorithm
while true do
local e = closest_edge(simplex)
local px,py = support(shape_a, shape_b, e.nx, e.ny)
local d = vector.dot(px,py, e.nx, e.ny)
if d - e.dist < 1e-6 then
return -d*e.nx, -d*e.ny
end
-- simplex = {..., simplex[e.i-1], px, py, simplex[e.i]
table.insert(simplex, e.i, py)
table.insert(simplex, e.i, px)
end
end
-- : : origin must be in plane between A and B
-- B o------o A since A is the furthest point on the MD
-- : : in direction of the origin.
local function do_line(simplex)
local bx,by, ax,ay = unpack(simplex)
local abx,aby = bx-ax, by-ay
local dx,dy = vector.perpendicular(abx,aby)
if vector.dot(dx,dy, -ax,-ay) < 0 then
dx,dy = -dx,-dy
end
return simplex, dx,dy
end
-- B .'
-- o-._ 1
-- | `-. .' The origin can only be in regions 1, 3 or 4:
-- | 4 o A 2 A lies on the edge of the MD and we came
-- | _.-' '. from left of BC.
-- o-' 3
-- C '.
local function do_triangle(simplex)
local cx,cy, bx,by, ax,ay = unpack(simplex)
local aox,aoy = -ax,-ay
local abx,aby = bx-ax, by-ay
local acx,acy = cx-ax, cy-ay
-- test region 1
local dx,dy = vector.perpendicular(abx,aby)
if vector.dot(dx,dy, acx,acy) > 0 then
dx,dy = -dx,-dy
end
if vector.dot(dx,dy, aox,aoy) > 0 then
-- simplex = {bx,by, ax,ay}
simplex[1], simplex[2] = bx,by
simplex[3], simplex[4] = ax,ay
simplex[5], simplex[6] = nil, nil
return simplex, dx,dy
end
-- test region 3
dx,dy = vector.perpendicular(acx,acy)
if vector.dot(dx,dy, abx,aby) > 0 then
dx,dy = -dx,-dy
end
if vector.dot(dx,dy, aox, aoy) > 0 then
-- simplex = {cx,cy, ax,ay}
simplex[3], simplex[4] = ax,ay
simplex[5], simplex[6] = nil, nil
return simplex, dx,dy
end
-- must be in region 4
return simplex
end
local function GJK(shape_a, shape_b)
local ax,ay = support(shape_a, shape_b, 1,0)
local simplex = {ax,ay}
local n = 2
local dx,dy = -ax,-ay
-- first iteration: line case
ax,ay = support(shape_a, shape_b, dx,dy)
if vector.dot(ax,ay, dx,dy) <= 0 then
return false
end
simplex[n+1], simplex[n+2] = ax,ay
simplex, dx, dy = do_line(simplex, dx, dy)
n = 4
-- all other iterations must be the triangle case
while true do
ax,ay = support(shape_a, shape_b, dx,dy)
if vector.dot(ax,ay, dx,dy) <= 0 then
return false
end
simplex[n+1], simplex[n+2] = ax,ay
simplex, dx, dy = do_triangle(simplex, dx,dy)
n = #simplex
if n == 6 then
return true, EPA(shape_a, shape_b, simplex)
end
end
end
return GJK
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