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|
local geom = {}
local function class(tbl)
setmetatable(tbl, tbl)
return tbl
end
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
--
-- point
--
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
geom.point = class{
__call = function(this, x, y)
local pt = {}
pt.x = x
pt.y = y
setmetatable(pt, {__index=this})
return pt
end,
distance_to = function(self, pt)
local d_x = self.x - pt.x
local d_y = self.y - pt.y
return math.sqrt(d_x*d_x + d_y*d_y)
end,
}
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
--
-- square
--
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
geom.square = class{
__call = function(this, center, span)
local square = {}
square.center = center
square.span = span
square.x = this.axis_range(center.x, span/2)
square.y = this.axis_range(center.y, span/2)
setmetatable(square, {__index=this})
return square
end,
axis_range = function(c, r) return {min=c-r, max=c+r} end,
-- returns true if a point is inside of the square
-- and false otherwise
-- (x/y mininum exclusive, maximum inclusive)
contains = function(self, point)
local x_overlap =
(point.x > self.x.min) and (point.x <= self.x.max)
local y_overlap =
(point.y > self.y.min) and (point.y <= self.y.max)
if x_overlap and y_overlap then
return true
end
return false
end,
-- check if the square intersects the given square
intersects = function(self, square)
local overlap = function(a, b)
return math.max(a.min, b.min) < math.min(a.max, b.max)
end
local x_overlap = overlap(self.x, square.x)
local y_overlap = overlap(self.y, square.y)
if x_overlap and y_overlap then return true end
return false
end,
-- return an array of four squares covering the same
-- area as their parent
divide = function(self)
local this = getmetatable(self).__index
local x = self.center.x
local y = self.center.y
local d = self.span / 4
return {
this(geom.point(x-d, y-d), d*2),
this(geom.point(x+d, y-d), d*2),
this(geom.point(x-d, y+d), d*2),
this(geom.point(x+d, y+d), d*2),
}
end
}
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
--
-- qt_node
--
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
geom.qt_node = class{
__call = function(this, center, span)
local node = {}
node.square = geom.square(center, span)
setmetatable(node, {__index=this})
return node
end,
is_leaf = function(self)
if self.children then return false end
return true
end,
insert = function(self, point)
if not self.square:contains(point) then
-- point isn't even in this region
return false
end
if self:is_leaf() and not self.point then
-- no preexisting point, just store it
self.point = point
return true
end
if self:is_leaf() then
-- subdivide and re-insert original point
-- and then insert new point again
local self_point = self.point
self.point = nil
self.children = {}
local this = getmetatable(self).__index
local child_regions = self.square:divide()
for _, region in ipairs(child_regions) do
table.insert(
self.children,
this(region.center, region.span)
)
end
self:insert(self_point)
self:insert(point)
return true
end
-- not a leaf node
for _, child in ipairs(self.children) do
if child:insert(point) then return true end
end
-- should never get here
return false
end
}
return geom
|
