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Add point location and broad phase
This commit is contained in:
Matthias Richter
parent
4554742579
commit
56737e7aa0
32
polygon.lua
32
polygon.lua
@ -144,6 +144,12 @@ Polygon = Class{name = "Polygon", function(self, ...)
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self.centroid.y = self.centroid.y + (p.y+q.y) * det
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end
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self.centroid = self.centroid / (6 * self.area)
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-- get outcircle
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self._radius = 0
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for i = 1,#vertices do
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self._radius = math.max(vertices[i]:dist(self.centroid), self._radius)
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end
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end}
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-- return vertices as x1,y1,x2,y2, ..., xn,yn
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@ -321,6 +327,32 @@ function Polygon:splitConvex()
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return convex
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end
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function Polygon:contains(x,y)
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-- test if an edge cuts the ray
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local function cut_ray(p,q)
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return ((p.y > y and q.y < y) or (p.y < y and q.y > y)) -- possible cut
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and (x - p.x < (y - p.y) * (q.x - p.x) / (q.y - p.y)) -- x < cut.x
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end
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-- test if the ray crosses boundary from interior to exterior.
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-- this is needed due to edge cases, when the ray passes through
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-- polygon corners
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local function cross_boundary(p,q)
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return (p.y == y and p.x > x and q.y < y)
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or (q.y == y and q.x > x and p.y < y)
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end
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local v = self.vertices
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local in_polygon = false
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for i = 1, #v - 1 do
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if cut_ray(v[i], v[i+1]) or cross_boundary(v[i], v[i+1]) then
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in_polygon = not in_polygon
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end
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end
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return in_polygon
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end
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-- module() as shortcut to module.Polygon()
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do
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local m = getmetatable(_M)
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257
shapes.lua
257
shapes.lua
@ -54,8 +54,14 @@ local function SAT(shape_one, axes_one, shape_two, axes_two)
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return collide, sep
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end
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---------------
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-- Base class
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local function outcircles_intersect(shape_one, shape_two)
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local x1,y1,r1 = shape_one:outcircle()
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local x2,y2,r2 = shape_two:outcircle()
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return (x1-x2)*(x1-x2) + (y1-y2)*(y1-y2) <= (r1+r2)*(r1+r2)
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end
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--
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-- base class
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--
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local Shape = Class{name = 'Shape', function(self, t)
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self._type = t
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@ -72,8 +78,8 @@ Shape.POLYGON = setmetatable({}, {__tostring = function() return 'POLYGON' end
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Shape.COMPOUND = setmetatable({}, {__tostring = function() return 'COMPOUND' end})
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Shape.CIRCLE = setmetatable({}, {__tostring = function() return 'CIRCLE' end})
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-------------------
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-- Polygon Shapes
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--
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-- class definitions
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--
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local ConvexPolygonShape = Class{name = 'ConvexPolygonShape', function(self, polygon)
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Shape.construct(self, Shape.POLYGON)
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@ -92,7 +98,6 @@ local ConcavePolygonShape = Class{name = 'ConcavePolygonShape', function(self, p
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end}
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ConcavePolygonShape:inherit(Shape)
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-- decides wether to use a convex or concave polygon
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function PolygonShape(polygon, ...)
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-- create from coordinates if needed
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if type(polygon) == "number" then
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@ -107,6 +112,16 @@ function PolygonShape(polygon, ...)
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return ConcavePolygonShape(polygon)
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end
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CircleShape = Class{name = 'CircleShape', function(self, cx,cy, radius)
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Shape.construct(self, Shape.CIRCLE)
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self._center = vector(cx,cy)
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self._radius = radius
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end}
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CircleShape:inherit(Shape)
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--
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-- collision functions
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--
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function ConvexPolygonShape:getAxes()
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local axes = {}
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local vert = self._polygon.vertices
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@ -126,36 +141,29 @@ function ConvexPolygonShape:projectOn(axis)
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return math.min(unpack(projection)), math.max(unpack(projection))
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end
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function CircleShape:projectOn(axis)
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-- v:projectOn(a) * a = v * a (see ConvexPolygonShape)
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-- therefore: (c +- a*r) * a = c*a +- |a|^2 * r
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local center = self._center * axis
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local shift = self._radius * axis:len2()
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return center - shift, center + shift
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end
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-- collision dispatching:
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-- let circle shape or compund shape handle the collision
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function ConvexPolygonShape:collidesWith(other)
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if other._type ~= Shape.POLYGON then
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return other:collidesWith(self)
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end
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-- else: type is POLYGON, use the SAT
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if not outcircles_intersect(self, other) then return false end
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return SAT(self, self:getAxes(), other, other:getAxes())
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end
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function ConvexPolygonShape:draw(mode)
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local mode = mode or 'line'
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love.graphics.polygon(mode, self._polygon:unpack())
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end
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function ConvexPolygonShape:center()
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return self._polygon.centroid:unpack()
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end
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function ConvexPolygonShape:move(x,y)
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-- y not given => x is a vector
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if y then x = vector(x,y) end
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self._polygon:move(x)
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end
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function ConvexPolygonShape:rotate(angle, cx,cy)
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if cx and cy then cx = vector(cx,cy) end
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self._polygon:rotate(angle, cx)
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end
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function ConcavePolygonShape:collidesWith(other)
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if not outcircles_intersect(self, other) then return false end
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local sep, collide, collisions = vector(0,0), false, 0
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for _,s in ipairs(self._shapes) do
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local status, separating_vector = s:collidesWith(other)
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@ -167,6 +175,126 @@ function ConcavePolygonShape:collidesWith(other)
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return collide, sep / collisions
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end
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function CircleShape:collidesWith(other)
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if other._type == Shape.CIRCLE then
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local d = self._center:dist(other._center)
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if d < self._radius + other._radius then
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return true, d * (self._center - other.center)
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end
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return false
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elseif other._type == Shape.COMPOUND then
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return other:collidesWith(self)
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end
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-- else: other._type == POLYGON
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if not outcircles_intersect(self, other) then return false end
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-- retrieve closest edge to center
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local points = other._polygon.vertices
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local closest, dist = points[1], (self._center - points[1]):len2()
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for i = 2,#points do
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local d = (self._center - points[i]):len2()
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if d < dist then
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closest, dist = points[i], d
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end
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end
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return SAT(self, {(closest-self._center):normalize_inplace()}, other, other:getAxes())
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end
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--
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-- point location/ray intersection
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--
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function ConvexPolygonShape:contains(x,y)
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return self._polygon:contains(x,y)
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end
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function ConcavePolygonShape:contains(x,y)
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return self._polygon:contains(x,y)
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end
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function CircleShape:contains(x,y)
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if y then x = vector(x,y) end
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return (x - self._center):len2() < self._radius * self._radius
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end
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--
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-- auxiliary
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--
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function ConvexPolygonShape:center()
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return self._polygon.centroid:unpack()
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end
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function ConcavePolygonShape:center()
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return self._polygon.centroid:unpack()
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end
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function CircleShape:center()
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return self._center:unpack()
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end
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function ConvexPolygonShape:outcircle()
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local cx,cy = self:center()
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return cx,cy, self._polygon._radius
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end
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function ConcavePolygonShape:outcircle()
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local cx,cy = self:center()
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return cx,cy, self._polygon._radius
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end
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function CircleShape:outcircle()
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local cx,cy = self:center()
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return cx,cy, self._radius
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end
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function ConvexPolygonShape:move(x,y)
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-- y not given => x is a vector
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if y then x = vector(x,y) end
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self._polygon:move(x)
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end
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function ConcavePolygonShape:move(x,y)
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-- y not give => x is a vector
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if y then x = vector(x,y) end
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self._polygon:move(x)
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for _,p in ipairs(self._shapes) do
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p:move(x)
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end
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end
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function CircleShape:move(x,y)
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-- y not given => x is a vector
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if y then x = vector(x,y) end
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self._center = self._center + x
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end
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function ConcavePolygonShape:rotate(angle,cx,cy)
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if cx and cy then cx = vector(cx,cy) end
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self._polygon:rotate(angle,cx)
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for _,p in ipairs(self._shapes) do
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p:rotate(angle, cx or self._polygon.centroid)
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end
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end
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function ConvexPolygonShape:rotate(angle, cx,cy)
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if cx and cy then cx = vector(cx,cy) end
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self._polygon:rotate(angle, cx)
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end
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function CircleShape:rotate(angle, cx,cy)
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if not cx then return end
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if cx and cy then cx = vector(cx,cy) end
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self._center = (self._center - cx):rotate_inplace(angle) + cx
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end
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function ConvexPolygonShape:draw(mode)
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local mode = mode or 'line'
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love.graphics.polygon(mode, self._polygon:unpack())
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end
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function ConcavePolygonShape:draw(mode)
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local mode = mode or 'line'
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if mode == 'line' then
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@ -178,89 +306,10 @@ function ConcavePolygonShape:draw(mode)
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end
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end
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function ConcavePolygonShape:center()
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return self._polygon.centroid:unpack()
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end
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function ConcavePolygonShape:move(x,y)
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-- y not give => x is a vector
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if y then x = vector(x,y) end
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self._polygon:move(x)
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for _,p in ipairs(self._shapes) do
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p:move(x)
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end
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end
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function ConcavePolygonShape:rotate(angle,cx,cy)
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if cx and cy then cx = vector(cx,cy) end
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self._polygon:rotate(angle,cx)
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for _,p in ipairs(self._shapes) do
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p:rotate(angle, cx or self._polygon.centroid)
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end
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end
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-------------------
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-- Perfect circle
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--
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CircleShape = Class{name = 'CircleShape', function(self, cx,cy, radius)
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Shape.construct(self, Shape.CIRCLE)
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self._center = vector(cx,cy)
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self._radius = radius
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end}
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CircleShape:inherit(Shape)
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function CircleShape:collidesWith(other)
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if other._type == Shape.CIRCLE then
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local d = self._center:dist(other._center)
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if d < self._radius + other._radius then
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return true, d * (self._center - other.center)
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end
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return false
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elseif other._type == Shape.COMPOUND then
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return other:collidesWith(self)
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end
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-- else: other._type == POLYGON
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-- retrieve closest edge to center
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local points = other._polygon.vertices
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local closest, dist = points[1], (self._center - points[1]):len2()
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for i = 2,#points do
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local d = (self._center - points[i]):len2()
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if d < dist then
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closest, dist = points[i], d
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end
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end
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return SAT(self, {(closest-self._center):normalize_inplace()}, other, other:getAxes())
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end
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function CircleShape:draw(mode, segments)
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local segments = segments or math.max(3, math.floor(math.pi * math.log(self._radius)))
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love.graphics.circle(mode, self._center.x, self._center.y, self._radius, segments)
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end
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function CircleShape:center()
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return self._center:unpack()
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end
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function CircleShape:move(x,y)
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-- y not given => x is a vector
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if y then x = vector(x,y) end
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self._center = self._center + x
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end
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function CircleShape:rotate(angle, cx,cy)
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if not cx then return end
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if cx and cy then cx = vector(cx,cy) end
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self._center = (self._center - cx):rotate_inplace(angle) + cx
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end
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function CircleShape:projectOn(axis)
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-- v:projectOn(a) * a = v * a (see ConvexPolygonShape)
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-- therefore: (c +- a*r) * a = c*a +- |a|^2 * r
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local center = self._center * axis
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local shift = self._radius * axis:len2()
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return center - shift, center + shift
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end
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function CircleShape:center()
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return self._center:unpack()
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end
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