From 56737e7aa0cecac6c44ffd868ea408cd670812a6 Mon Sep 17 00:00:00 2001 From: Matthias Richter Date: Sun, 6 Feb 2011 17:40:06 +0100 Subject: [PATCH] Add point location and broad phase --- polygon.lua | 32 +++++++ shapes.lua | 257 +++++++++++++++++++++++++++++++--------------------- 2 files changed, 185 insertions(+), 104 deletions(-) diff --git a/polygon.lua b/polygon.lua index ab56ff3..39bec54 100644 --- a/polygon.lua +++ b/polygon.lua @@ -144,6 +144,12 @@ Polygon = Class{name = "Polygon", function(self, ...) self.centroid.y = self.centroid.y + (p.y+q.y) * det end self.centroid = self.centroid / (6 * self.area) + + -- get outcircle + self._radius = 0 + for i = 1,#vertices do + self._radius = math.max(vertices[i]:dist(self.centroid), self._radius) + end end} -- return vertices as x1,y1,x2,y2, ..., xn,yn @@ -321,6 +327,32 @@ function Polygon:splitConvex() return convex end +function Polygon:contains(x,y) + -- test if an edge cuts the ray + local function cut_ray(p,q) + return ((p.y > y and q.y < y) or (p.y < y and q.y > y)) -- possible cut + and (x - p.x < (y - p.y) * (q.x - p.x) / (q.y - p.y)) -- x < cut.x + end + + -- test if the ray crosses boundary from interior to exterior. + -- this is needed due to edge cases, when the ray passes through + -- polygon corners + local function cross_boundary(p,q) + return (p.y == y and p.x > x and q.y < y) + or (q.y == y and q.x > x and p.y < y) + end + + local v = self.vertices + local in_polygon = false + for i = 1, #v - 1 do + if cut_ray(v[i], v[i+1]) or cross_boundary(v[i], v[i+1]) then + in_polygon = not in_polygon + end + end + return in_polygon +end + + -- module() as shortcut to module.Polygon() do local m = getmetatable(_M) diff --git a/shapes.lua b/shapes.lua index 1ee0d64..66d320a 100644 --- a/shapes.lua +++ b/shapes.lua @@ -54,8 +54,14 @@ local function SAT(shape_one, axes_one, shape_two, axes_two) return collide, sep end ---------------- --- Base class +local function outcircles_intersect(shape_one, shape_two) + local x1,y1,r1 = shape_one:outcircle() + local x2,y2,r2 = shape_two:outcircle() + return (x1-x2)*(x1-x2) + (y1-y2)*(y1-y2) <= (r1+r2)*(r1+r2) +end + +-- +-- base class -- local Shape = Class{name = 'Shape', function(self, t) self._type = t @@ -72,8 +78,8 @@ Shape.POLYGON = setmetatable({}, {__tostring = function() return 'POLYGON' end Shape.COMPOUND = setmetatable({}, {__tostring = function() return 'COMPOUND' end}) Shape.CIRCLE = setmetatable({}, {__tostring = function() return 'CIRCLE' end}) -------------------- --- Polygon Shapes +-- +-- class definitions -- local ConvexPolygonShape = Class{name = 'ConvexPolygonShape', function(self, polygon) Shape.construct(self, Shape.POLYGON) @@ -92,7 +98,6 @@ local ConcavePolygonShape = Class{name = 'ConcavePolygonShape', function(self, p end} ConcavePolygonShape:inherit(Shape) --- decides wether to use a convex or concave polygon function PolygonShape(polygon, ...) -- create from coordinates if needed if type(polygon) == "number" then @@ -107,6 +112,16 @@ function PolygonShape(polygon, ...) return ConcavePolygonShape(polygon) end +CircleShape = Class{name = 'CircleShape', function(self, cx,cy, radius) + Shape.construct(self, Shape.CIRCLE) + self._center = vector(cx,cy) + self._radius = radius +end} +CircleShape:inherit(Shape) + +-- +-- collision functions +-- function ConvexPolygonShape:getAxes() local axes = {} local vert = self._polygon.vertices @@ -126,36 +141,29 @@ function ConvexPolygonShape:projectOn(axis) return math.min(unpack(projection)), math.max(unpack(projection)) end +function CircleShape:projectOn(axis) + -- v:projectOn(a) * a = v * a (see ConvexPolygonShape) + -- therefore: (c +- a*r) * a = c*a +- |a|^2 * r + local center = self._center * axis + local shift = self._radius * axis:len2() + return center - shift, center + shift +end + +-- collision dispatching: +-- let circle shape or compund shape handle the collision function ConvexPolygonShape:collidesWith(other) if other._type ~= Shape.POLYGON then return other:collidesWith(self) end -- else: type is POLYGON, use the SAT + if not outcircles_intersect(self, other) then return false end return SAT(self, self:getAxes(), other, other:getAxes()) end -function ConvexPolygonShape:draw(mode) - local mode = mode or 'line' - love.graphics.polygon(mode, self._polygon:unpack()) -end - -function ConvexPolygonShape:center() - return self._polygon.centroid:unpack() -end - -function ConvexPolygonShape:move(x,y) - -- y not given => x is a vector - if y then x = vector(x,y) end - self._polygon:move(x) -end - -function ConvexPolygonShape:rotate(angle, cx,cy) - if cx and cy then cx = vector(cx,cy) end - self._polygon:rotate(angle, cx) -end - function ConcavePolygonShape:collidesWith(other) + if not outcircles_intersect(self, other) then return false end + local sep, collide, collisions = vector(0,0), false, 0 for _,s in ipairs(self._shapes) do local status, separating_vector = s:collidesWith(other) @@ -167,6 +175,126 @@ function ConcavePolygonShape:collidesWith(other) return collide, sep / collisions end +function CircleShape:collidesWith(other) + if other._type == Shape.CIRCLE then + local d = self._center:dist(other._center) + if d < self._radius + other._radius then + return true, d * (self._center - other.center) + end + return false + elseif other._type == Shape.COMPOUND then + return other:collidesWith(self) + end + + -- else: other._type == POLYGON + if not outcircles_intersect(self, other) then return false end + -- retrieve closest edge to center + local points = other._polygon.vertices + local closest, dist = points[1], (self._center - points[1]):len2() + for i = 2,#points do + local d = (self._center - points[i]):len2() + if d < dist then + closest, dist = points[i], d + end + end + return SAT(self, {(closest-self._center):normalize_inplace()}, other, other:getAxes()) +end + +-- +-- point location/ray intersection +-- +function ConvexPolygonShape:contains(x,y) + return self._polygon:contains(x,y) +end + +function ConcavePolygonShape:contains(x,y) + return self._polygon:contains(x,y) +end + +function CircleShape:contains(x,y) + if y then x = vector(x,y) end + return (x - self._center):len2() < self._radius * self._radius +end + +-- +-- auxiliary +-- +function ConvexPolygonShape:center() + return self._polygon.centroid:unpack() +end + +function ConcavePolygonShape:center() + return self._polygon.centroid:unpack() +end + +function CircleShape:center() + return self._center:unpack() +end + + +function ConvexPolygonShape:outcircle() + local cx,cy = self:center() + return cx,cy, self._polygon._radius +end + +function ConcavePolygonShape:outcircle() + local cx,cy = self:center() + return cx,cy, self._polygon._radius +end + +function CircleShape:outcircle() + local cx,cy = self:center() + return cx,cy, self._radius +end + + +function ConvexPolygonShape:move(x,y) + -- y not given => x is a vector + if y then x = vector(x,y) end + self._polygon:move(x) +end + +function ConcavePolygonShape:move(x,y) + -- y not give => x is a vector + if y then x = vector(x,y) end + self._polygon:move(x) + for _,p in ipairs(self._shapes) do + p:move(x) + end +end + +function CircleShape:move(x,y) + -- y not given => x is a vector + if y then x = vector(x,y) end + self._center = self._center + x +end + + +function ConcavePolygonShape:rotate(angle,cx,cy) + if cx and cy then cx = vector(cx,cy) end + self._polygon:rotate(angle,cx) + for _,p in ipairs(self._shapes) do + p:rotate(angle, cx or self._polygon.centroid) + end +end + +function ConvexPolygonShape:rotate(angle, cx,cy) + if cx and cy then cx = vector(cx,cy) end + self._polygon:rotate(angle, cx) +end + +function CircleShape:rotate(angle, cx,cy) + if not cx then return end + if cx and cy then cx = vector(cx,cy) end + self._center = (self._center - cx):rotate_inplace(angle) + cx +end + + +function ConvexPolygonShape:draw(mode) + local mode = mode or 'line' + love.graphics.polygon(mode, self._polygon:unpack()) +end + function ConcavePolygonShape:draw(mode) local mode = mode or 'line' if mode == 'line' then @@ -178,89 +306,10 @@ function ConcavePolygonShape:draw(mode) end end -function ConcavePolygonShape:center() - return self._polygon.centroid:unpack() -end - -function ConcavePolygonShape:move(x,y) - -- y not give => x is a vector - if y then x = vector(x,y) end - self._polygon:move(x) - for _,p in ipairs(self._shapes) do - p:move(x) - end -end - -function ConcavePolygonShape:rotate(angle,cx,cy) - if cx and cy then cx = vector(cx,cy) end - self._polygon:rotate(angle,cx) - for _,p in ipairs(self._shapes) do - p:rotate(angle, cx or self._polygon.centroid) - end -end - -------------------- --- Perfect circle --- -CircleShape = Class{name = 'CircleShape', function(self, cx,cy, radius) - Shape.construct(self, Shape.CIRCLE) - self._center = vector(cx,cy) - self._radius = radius -end} -CircleShape:inherit(Shape) - -function CircleShape:collidesWith(other) - if other._type == Shape.CIRCLE then - local d = self._center:dist(other._center) - if d < self._radius + other._radius then - return true, d * (self._center - other.center) - end - return false - elseif other._type == Shape.COMPOUND then - return other:collidesWith(self) - end - -- else: other._type == POLYGON - -- retrieve closest edge to center - local points = other._polygon.vertices - local closest, dist = points[1], (self._center - points[1]):len2() - for i = 2,#points do - local d = (self._center - points[i]):len2() - if d < dist then - closest, dist = points[i], d - end - end - return SAT(self, {(closest-self._center):normalize_inplace()}, other, other:getAxes()) -end - function CircleShape:draw(mode, segments) local segments = segments or math.max(3, math.floor(math.pi * math.log(self._radius))) love.graphics.circle(mode, self._center.x, self._center.y, self._radius, segments) end -function CircleShape:center() - return self._center:unpack() -end -function CircleShape:move(x,y) - -- y not given => x is a vector - if y then x = vector(x,y) end - self._center = self._center + x -end -function CircleShape:rotate(angle, cx,cy) - if not cx then return end - if cx and cy then cx = vector(cx,cy) end - self._center = (self._center - cx):rotate_inplace(angle) + cx -end - -function CircleShape:projectOn(axis) - -- v:projectOn(a) * a = v * a (see ConvexPolygonShape) - -- therefore: (c +- a*r) * a = c*a +- |a|^2 * r - local center = self._center * axis - local shift = self._radius * axis:len2() - return center - shift, center + shift -end - -function CircleShape:center() - return self._center:unpack() -end