geom = {} function geom.on_shape(x,y, drawing, shape) if shape.mode == 'freehand' then return geom.on_freehand(x,y, drawing, shape) elseif shape.mode == 'line' then return geom.on_line(x,y, drawing, shape) elseif shape.mode == 'manhattan' then local p1 = drawing.points[shape.p1] local p2 = drawing.points[shape.p2] if p1.x == p2.x then if x ~= p1.x then return false end local y1,y2 = p1.y, p2.y if y1 > y2 then y1,y2 = y2,y1 end return y >= y1-2 and y <= y2+2 elseif p1.y == p2.y then if y ~= p1.y then return false end local x1,x2 = p1.x, p2.x if x1 > x2 then x1,x2 = x2,x1 end return x >= x1-2 and x <= x2+2 end elseif shape.mode == 'polygon' or shape.mode == 'rectangle' or shape.mode == 'square' then return geom.on_polygon(x,y, drawing, shape) elseif shape.mode == 'circle' then local center = drawing.points[shape.center] local dist = geom.dist(center.x,center.y, x,y) return dist > shape.radius*0.95 and dist < shape.radius*1.05 elseif shape.mode == 'arc' then local center = drawing.points[shape.center] local dist = geom.dist(center.x,center.y, x,y) if dist < shape.radius*0.95 or dist > shape.radius*1.05 then return false end return geom.angle_between(center.x,center.y, x,y, shape.start_angle,shape.end_angle) elseif shape.mode == 'deleted' then else assert(false, ('unknown drawing mode %s'):format(shape.mode)) end end function geom.on_freehand(x,y, drawing, shape) local prev for _,p in ipairs(shape.points) do if prev then if geom.on_line(x,y, drawing, {p1=prev, p2=p}) then return true end end prev = p end return false end function geom.on_line(x,y, drawing, shape) local p1,p2 if type(shape.p1) == 'number' then p1 = drawing.points[shape.p1] p2 = drawing.points[shape.p2] else p1 = shape.p1 p2 = shape.p2 end if p1.x == p2.x then if math.abs(p1.x-x) > 2 then return false end local y1,y2 = p1.y,p2.y if y1 > y2 then y1,y2 = y2,y1 end return y >= y1-2 and y <= y2+2 end -- has the right slope and intercept local m = (p2.y - p1.y) / (p2.x - p1.x) local yp = p1.y + m*(x-p1.x) if yp < y-2 or yp > y+2 then return false end -- between endpoints local k = (x-p1.x) / (p2.x-p1.x) return k > -0.005 and k < 1.005 end function geom.on_polygon(x,y, drawing, shape) local prev for _,p in ipairs(shape.vertices) do if prev then if geom.on_line(x,y, drawing, {p1=prev, p2=p}) then return true end end prev = p end return geom.on_line(x,y, drawing, {p1=shape.vertices[1], p2=shape.vertices[#shape.vertices]}) end -- are (x3,y3) and (x4,y4) on the same side of the line between (x1,y1) and (x2,y2) function geom.same_side(x1,y1, x2,y2, x3,y3, x4,y4) if x1 == x2 then return math.sign(x3-x1) == math.sign(x4-x1) end if y1 == y2 then return math.sign(y3-y1) == math.sign(y4-y1) end local m = (y2-y1)/(x2-x1) return math.sign(m*(x3-x1) + y1-y3) == math.sign(m*(x4-x1) + y1-y4) end function math.sign(x) if x > 0 then return 1 elseif x == 0 then return 0 elseif x < 0 then return -1 end end function geom.angle_with_hint(x1, y1, x2, y2, hint) local result = geom.angle(x1,y1, x2,y2) if hint then -- Smooth the discontinuity where angle goes from positive to negative. -- The hint is a memory of which way we drew it last time. while result > hint+math.pi/10 do result = result-math.pi*2 end while result < hint-math.pi/10 do result = result+math.pi*2 end end return result end -- result is from -π/2 to 3π/2, approximately adding math.atan2 from Lua 5.3 -- (LÖVE is Lua 5.1) function geom.angle(x1,y1, x2,y2) local result = math.atan((y2-y1)/(x2-x1)) if x2 < x1 then result = result+math.pi end return result end -- is the line between x,y and cx,cy at an angle between s and e? function geom.angle_between(ox,oy, x,y, s,e) local angle = geom.angle(ox,oy, x,y) if s > e then s,e = e,s end -- I'm not sure this is right or ideal.. angle = angle-math.pi*2 if s <= angle and angle <= e then return true end angle = angle+math.pi*2 if s <= angle and angle <= e then return true end angle = angle+math.pi*2 return s <= angle and angle <= e end function geom.dist(x1,y1, x2,y2) return ((x2-x1)^2+(y2-y1)^2)^0.5 end