geom.lua

   1 geom = {}
   2
   3 function geom.on_shape(x,y, drawing, shape)
   4   if shape.mode == 'freehand' then
   5     return geom.on_freehand(x,y, drawing, shape)
   6   elseif shape.mode == 'line' then
   7     return geom.on_line(x,y, drawing, shape)
   8   elseif shape.mode == 'manhattan' then
   9     local p1 = drawing.points[shape.p1]
  10     local p2 = drawing.points[shape.p2]
  11     if p1.x == p2.x then
  12       if x ~= p1.x then return false end
  13       local y1,y2 = p1.y, p2.y
  14       if y1 > y2 then
  15         y1,y2 = y2,y1
  16       end
  17       return y >= y1-2 and y <= y2+2
  18     elseif p1.y == p2.y then
  19       if y ~= p1.y then return false end
  20       local x1,x2 = p1.x, p2.x
  21       if x1 > x2 then
  22         x1,x2 = x2,x1
  23       end
  24       return x >= x1-2 and x <= x2+2
  25     end
  26   elseif shape.mode == 'polygon' or shape.mode == 'rectangle' or shape.mode == 'square' then
  27     return geom.on_polygon(x,y, drawing, shape)
  28   elseif shape.mode == 'circle' then
  29     local center = drawing.points[shape.center]
  30     local dist = geom.dist(center.x,center.y, x,y)
  31     return dist > shape.radius*0.95 and dist < shape.radius*1.05
  32   elseif shape.mode == 'arc' then
  33     local center = drawing.points[shape.center]
  34     local dist = geom.dist(center.x,center.y, x,y)
  35     if dist < shape.radius*0.95 or dist > shape.radius*1.05 then
  36       return false
  37     end
  38     return geom.angle_between(center.x,center.y, x,y, shape.start_angle,shape.end_angle)
  39   elseif shape.mode == 'deleted' then
  40   else
  41     assert(false, ('unknown drawing mode %s'):format(shape.mode))
  42   end
  43 end
  44
  45 function geom.on_freehand(x,y, drawing, shape)
  46   local prev
  47   for _,p in ipairs(shape.points) do
  48     if prev then
  49       if geom.on_line(x,y, drawing, {p1=prev, p2=p}) then
  50         return true
  51       end
  52     end
  53     prev = p
  54   end
  55   return false
  56 end
  57
  58 function geom.on_line(x,y, drawing, shape)
  59   local p1,p2
  60   if type(shape.p1) == 'number' then
  61     p1 = drawing.points[shape.p1]
  62     p2 = drawing.points[shape.p2]
  63   else
  64     p1 = shape.p1
  65     p2 = shape.p2
  66   end
  67   if p1.x == p2.x then
  68     if math.abs(p1.x-x) > 2 then
  69       return false
  70     end
  71     local y1,y2 = p1.y,p2.y
  72     if y1 > y2 then
  73       y1,y2 = y2,y1
  74     end
  75     return y >= y1-2 and y <= y2+2
  76   end
  77   -- has the right slope and intercept
  78   local m = (p2.y - p1.y) / (p2.x - p1.x)
  79   local yp = p1.y + m*(x-p1.x)
  80   if yp < y-2 or yp > y+2 then
  81     return false
  82   end
  83   -- between endpoints
  84   local k = (x-p1.x) / (p2.x-p1.x)
  85   return k > -0.005 and k < 1.005
  86 end
  87
  88 function geom.on_polygon(x,y, drawing, shape)
  89   local prev
  90   for _,p in ipairs(shape.vertices) do
  91     if prev then
  92       if geom.on_line(x,y, drawing, {p1=prev, p2=p}) then
  93         return true
  94       end
  95     end
  96     prev = p
  97   end
  98   return geom.on_line(x,y, drawing, {p1=shape.vertices[1], p2=shape.vertices[#shape.vertices]})
  99 end
 100
 101 -- are (x3,y3) and (x4,y4) on the same side of the line between (x1,y1) and (x2,y2)
 102 function geom.same_side(x1,y1, x2,y2, x3,y3, x4,y4)
 103   if x1 == x2 then
 104     return math.sign(x3-x1) == math.sign(x4-x1)
 105   end
 106   if y1 == y2 then
 107     return math.sign(y3-y1) == math.sign(y4-y1)
 108   end
 109   local m = (y2-y1)/(x2-x1)
 110   return math.sign(m*(x3-x1) + y1-y3) == math.sign(m*(x4-x1) + y1-y4)
 111 end
 112
 113 function math.sign(x)
 114   if x > 0 then
 115     return 1
 116   elseif x == 0 then
 117     return 0
 118   elseif x < 0 then
 119     return -1
 120   end
 121 end
 122
 123 function geom.angle_with_hint(x1, y1, x2, y2, hint)
 124   local result = geom.angle(x1,y1, x2,y2)
 125   if hint then
 126     -- Smooth the discontinuity where angle goes from positive to negative.
 127     -- The hint is a memory of which way we drew it last time.
 128     while result > hint+math.pi/10 do
 129       result = result-math.pi*2
 130     end
 131     while result < hint-math.pi/10 do
 132       result = result+math.pi*2
 133     end
 134   end
 135   return result
 136 end
 137
 138 -- result is from -π/2 to 3π/2, approximately adding math.atan2 from Lua 5.3
 139 -- (LÖVE is Lua 5.1)
 140 function geom.angle(x1,y1, x2,y2)
 141   local result = math.atan((y2-y1)/(x2-x1))
 142   if x2 < x1 then
 143     result = result+math.pi
 144   end
 145   return result
 146 end
 147
 148 -- is the line between x,y and cx,cy at an angle between s and e?
 149 function geom.angle_between(ox,oy, x,y, s,e)
 150   local angle = geom.angle(ox,oy, x,y)
 151   if s > e then
 152     s,e = e,s
 153   end
 154   -- I'm not sure this is right or ideal..
 155   angle = angle-math.pi*2
 156   if s <= angle and angle <= e then
 157     return true
 158   end
 159   angle = angle+math.pi*2
 160   if s <= angle and angle <= e then
 161     return true
 162   end
 163   angle = angle+math.pi*2
 164   return s <= angle and angle <= e
 165 end
 166
 167 function geom.dist(x1,y1, x2,y2) return ((x2-x1)^2+(y2-y1)^2)^0.5 end