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