Isometric Tile Index From Position

BlitzMax Forums/BlitzMax Programming/Isometric Tile Index From Position

beanage (Posted 2010) [#1]

Hey, this is a solution I had a hard time to find myself, so I thought I'd share it with you. It basically allows you to convert from a 2d position to the x/y index of the underlying isometric tile. With a horrible amount of border cases to consider, you really won't wanna reinvent the wheel there. Feel free to use, modify, sell, marry my code :) Theres propably a dozen approaches, what I can claim about mine is that it is fast, numerically stable, and last but not least working perfectly accurate. Here is a screenshot of the testing application I wrote for the algorithm: Here is the coresponding code. Check out the <getTileIndizesAtPosition> Method to see the algorithm. Eventually part of the code originates from an upcoming engine of mine, so don't wonder about identifiers like "isoWorld" :) SuperStrict AppTitle = "Isometric Index Algorithm Demo" Global TILESIZE:Int = 50 Global DEBUGINFO:Double[7] '[n,y,m,x,h,m_,n_] Type isoWorld Field _terrain:isoTerritory[][] '[y][x] Field _scale:Double = TILESIZE Field _tile_w:Int = 2 Field _tile_h:Int = 1 Field _width:Double = 500.0 Field _height:Double = 500.0 Method _initTerritory( divx_:Int, divy_:Int, load_instant_:Int ) Local w_:Double = _width/ Double divx_ Local h_:Double = _width/ Double divx_ Local m_:Int = w_/ _scale Local n_:Int = h_/ _scale _terrain = _terrain[..divy_ ] For Local j_:Int = 0 Until divy_ _terrain[ j_ ] = _terrain[ j_][..divx_ ] For Local i_:Int = 0 Until divx_ _terrain[ j_][i_ ] = isoTerritory.Create(Self, i_, j_, m_, n_, w_, h_) Next Next End Method Method getTileScale:Double() Return _scale End Method Method getTileHWratio:Double() Return (Double _tile_h)/(Double _tile_w) End Method Method getTerritory:isoTerritory( i_:Int, j_:Int ) If (j_< _terrain.Length) And (j_>= 0) If (i_< _terrain[ j_ ].Length) And (i_>= 0) Return _terrain[ j_][i_ ] End If End If End Method End Type Type isoTerritory Field _world:isoWorld Field _w:Double Field _h:Double Field _i:Int Field _j:Int Field _objects:Object[][] '[x][y] TList|isoObject Function Create:isoTerritory( world_:isoWorld, i_:Int, j_:Int, m_:Int, n_:Int, w_:Double, h_:Double ) Local ret_:isoTerritory = New isoTerritory ret_._world = world_ ret_._w = w_ ret_._h = h_ ret_._i = i_ ret_._j = j_ 'init object list arrays ret_._objects = ret_._objects[..n_ ] For Local k_:Int = 0 Until n_ ret_._objects[ k_ ] = ret_._objects[ k_ ][..m_ ] Next Return ret_ End Function Method getNumTilesW:Int() Return _objects[0].Length End Method Method getNumTilesH:Int() Return _objects.Length End Method Function DoublesAreEqual:Int( d1_:Double, d2_:Double ) Return Abs(d1_- d2_)< .00001! End Function Method getTileIndizesAtPosition:Int( pos_:Double[], out_i_:Int Ptr, out_j_:Int Ptr ) 'returns false if no tile at that position. pos must be relative to the territory. If pos_.Length> 1 'just to make it sure Local halfsize_:Double = _world.getTileScale()/ 2 Local y_:Double = pos_[1] 'y pos Local n_:Int = y_/ halfsize_ 'tile line index (presumption) If n_ Then n_:- 1 '################ DEBUGINFO[2] = n_ '################ y_ = (n_+ 1)* halfsize_ - y_ 'make y relative to tile '################ DEBUGINFO[1] = y_ '################ Local off_:Double = ( n_ Mod 2 )* halfsize_ 'tile border function offset Local m_:Int = ( pos_[0]- off_ )/ _world.GetTileScale() 'tile row index (presumption) '################ DEBUGINFO[4] = m_ '################ Local x_:Double = ( ( pos_[0] - off_ ) Mod _world.getTileScale() )+ off_ '################ DEBUGINFO[3] = x_ '################ out_i_[0] = m_ out_j_[0] = n_ If Not DoublesAreEqual(x_, halfsize_+ off_) 'calculate h Local h_:Double If x_< ( halfsize_+ off_ ) h_ = x_- off_ If Abs(y_)> h_ 'find neighbouring tile.. If m_ And Not off_ out_i_[0]:- 1 ElseIf .. ( off_ And ( Abs(y_) < (off_- x_) ) And Not m_ ) .. 'this covers a special case where <n> is indented (off > 0) and <m> is zero. Or Not ( off_ Or m_ ) Return False End If Else Return True End If Else h_ = halfsize_- ( x_- off_- halfsize_ ) If Abs(y_)> h_ 'find neighbouring tile.. If off_ And ( m_ < ( getNumTilesW()- 1 ) ) out_i_[0]:+ 1 ElseIf off_ Return False End If Else Return True End If End If '################ DEBUGINFO[0] = h_ '################ If ( y_< 0 ) And ( n_< getNumTilesH()- 1 ) out_j_[0]:+ 1 ElseIf ( y_> 0 ) And n_ out_j_[0]:- 1 Else Return False End If '################ Else DEBUGINFO[4] = -1 '################ End If End If Return True End Method End Type Global world:isoWorld = New isoWorld world._initTerritory(1, 1, 0) Global territory:isoTerritory = world.getTerritory(0, 0) Function drawTerritory() Local mpos_:Double[] = [Double MouseX(), Double MouseY()] Local reti_:Int Local retj_:Int If Not territory.getTileIndizesAtPosition(mpos_, VarPtr reti_, VarPtr retj_) reti_ = -1 retj_ = -1 End If DEBUGINFO[5] = retj_ DEBUGINFO[6] = reti_ For Local j_:Int = 0 Until territory.getNumTilesH() For Local i_:Int = 0 Until territory.getNumTilesW() If ( reti_ = i_ ) And ( retj_ = j_ ) SetColor 255, 0, 0 Else SetColor 255, 255, 255 End If Local x_:Int = i_* TILESIZE + ( j_ Mod 2 )* TILESIZE/ 2 Local y_:Int = j_* TILESIZE/ 2 Local swh_:Int[] = [TextWidth(String(i_)), TextHeight(String(i_))] DrawLine x_+ 1, y_+ TILESIZE/ 2, x_+ TILESIZE/ 2, y_+ 1 DrawLine x_+ TILESIZE/ 2, y_+ 1, x_+ TILESIZE - 1, y_+ TILESIZE/ 2 DrawLine x_+ TILESIZE - 1, y_+ TILESIZE/ 2, x_+ TILESIZE/ 2, y_+ TILESIZE - 1 DrawLine x_+ 1, y_+ TILESIZE/ 2, x_+ TILESIZE/ 2, y_+ TILESIZE - 1 DrawText i_, x_ + TILESIZE/ 2 - swh_[0]/ 2, y_ + TILESIZE/ 2 - swh_[1]/ 2 Next Next End Function Function DrawDebugInfo:Int( x_:Int, y_:Int, boxw_:Int, caption_:String, value_:String ) caption_:+ ":" Local w_:Int = TextWidth(caption_) Local h_:Int = TextHeight(caption_) SetColor 128, 128, 128 DrawRect x_- 5, y_- 5, boxw_, h_+ 10 SetColor 255, 255, 255 DrawText caption_, x_, y_ SetColor 0, 0, 0 DrawText value_, x_+ boxw_- TextWidth(value_)- 10, y_ Return h_+ 10 End Function Graphics 800, 600 Repeat Cls drawTerritory Local y_:Int = 600- (TextHeight("X") + 10) For Local i_:Int = 0 To 6 Local caption_:String Select i_ Case 6 caption_ = "Final horizontal index " Case 5 caption_ = "Final vertical index" Case 2 'n caption_ = "Vertical index guess" Case 1 'y caption_ = "Y relative to y index guess" Case 4 'm caption_ = "Horizontal index guess" Case 3 'x caption_ = "X relative to tile" Case 0 'h caption_ = "Calculated h(x)" End Select DrawDebugInfo 10, y_, 400, caption_, String(DEBUGINFO[i_])[..5] y_:- 30 Next SetColor 0, 255, 0 DrawLine MouseX(), MouseY()- 10, MouseX(), MouseY()+ 10 DrawLine MouseX()- 10, MouseY(), MouseX()+ 10, MouseY() Flip False Until AppTerminate() Or KeyHit(KEY_ESCAPE)

Jesse (Posted 2010) [#2]

nice! Thanks.

slenkar (Posted 2010) [#3]

thanks i use iso myself, ill check it out

BladeRunner (Posted 2010) [#4]

Function PickTile( px, py ) Local tg#, x, y, tx, ty ; transform coords. x = Floor(( px +(py -23)*2 ) /92.0) ; 23 = Tileheight /2, 92 = Tilewidth y = Floor(( py -(px -46)*0.5 ) /46.0) ; 46 = Tilewidth /2, 46 = Tileheight ; transform indices tx = Floor((x-y)/2) ty = y +x ; set picked coords PickedTileX = tx PickedTileY = ty End Function Was in B3D, should work here too after changing it to MaxCode The bordercheck can be done with little additional work.

Me.32 (Posted 2010) [#5]

- delete

beanage (Posted 2010) [#6]

Thanks for your kind comments! @Blade Runner: That looks like a reasonable alternative! For now I am happy with my solution (but TBH yours seems tighter, tougher and faster, and I have no idea how its doing what its supposed to do ;). Certainly looks like I reinvented the wheel :/. How does it work? -- edit Ah I think I understand it now. You are taking the rotation approach, dont you? Well, mine is less analytic and more pragmatic :) (after all perfectly adjusted to my requirements)

slenkar (Posted 2010) [#7]

in your demo the tiles are the same width as height but in the code it says they are 2:1 twice as wide as high, ?? ALso can you get scrolling to work?