How Do I Define A Slowly Tilting Plane On An LED Cube? (Warning, math ahead)

please watch video starting @ 0:43:
http://www.youtube.com/watch?v=03bkigwyox0.
i'm attempting recreate plane of leds tilting xy-plane xz-plane.

i have 4x4x4 cube.

here i've figured out far:
r = (0, 0, 0) + s(1, 0, 0) + t(0, y, z) y variable going 1->0 , z variable going 0->1

i can define 2 functions first increment z 0 1 , y 1 0, don't think elegant. thinking should done concurrently using 1 incrementor variable reduces y , increases z @ same time.

so here function (written , being testing in java):

code: [select]


   public static void main(string[] args){
       double incrementor = 0.2; //0 -> 1;
       for(int s = 0; s<4; s++){
           for(int t=0; t<4; t++){
               int x = s;
               int y = (int)((t*(1-incrementor)) + 0.5); //1 -> 0
               int z = (int)((t*incrementor)+ 0.5);     //0 - 1
               system.out.println("co-ordinates: (" + x + ", " + y + ", " + z + ")");
           }
        system.out.println();
       }
   }


now here problem: can restrict x values range 0 3 setting loop of s parameter go through 0 3. notice t variable. noticed when set 0 3, x , y values don't reach length of cube (i.e. y never equals 3). furthermore, because of rounding, plane 'doubles' up. say, @ y=2, leds @ z=0 , z=1 both on. not plane

i appreciate time reading , advice or code snippets or links.

maybe if deal in terms of "plane" series of parallel lines.
http://en.wikipedia.org/wiki/bresenham%27s_line_algorithm
but, still, compromise inevitable.

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