How
to draw the Rubik’s Cube?
(Compare with the method drawCube (int number) in DrawRubiksCube.class)
First we produce one little cube drawing and scaling
only its visible sides . Each little cube is added to its own TransformGroup.
This TransformGroup sets the little cube to its position in the Rubik’s
Cube.
In this way the whole Rubik’s Cube is put together.
All the TransformGroups of the little cubes are
combined to one TransformGroup.
So it is possible to manipulate the little cubes
(scaling/ setting transparency/ making the inside of the little cubes visible)
and the Rubik’s Cube (scaling/ rotating).
Our algorithm draws the Rubik’s Cube in the following way:
The parameter number of drawCube (int number) decides
if a 2x2x2, 3x3x3, 4x4x4, 5x5x5 or 6x6x6 Cube is drawn.
A vertical column is fixed. The lowest row is drawn
from front to back, then the row above and so on.
In this manner all the other columns are drawn.
Problem:
The Rubik’s Cube must be set exactly in the origin,
so that the animation of each possible Rubik’s Cube is correct.
How to calculate the positions of each little cube?
Our solution:
The length of the edges is given and for each size
of the Rubik’s Cube the same.
Then you have to spread the number of the little
cubes in one row /column over the given length of the edge.
(E.g. in a 3x3x3 Rubik’s Cube you have to distribute
3 little cubes)
You have to calculate exactly the start position
of the first little cube . After that you have to determine the distance
between the centres of the little cubes, so that the cubes can be set to
the right position. Dependent on the distance you have to scale the surfaces
of the little cubes.
In our program the start positions of the different
Rubik’s Cubes are constant values.
The distance and the scale are computed at runtime.
The distance and the scale are computed at runtime.
The first little cube is set to the start position. All the following cubes are set in the computed distance.
Here
are the formulas we have used to calculate the start position:
- Length of the edge = 0.42 (this value was laid down by us)
- Surface area of one little cube = length of the edge / number of the little cubes in one row
- Distance to the next little cube = 2 * surface area of one little cube
- Start position = ((number of the little cubes in one row – 1) * distance to the next little cube) / 2
