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June 2000 Programmer's Challenge
Rub*k Rotation
Mail solutions to:
progchallenge@mactech.com
Due Date: 11:59pm ET, Saturday, 3 June 2000
Readers sometimes write me to ask whether they can solve the Challenge on a platform other than a Mac. Now, I’m not sure why a reader of this publication would want to do that, but in many cases the Challenge is platform agnostic and quite amenable to solution an another machine. Sometimes I get mail thanking me for creating non-Mac-specific problems. Then again, I also get mail asking why problems that have nothing to do with the Mac appear in a Macintosh publication. Paraphrasing Lincoln, you can’t please all of the people all of the time. But it has been a while since we’ve had a Macintosh-specific problem, so we’re going to offer one this month.
The last Challenge I competed in required readers to solve the puzzle known as Rub*k’s Cube, a 3x3 cube of smaller cubies where each cube face was colored with a different color. Solving that Challenge took me right to the midnight deadline, past many midnights before that one, and actually pushed me over the edge into Challenge retirement (as a contestant, anyway). As I write this column, having watched another midnight come and go, I thought we’d revisit the Cube, but from a completely different perspective.
Your Challenge this month is to write a program that will display the cube, animating both rotations of the cube and the moves used to solve the cube. The prototype for the code you should write is:
typedef enum { /* identify the cube face */
kFront=0, kBack, kLeft, kRight, kUp, kDown
} CubeFace;
typedef enum { /* identify the axes of rotation */
kFrontBack=0, kLeftRight, kUpDown
/* rotation axis kXY is oriented viewing face X, through the cube, toward face Y */
} CubeAxis;
typedef enum {
kClockwise=1, kCounterClockwise=-1
} TurnDirection;
void InitCube(
CWindowPtr cubeWindow, /* window where the rotating cube should be rendered */
const RGBColor cubeColors[6], /* colors to use in rendering, indexed by CubeFace */
const short cubieColors[6][3][3], /* cubieColors is the index into cubeColors for individual cubies */
short cubeWidth, /* size in pixels of a cube in the standard orientation (kFront visible) */
short stepSize /* granularity to redraw, stepSize steps is one full 360 degree rotation */);
void QuarterTurn(
CubeFace face, /* turn this face one quarter turn */
TurnDirection direction /* turn the face in this direction */
/* turn orientation is looking at the face from outside the cube toward the center of the cube */);
void RotateCube(
CubeAxis axis, /* rotate cube about the specified axis */
TurnDirection direction, /* rotate the cube in this direction about the specified axis */
/* clockwise about the kFrontBack face is determined viewing from the kFront face, through the cube to the kBack face */
short stepsToTurn
);
void TermCube(void);
This Challenge will start with a call to your InitCube routine providing a number of problem parameters. The window in which you should render the cube, a color window with a pixelSize of 32 bits, will be provided in cubeWindow. The colors making up the cube faces will be provided in cubeColors, and the individual cubie colors will be specified by cubieColors as indices into cubeColors. You should center your display of the cube in the cubeWindow, and size the cube so that it is cubeWidth pixels on a side, in its initial position, oriented along the u-v axes, and viewed along the cube normal. InitCube should draw the cube in its initial posiiton, viewing the kFront face along the kFrontBack axis, with the kUp face at the top of the cube, perpendicular to the view plane. The cube may be displayed with a perspective projection, from a reasonable distance, or from an orthographic projection from infinity.
The final parameter provided to InitCube is the stepSize, used by the QuarterTurn and RotateCube calls in animating cube turns and rotations. The stepSize parameter specifies how granular the animations and rotations should be, with stepSize rotation steps constituting one full rotation. The value of stepSize will be a multiple of 4, so that quarter turns will contain an integral number of steps.
The QuarterTurn routine is called to turn the 9 cubies on one face of the cube by 90 degrees relative to the rest of the cube. When QuarterTurn is called, you should rotate the specified face in the specified direction, animated in increments determined by stepSize. Any internal portions of the cube not normally visible, but visible during the turn, should be displayed in a gray or black color of your choice.
The RotateCube routine is called to rotate the entire cube, respectively. When RotateCube is called, you should rotate the entire cube about the specified cube axis in the specified direction. As multiple calls are made to RotateCube, the axes of rotation will become arbitrarily oriented with respect to the view vector, although the cube will remain centered in the cubeWindow.
Finally, the TermCube routine will be called at the end of the test, allowing you to clean up any memory you might have allocated before returning. There may be multiple test cases, each bracketed with an InitCube and a TermCube call.
The commentary in the code for the CubeAxis describe the orientation used to perform clockwise and counterclockwise rotations of the cube. Similarly, the commentary for the CubeFace in the QuarterTurn prototype describes the orientation for performing face quarter turns. If these explanations are not clear, please send me a note on the Challenge mailing list for clarification.
Scoring will be based first on the quality of the accuracy of the display, and the absence of tearing or other display anomalies. Among the accurate entries with acceptable display quality, the winner will be the solution requiring the least execution time.
This will be a native PowerPC Challenge, using the CodeWarrior Pro 5 environment. Solutions may be coded in C, C++, or Pascal. Solutions in Java will also be accepted, but Java entries must be accompanied by a test driver that uses the interface provided in the problem statement.
Test code for this Challenge is available.
You can get a head start on the Challenge by reading the
Programmer's Challenge mailing list. It will be posted to the list on
or before the 12th of the preceding month. To join, send an email to
listserv@listmail.xplain.com
with the subject "subscribe challenge-A". You can also join the
discussion list by sending a message with the subject "subscribe
challenge-D".
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