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Volume Number: 16 (2000)
Issue Number: 9
Column Tag: Programmer's Challenge
Programmer's Challenge
by Bob Boonstra, Westford, MA
Busy Beavers
Before we get to this month's Challenge, I have to confess being a little distracted. No, not because the annual holiday up at the lake is just a few days away, although I'll also confess that the prospect of a couple of weeks away from the Real Job is most appealing. No, the distraction is because UPS just delivered another addition to the family of computers at the Boonstra household. The most recent additions have been iMacs for the Junior members of the family, but this one is for Me. A new G4. No, not one of the new dual-processor models introduced by Apple at JavitsWorld. (Those of us in Boston cannot acknowledge use of the term MacWorld for anything on the Right Coast that doesn't happen in Bean Town.) Dual processors might mean something to those PhotoShop users among you, but they don't do much for the Rest of Us until Mac OS X comes along. No, the new addition is one of those now-obsolete single-processor G4-500 models that have (finally) dropped a little in price. As those of you who participate in the Challenge contests know, I've been limping along with an old 8500, enhanced over the years with a faster 604e, then a dual 604e upgrade (BeOS, oh BeOS, wherefore art thou BeOS?), and finally with a G3 board. Several readers have asked in the past about whether AltiVec technology could be used in the Challenge, but, sadly, I didn't have a G4 to use in the evaluation. A problem now rectified, or at least it will be once I complete the file transfers proceeding even as I write.
Now that you all know about my new toy, we can get on to the business at hand. This month's problem was suggested by F. C Kuechmann, who earns two Challenge points for the suggestion. Your Challenge this month is to create a Busy Beaver Turing Machine and write a program that simulates its execution.
The Busy Beaver problem was invented in the early 1960s by Tibor Rado of Ohio State University. He asked the following question about 2-symbol Turing machines: what is the largest number of 1s that a Turing machine with n states could write to a tape initially filled with 0s. That "busy beaver" number, or BB(n), has some interesting properties. For example, by reasoning about the Halting Problem, one can show that BB(n) grows faster than any computable sequence.
An internet search shows that the Busy Beaver problem continues to attract interest. Until 1985, the largest value for a 5-state busy beaver produced 501 1s. Then George Uhing found a 5-state machine that produced 1915 1s before halting. And in 1987, Heiner Marxen (and Jürgen Buntrock showed that BB(5) is at least 4098.
For reference, you can start with the following URLs: Marxen's page at <http://www.drb.insel.de/~heiner/BB/index.html>, and <http://grail.cba.csuohio.edu/~somos/bb.html>
The prototype for the code you should write is:
typedef unsigned long ulong; typedef enum {kMoveLeft=-1,kHalt=0, kMoveRight=1} MoveDir; typedef struct TMRule { /* Turing Machine rule */ ulong oldState; /* this rule applies when the machine state is oldState */ Boolean inputSymbol; /* and the current input symbol is inputSymbol */ ulong newState; /* set current state to newState when this rule fires */ Boolean outputSymbol; /* write outputSymbol to tape when this rule fires */ char moveDirection; /* kMoveLeft, kMoveRight, or kHalt */ } TMRule; ulong /* return number of rules */ BusyBeaver5( TMRule theTMRules[], /* preallocated storage, return the rules for your BB machine */ ); Boolean /* return true for success */ RunTuringMachine( TMRule theTMRules[], /* preallocated storage, return the rules for your BB machine */ ulong numberOfTMRules, /* the number of rules in theTMRules */ ulong numBytesInHalfTape, /* half-size of the "infinite" Turing Machine tape */ unsigned char *tmTape, /* pointer to preallocated Turing Machine tape storage */ /* Each byte contains 8 tape symbols, each symbol is 0 or 1. */ /* The tape extends from tmTape[-numBytesInHalfTape] to tmTape[numBytesInHalfTape -1] */ /* Tape position 0 is (tmTape[0] & 0x80), tape position 1 is (tmTape[0] & 0x40) tape position -1 is (tmTape[-1] & 0x01), etc. */ ulong *numberOf1sGenerated, /* return the number of 1s placed on the tape */ ulong *numberOfRulesExecuted /* return the number of rules executed when running BB, including the halt rule */ );
The first thing you need to do is to select the 5-state Busy Beaver Turing Machine that you will simulate in your RunTuringMachine routine. Since scoring is based on how busy your beaver is, that is, on how many 1s it produces on the simulated Turing Machine tape, you want to give some careful thought to this selection. This Turing Machine should returned by your BusyBeaver5 using the TMRule data structure. BusyBeaver5 may return a hard-coded Turing Machine; it does not need to identify the busy beaver at run time.
My test code will then provide the output of BusyBeaver5 to your RunTuringMachine routine, which should simulate the execution of the input Turing Machine. RunTuringMachine will be provided with a blank (zero-filled) tape tmTape that is 2*numBytesInHalfTape in size. The "read head" of the Turing Machine is initially positioned over position [0] of the tape. On exit, tmTape should contain the output of the Turing Machine being simulated. In addition, you should return in the appropriate output parameters the number of 1s on the output tape and the number of state transitions that occurred during your execution of the Turing Machine. RunTuringMachine should return TRUE if it was able to successfully execute the Turing Machine, and FALSE if it failed for some reason, such as running out of simulated tape. (It is not my intention to provide a simulated tape that is too short, but your code should fail gracefully if that happens during testing.)
RunTuringMachine must provide a general Turing Machine simulation, not dependent on the Busy Beaver problem or on the content of the initial input tape. I may choose to verify correctness of your RunTuringMachine code against other input besides that produced by BusyBeaver5.
The winner will be the solution that identifies the 5-state Busy Beaver generating the most 1s on the output tape. Among solutions with equal numbers of 1s, the solution that produces the output in the fewest number of Turing Machine steps will be the winner. And, for solutions that produce the same output in the same number of steps, the winner will be the solution that executes the Turing Machine in the least execution time. While my hope is that one of you might break new ground in the field of busy beaver research, my expectation is that the winning solution will be determined by the execution time criterion.
This will be a native PowerPC Challenge, using the CodeWarrior Pro 5 environment. Solutions may be coded in C, C++, or Pascal. As is our tradition for the September Column, we'll also allow solutions that are completely or partially coded in assembly language. And, yes, this time you can take advantage of the AltiVec features of the G4.
Three Months Ago Winner
Congratulations to Willeke Rieken (The Netherlands) for submitting the winning solution to the June Rub*k Rotation Programmer's Challenge. Readers may recall that the Rub*k Rotation Challenge required contestants to display an image of the famous puzzle and respond to commands to rotate the entire cube or individual cube faces. Scoring was based on correctness of the solution, in this case the smoothness of the displayed rotations, and on execution time.
The fact that Willeke was the only person to submit an entry does not detract from his solution in the slightest, although it did significantly increase his chances of winning. (You can't win if you don't play!) Willeke elected to use QuickDraw3D to implement his solution, motivated by a desire to gain some experience with the QD3D API. His code creates 26 individual cubies (the center cubie is never visible) using the AddCubie routine. Although it might look like a lot of work to set up the cube, the effort pays off in the simplicity with which one can rotate the cube (RotateCube), turn a face of the cube (QuarterTurn), and draw the entire cube (DrawCube), regardless of orientation.
With only one entry, I'll omit the usual table describing the parameters of the solution, and simply observe that this victory vaults Willeke into 4th place in the overall Challenge standings. And remember, you can't win if you don't ...., oh, I'm repeating myself.
Top Contestants
Listed here are the Top Contestants for the Programmer's Challenge, including everyone who has accumulated 10 or more points during the past two years. The numbers below include points awarded over the 24 most recent contests, including points earned by this month's entrants.
Rank | Name | Points |
1. | Munter, Ernst | 245 |
2. | Saxton, Tom | 126 |
3. | Maurer, Sebastian | 78 |
4. | Rieken, Willeke | 65 |
5. | Boring, Randy | 50 |
6. | Shearer, Rob | 47 |
7. | Taylor, Jonathan | 26 |
8. | Brown, Pat | 20 |
9. | Heathcock, JG | 16 |
10. | Downs, Andrew | 12 |
11. | Jones, Dennis | 12 |
12. | Day, Mark | 10 |
13. | Duga, Brady | 10 |
14. | Fazekas, Miklos | 10 |
15. | Murphy, ACC | 10 |
16. | Selengut, Jared | 10 |
17. | Strout, Joe | 10 |
There are three ways to earn points: (1) scoring in the top 5 of any Challenge, (2) being the first person to find a bug in a published winning solution or, (3) being the first person to suggest a Challenge that I use. The points you can win are:
1st place | 20 points |
2nd place | 10 points |
3rd place | 7 points |
4th place | 4 points |
5th place | 2 points |
finding bug | 2 points |
suggesting Challenge | 2 points |
Here is Willeke's winning Rub*k Rotation solution:
RubikRotation.c Copyright © 2000 Willeke Rieken /* draws (a simplified version of) Rubik's cube and animates rotations of the cube and of the faces of the cube. I'm using QD3D because I never used it and it seemed more fun than a diy method and drowning in sin and cos and I still think it is. the model object for the cube consists of 26 group objects for each cubie and a rotation object. the rotation object contains all previous rotations of the whole cube added together. each cubie object contains a box object and a rotation object. a cubie rotation object contains all previous rotations of the cubie that was caused by rotating a face of the cube. during rotation of the cube an extra rotation object is submitted. after the rotation the rotation object of the cube is adjusted. during rotation of a face an exta rotation object is added to every cubie in the face. after the rotation the extra rotation object is removed and the rotation object of the cubie is adjusted. references to the rotation object of the cube and to the cubie objects are kept in globals. */ #include <QD3D.h> #include <QD3DDrawContext.h> #include <QD3DRenderer.h> #include <QD3DShader.h> #include <QD3DCamera.h> #include <QD3DLight.h> #include <QD3DGeometry.h> #include <QD3DGroup.h> #include <QD3DMath.h> #include <QD3DTransform.h> #include <QD3DView.h> #include <QD3DAcceleration.h> #include <QD3DErrors.h> #include "RubikRotation.h" TQ3ViewObject gView; // the view for the scene TQ3StyleObject gInterpolation; // interpolation style used when rendering TQ3StyleObject gBackFacing; // whether to draw shapes that face away from the camera TQ3StyleObject gFillStyle; // whether drawn as solid filled object or decomposed to components TQ3GroupObject gCubeModel; // the cube TQ3GroupObject gCubies[3][3][3]; // the cubies TQ3TransformObject gCubeRotation; // cumulation of every rotation of the whole cube until now TQ3TransformObject gTempCubeRotation; // used during rotation of the cube float gStepSize; static TQ3DrawContextObject MyNewDrawContext(CWindowPtr theWindow) // create context { TQ3DrawContextData myDrawContextData; TQ3MacDrawContextData myMacDrawContextData; TQ3ColorARGB clearColor; TQ3DrawContextObject myDrawContext ; // Set the background color clearColor.a = 1.0; clearColor.r = 1.0; clearColor.g = 1.0; clearColor.b = 1.0; // Fill in draw context data myDrawContextData.clearImageMethod = kQ3ClearMethodWithColor; myDrawContextData.clearImageColor = clearColor; myDrawContextData.paneState = kQ3False; myDrawContextData.maskState = kQ3False; myDrawContextData.doubleBufferState = kQ3True; myMacDrawContextData.drawContextData = myDrawContextData; myMacDrawContextData.window = theWindow; myMacDrawContextData.library = kQ3Mac2DLibraryNone; myMacDrawContextData.viewPort = 0; myMacDrawContextData.grafPort = 0; // Create draw context myDrawContext = Q3MacDrawContext_New(&myMacDrawContextData) ; return myDrawContext ; } static TQ3CameraObject MyNewOrthographicCamera(CWindowPtr theWindow, short cubeWidth) // create orthographic camera { TQ3OrthographicCameraData orthographicData; TQ3CameraObject camera; TQ3Point3D from = {0.0, 1.5, 7.0}; TQ3Point3D to = {0.0, 0.0, 0.0}; TQ3Vector3D up = {0.0, 1.0, 0.0}; orthographicData.cameraData.placement.cameraLocation = from; orthographicData.cameraData.placement.pointOfInterest = to; orthographicData.cameraData.placement.upVector = up; orthographicData.cameraData.range.hither = 1.0; orthographicData.cameraData.range.yon = 1000.0; orthographicData.cameraData.viewPort.origin.x = -1.0; orthographicData.cameraData.viewPort.origin.y = 1.0; orthographicData.cameraData.viewPort.width = 2.0; orthographicData.cameraData.viewPort.height = 2.0; // calculate view plane, size of the cube is 3.0 in QD3Points orthographicData.left = -1.5 * ((float)(theWindow->portRect.right - theWindow->portRect.left)) / (float)(cubeWidth + 1); orthographicData.top = orthographicData.left; orthographicData.right = -orthographicData.left; orthographicData.bottom = orthographicData.right; camera = Q3OrthographicCamera_New(&orthographicData); return camera; } static TQ3CameraObject MyNewViewPlaneCamera(CWindowPtr theWindow, short cubeWidth) { // create perspective camera TQ3ViewPlaneCameraData viewPlaneData; TQ3CameraObject camera; TQ3Point3D from = {0.0, 0.0, 7.0}; TQ3Point3D to = {0.0, 0.0, 1.5}; TQ3Vector3D up = {0.0, 1.0, 0.0}; viewPlaneData.cameraData.placement.cameraLocation = from; viewPlaneData.cameraData.placement.pointOfInterest = to; viewPlaneData.cameraData.placement.upVector = up; viewPlaneData.cameraData.range.hither = 1.0; viewPlaneData.cameraData.range.yon = 1000.0; viewPlaneData.cameraData.viewPort.origin.x = -1.0; viewPlaneData.cameraData.viewPort.origin.y = 1.0; viewPlaneData.cameraData.viewPort.width = 2.0; viewPlaneData.cameraData.viewPort.height = 2.0; // calculate view plane, size of the cube is 3.0 in QD3Points viewPlaneData.viewPlane = 5.5; viewPlaneData.halfWidthAtViewPlane = 1.5 * ((float)(theWindow->portRect.right - theWindow->portRect.left)) / (float)(cubeWidth + 1); viewPlaneData.halfHeightAtViewPlane = viewPlaneData.halfWidthAtViewPlane; viewPlaneData.centerXOnViewPlane = 0.0; viewPlaneData.centerYOnViewPlane = 0.0; camera = Q3ViewPlaneCamera_New(&viewPlaneData); return camera; } static TQ3GroupObject MyNewAmbientOnlyLights() { TQ3GroupObject myLightList; TQ3LightData myLightData; TQ3LightObject myAmbientLight; TQ3ColorRGB whiteLight = {1.0, 1.0, 1.0}; // Set up light data for ambient light. myLightData.isOn = kQ3True; myLightData.color = whiteLight; // Create ambient light. myLightData.brightness = 1.0; myAmbientLight = Q3AmbientLight_New(&myLightData); // Create light group and add each of the lights into the group. myLightList = Q3LightGroup_New(); Q3Group_AddObject(myLightList, myAmbientLight); Q3Object_Dispose(myAmbientLight) ; return myLightList; } static TQ3GroupObject MyNewLights() { TQ3GroupObject myLightList; TQ3LightData myLightData; TQ3PointLightData myPointLightData; TQ3DirectionalLightData myDirectionalLightData; TQ3LightObject myAmbientLight, myPointLight, myFillLight; TQ3Point3D pointLocation = {-10.0, 0.0, 10.0}; TQ3Vector3D fillDirection = {10.0, 0.0, 10.0}; TQ3ColorRGB whiteLight = {1.0, 1.0, 1.0}; // Set up light data for ambient light. // This light data will be used for point and fill light also. myLightData.isOn = kQ3True; myLightData.color = whiteLight; // Create ambient light. myLightData.brightness = 0.25; myAmbientLight = Q3AmbientLight_New(&myLightData); // Create point light. myLightData.brightness = 1.0; myPointLightData.lightData = myLightData; myPointLightData.castsShadows = kQ3False; myPointLightData.attenuation = kQ3AttenuationTypeNone; myPointLightData.location = pointLocation; myPointLight = Q3PointLight_New(&myPointLightData); // Create fill light. myLightData.brightness = 0.2; myDirectionalLightData.lightData = myLightData; myDirectionalLightData.castsShadows = kQ3False; myDirectionalLightData.direction = fillDirection; myFillLight = Q3DirectionalLight_New(&myDirectionalLightData); // Create light group and add each of the lights into the group. myLightList = Q3LightGroup_New(); Q3Group_AddObject(myLightList, myAmbientLight); Q3Group_AddObject(myLightList, myPointLight); Q3Group_AddObject(myLightList, myFillLight); Q3Object_Dispose(myAmbientLight); Q3Object_Dispose(myPointLight); Q3Object_Dispose(myFillLight); return myLightList; } static TQ3ViewObject MyNewView(CWindowPtr theWindow, short cubeWidth) { TQ3ViewObject myView; TQ3DrawContextObject myDrawContext; TQ3RendererObject myRenderer; TQ3CameraObject myCamera; TQ3GroupObject myLights; myView = Q3View_New(); // Create and set draw context. myDrawContext = MyNewDrawContext(theWindow); Q3View_SetDrawContext(myView, myDrawContext); Q3Object_Dispose(myDrawContext) ; // Create and set renderer. // use the interactive software renderer myRenderer = Q3Renderer_NewFromType(kQ3RendererTypeInteractive); Q3View_SetRenderer(myView, myRenderer); // these two lines set us up to use the best possible renderer, // including hardware if it is installed. Q3InteractiveRenderer_SetDoubleBufferBypass(myRenderer, kQ3True); Q3InteractiveRenderer_SetPreferences(myRenderer, kQAVendor_BestChoice, 0); /* for software renderer, without hardware accelleration, replace with: Q3InteractiveRenderer_SetPreferences(myRenderer, kQAVendor_Apple, kQAEngine_AppleSW); */ Q3Object_Dispose(myRenderer); // Create and set camera. myCamera = MyNewViewPlaneCamera(theWindow, cubeWidth); /* for an orthographic camera, replace with: myCamera = MyNewOrthographicCamera(theWindow, cubeWidth); */ Q3View_SetCamera(myView, myCamera); Q3Object_Dispose(myCamera) ; // Create and set lights. myLights = MyNewAmbientOnlyLights(); /* for better looking lights, replace with: myLights = MyNewLights(); */ Q3View_SetLightGroup(myView, myLights); Q3Object_Dispose(myLights); return myView; } static void DrawCube() { TQ3ViewStatus myStatus; Q3View_StartRendering(gView); do { Q3Style_Submit(gInterpolation, gView); Q3Style_Submit(gBackFacing, gView); Q3Style_Submit(gFillStyle, gView); if (gTempCubeRotation) Q3Transform_Submit(gTempCubeRotation, gView); Q3DisplayGroup_Submit(gCubeModel, gView); myStatus = Q3View_EndRendering(gView); } while (myStatus == kQ3ViewStatusRetraverse); } static void AddCubie(TQ3GroupObject theGroup, long theX, long theY, long theZ, TQ3ColorRGB *theLeftColor, TQ3ColorRGB *theRightColor, TQ3ColorRGB *theFrontColor, TQ3ColorRGB *theBackColor, TQ3ColorRGB *theTopColor, TQ3ColorRGB *theBottomColor) { TQ3GeometryObject myBox; TQ3BoxData myBoxData; TQ3SetObject faces[6]; TQ3GroupObject aCubie; TQ3TransformObject aTransformation; TQ3Matrix4x4 aMatrix; short face; // create a rotation object, it doesn't rotate yet // but it will be adjusted after rotating the face aCubie = Q3DisplayGroup_New(); Q3Matrix4x4_SetIdentity(&aMatrix); aTransformation = Q3MatrixTransform_New(&aMatrix); Q3Group_AddObject(aCubie, aTransformation); Q3Object_Dispose(aTransformation); // create the box itself myBoxData.faceAttributeSet = faces; myBoxData.boxAttributeSet = nil; myBoxData.faceAttributeSet[0] = Q3AttributeSet_New(); Q3AttributeSet_Add(myBoxData.faceAttributeSet[0], kQ3AttributeTypeDiffuseColor, theLeftColor); myBoxData.faceAttributeSet[1] = Q3AttributeSet_New(); Q3AttributeSet_Add(myBoxData.faceAttributeSet[1], kQ3AttributeTypeDiffuseColor, theRightColor); myBoxData.faceAttributeSet[2] = Q3AttributeSet_New(); Q3AttributeSet_Add(myBoxData.faceAttributeSet[2], kQ3AttributeTypeDiffuseColor, theFrontColor); myBoxData.faceAttributeSet[3] = Q3AttributeSet_New(); Q3AttributeSet_Add(myBoxData.faceAttributeSet[3], kQ3AttributeTypeDiffuseColor, theBackColor); myBoxData.faceAttributeSet[4] = Q3AttributeSet_New(); Q3AttributeSet_Add(myBoxData.faceAttributeSet[4], kQ3AttributeTypeDiffuseColor, theTopColor); myBoxData.faceAttributeSet[5] = Q3AttributeSet_New(); Q3AttributeSet_Add(myBoxData.faceAttributeSet[5], kQ3AttributeTypeDiffuseColor, theBottomColor); Q3Point3D_Set(&myBoxData.origin, -1.5 + theX, 0.5 - theY, 0.5 - theZ); Q3Vector3D_Set(&myBoxData.orientation, 0, 1, 0); Q3Vector3D_Set(&myBoxData.majorAxis, 0, 0, 1); Q3Vector3D_Set(&myBoxData.minorAxis, 1, 0, 0); myBox = Q3Box_New(&myBoxData); for (face = 0; face < 6; face++) if (myBoxData.faceAttributeSet[face] != 0) Q3Object_Dispose(myBoxData.faceAttributeSet[face]); Q3Group_AddObject(aCubie, myBox); Q3Object_Dispose(myBox); Q3Group_AddObject(theGroup, aCubie); gCubies[theX][theY][theZ] = aCubie; } static TQ3GroupObject MyNewModel(const RGBColor cubeColors[6], const short cubieColors[6][3][3]) { TQ3GroupObject myGroup = 0; TQ3ShaderObject myIlluminationShader ; TQ3Matrix4x4 aMatrix; TQ3ColorRGB Q3CubeColors[6]; TQ3ColorRGB aGray = {0.25, 0.25, 0.25}; long face; // convert RGBColor to TQ3ColorRGB for (face = 0; face < 6; face++) { Q3CubeColors[face].r = (float)cubeColors[face].red / 0xffff; Q3CubeColors[face].g = (float)cubeColors[face].green / 0xffff; Q3CubeColors[face].b = (float)cubeColors[face].blue / 0xffff; } // Create a group for the complete model. if ((myGroup = Q3DisplayGroup_New()) != 0) { // Define a shading type for the group // and add the shader to the group myIlluminationShader = Q3NULLIllumination_New(); /* for a better looking cube, replace with myIlluminationShader = Q3LambertIllumination_New(); or myIlluminationShader = Q3PhongIllumination_New(); */ Q3Group_AddObject(myGroup, myIlluminationShader); Q3Object_Dispose(myIlluminationShader); // create a rotation object, it doesn't rotate yet // but it will be adjusted after rotating the cube Q3Matrix4x4_SetIdentity(&aMatrix); gCubeRotation = Q3MatrixTransform_New(&aMatrix); Q3Group_AddObject(myGroup, gCubeRotation); // add boxes for the cubies // left top front AddCubie(myGroup, 0, 0, 0, &Q3CubeColors[cubieColors[kLeft][2][0]], &aGray, &Q3CubeColors[cubieColors[kFront][0][0]], &aGray, &Q3CubeColors[cubieColors[kUp][0][2]], &aGray); // middle top front AddCubie(myGroup, 1, 0, 0, &aGray, &aGray, &Q3CubeColors[cubieColors[kFront][1][0]], &aGray, &Q3CubeColors[cubieColors[kUp][1][2]], &aGray); // right top front AddCubie(myGroup, 2, 0, 0, &aGray, &Q3CubeColors[cubieColors[kRight][0][0]], &Q3CubeColors[cubieColors[kFront][2][0]], &aGray, &Q3CubeColors[cubieColors[kUp][2][2]], &aGray); // left top middle AddCubie(myGroup, 0, 0, 1, &Q3CubeColors[cubieColors[kLeft][1][0]], &aGray, &aGray, &aGray, &Q3CubeColors[cubieColors[kUp][0][1]], &aGray); // middle top middle AddCubie(myGroup, 1, 0, 1, &aGray, &aGray, &aGray, &aGray, &Q3CubeColors[cubieColors[kUp][1][1]], &aGray); // right top middle AddCubie(myGroup, 2, 0, 1, &aGray, &Q3CubeColors[cubieColors[kRight][1][0]], &aGray, &aGray, &Q3CubeColors[cubieColors[kUp][2][1]], &aGray); // left top back AddCubie(myGroup, 0, 0, 2, &Q3CubeColors[cubieColors[kLeft][0][0]], &aGray, &aGray, &Q3CubeColors[cubieColors[kBack][2][0]], &Q3CubeColors[cubieColors[kUp][0][0]], &aGray); // middle top back AddCubie(myGroup, 1, 0, 2, &aGray, &aGray, &aGray, &Q3CubeColors[cubieColors[kBack][1][0]], &Q3CubeColors[cubieColors[kUp][1][0]], &aGray); // right top back AddCubie(myGroup, 2, 0, 2, &aGray, &Q3CubeColors[cubieColors[kRight][2][0]], &aGray, &Q3CubeColors[cubieColors[kBack][0][0]], &Q3CubeColors[cubieColors[kUp][2][0]], &aGray); // left middle front AddCubie(myGroup, 0, 1, 0, &Q3CubeColors[cubieColors[kLeft][2][1]], &aGray, &Q3CubeColors[cubieColors[kFront][0][1]], &aGray, &aGray, &aGray); // middle middle front AddCubie(myGroup, 1, 1, 0, &aGray, &aGray, &Q3CubeColors[cubieColors[kFront][1][1]], &aGray, &aGray, &aGray); // right middle front AddCubie(myGroup, 2, 1, 0, &aGray, &Q3CubeColors[cubieColors[kRight][0][1]], &Q3CubeColors[cubieColors[kFront][2][1]], &aGray, &aGray, &aGray); // left middle middle AddCubie(myGroup, 0, 1, 1, &Q3CubeColors[cubieColors[kLeft][1][1]], &aGray, &aGray, &aGray, &aGray, &aGray); // middle middle middle /* invisible AddCubie(myGroup, 1, 1, 1, &aGray, &aGray, &aGray, &aGray, &aGray, &aGray); */ // right middle middle AddCubie(myGroup, 2, 1, 1, &aGray, &Q3CubeColors[cubieColors[kRight][1][1]], &aGray, &aGray, &aGray, &aGray); // left middle back AddCubie(myGroup, 0, 1, 2, &Q3CubeColors[cubieColors[kLeft][0][1]], &aGray, &aGray, &Q3CubeColors[cubieColors[kBack][2][1]], &aGray, &aGray); // middle middle back AddCubie(myGroup, 1, 1, 2, &aGray, &aGray, &aGray, &Q3CubeColors[cubieColors[kBack][1][1]], &aGray, &aGray); // right middle back AddCubie(myGroup, 2, 1, 2, &aGray, &Q3CubeColors[cubieColors[kRight][2][1]], &aGray, &Q3CubeColors[cubieColors[kBack][0][1]], &aGray, &aGray); // left bottom front AddCubie(myGroup, 0, 2, 0, &Q3CubeColors[cubieColors[kLeft][2][2]], &aGray, &Q3CubeColors[cubieColors[kFront][0][2]], &aGray, &aGray, &Q3CubeColors[cubieColors[kDown][0][0]]); // middle bottom front AddCubie(myGroup, 1, 2, 0, &aGray, &aGray, &Q3CubeColors[cubieColors[kFront][1][2]], &aGray, &aGray, &Q3CubeColors[cubieColors[kDown][1][0]]); // right bottom front AddCubie(myGroup, 2, 2, 0, &aGray, &Q3CubeColors[cubieColors[kRight][0][2]], &Q3CubeColors[cubieColors[kFront][2][2]], &aGray, &aGray, &Q3CubeColors[cubieColors[kDown][2][0]]); // left bottom middle AddCubie(myGroup, 0, 2, 1, &Q3CubeColors[cubieColors[kLeft][1][2]], &aGray, &aGray, &aGray, &aGray, &Q3CubeColors[cubieColors[kDown][0][1]]); // middle bottom middle AddCubie(myGroup, 1, 2, 1, &aGray, &aGray, &aGray, &aGray, &aGray, &Q3CubeColors[cubieColors[kDown][1][1]]); // right bottom middle AddCubie(myGroup, 2, 2, 1, &aGray, &Q3CubeColors[cubieColors[kRight][1][2]], &aGray, &aGray, &aGray, &Q3CubeColors[cubieColors[kDown][2][1]]); // left bottom back AddCubie(myGroup, 0, 2, 2, &Q3CubeColors[cubieColors[kLeft][0][2]], &aGray, &aGray, &Q3CubeColors[cubieColors[kBack][2][2]], &aGray, &Q3CubeColors[cubieColors[kDown][0][2]]); // middle bottom back AddCubie(myGroup, 1, 2, 2, &aGray, &aGray, &aGray, &Q3CubeColors[cubieColors[kBack][1][2]], &aGray, &Q3CubeColors[cubieColors[kDown][1][2]]); // right bottom back AddCubie(myGroup, 2, 2, 2, &aGray, &Q3CubeColors[cubieColors[kRight][2][2]], &aGray, &Q3CubeColors[cubieColors[kBack][0][2]], &aGray, &Q3CubeColors[cubieColors[kDown][2][2]]); } return myGroup; } void InitCube( CWindowPtr cubeWindow, const RGBColor cubeColors[6], const short cubieColors[6][3][3], short cubeWidth, short stepSize ) { long x, y, z; for (x = 0; x < 3; x++) for (y = 0; y < 3; y++) for (z = 0; z < 3; z++) gCubies[x][y][z] = 0; SetPort((GrafPtr)cubeWindow); gStepSize = stepSize; gTempCubeRotation = 0; gCubeRotation = 0; Q3Initialize(); // sets up the 3d data for the scene // Create view for QuickDraw 3D. gView = MyNewView(cubeWindow, cubeWidth); // the main display group: gCubeModel = MyNewModel(cubeColors, cubieColors); // the drawing styles: gInterpolation = Q3InterpolationStyle_New(kQ3InterpolationStyleNone); gBackFacing = Q3BackfacingStyle_New(kQ3BackfacingStyleRemove); gFillStyle = Q3FillStyle_New(kQ3FillStyleFilled); DrawCube(); } void QuarterTurn( CubeFace face, TurnDirection direction ) { long i, x, y, z; long aFirstX, aLastX, aFirstY, aLastY, aFirstZ, aLastZ; TQ3Matrix4x4 aCubieMatrix, aRotationMatrix; TQ3RotateAboutAxisTransformData aRotationdata; TQ3TransformObject aFaceRotation; TQ3GroupPosition aPos; TQ3GroupObject aCubie; long stepsToTurn; aFirstX = 0; aLastX = 3; aFirstY = 0; aLastY = 3; aFirstZ = 0; aLastZ = 3; // create a rotation object switch(face) { case kFront: { if (direction == kClockwise) Q3Vector3D_Set(&aRotationdata.orientation, 0.0, 0.0, -1.0); else Q3Vector3D_Set(&aRotationdata.orientation, 0.0, 0.0, 1.0); aLastZ = 1; break; } case kBack: { if (direction == kClockwise) Q3Vector3D_Set(&aRotationdata.orientation, 0.0, 0.0, 1.0); else Q3Vector3D_Set(&aRotationdata.orientation, 0.0, 0.0, -1.0); aFirstZ = 2; break; } case kLeft: { if (direction == kClockwise) Q3Vector3D_Set(&aRotationdata.orientation, 1.0, 0.0, 0.0); else Q3Vector3D_Set(&aRotationdata.orientation, -1.0, 0.0, 0.0); aLastX = 1; break; } case kRight: { if (direction == kClockwise) Q3Vector3D_Set(&aRotationdata.orientation, -1.0, 0.0, 0.0); else Q3Vector3D_Set(&aRotationdata.orientation, 1.0, 0.0, 0.0); aFirstX = 2; break; } case kUp: { if (direction == kClockwise) Q3Vector3D_Set(&aRotationdata.orientation, 0.0, -1.0, 0.0); else Q3Vector3D_Set(&aRotationdata.orientation, 0.0, 1.0, 0.0); aLastY = 1; break; } case kDown: { if (direction == kClockwise) Q3Vector3D_Set(&aRotationdata.orientation, 0.0, 1.0, 0.0); else Q3Vector3D_Set(&aRotationdata.orientation, 0.0, -1.0, 0.0); aFirstY = 2; break; } } Q3Point3D_Set(&aRotationdata.origin, 0.0, 0.0, 0.0); aRotationdata.radians = 0.0; aFaceRotation = Q3RotateAboutAxisTransform_New(&aRotationdata); // add the rotation object to each cubie in the face for (x = aFirstX; x < aLastX; x++) for (y = aFirstY; y < aLastY; y++) for (z = aFirstZ; z < aLastZ; z++) { Q3Group_GetFirstPosition(gCubies[x][y][z], &aPos); Q3Group_AddObjectBefore(gCubies[x][y][z], aPos, aFaceRotation); } // draw and adjust the angle stepsToTurn = gStepSize / 4; for (i = 1; i < stepsToTurn; i++) { Q3RotateAboutAxisTransform_SetAngle(aFaceRotation, (2.0 * kQ3Pi * i / gStepSize)); DrawCube(); } // set the angle to 90° and adjust the rotation of each cubie Q3RotateAboutAxisTransform_SetAngle(aFaceRotation, (kQ3Pi / 2.0)); Q3Transform_GetMatrix(aFaceRotation, &aRotationMatrix); if (aFaceRotation) Q3Object_Dispose(aFaceRotation); for (x = aFirstX; x < aLastX; x++) for (y = aFirstY; y < aLastY; y++) for (z = aFirstZ; z < aLastZ; z++) { Q3Group_GetFirstPosition(gCubies[x][y][z], &aPos); aFaceRotation = Q3Group_RemovePosition(gCubies[x][y][z], aPos); if (aFaceRotation) Q3Object_Dispose(aFaceRotation); Q3Group_GetFirstPositionOfType(gCubies[x][y][z], kQ3TransformTypeMatrix, &aPos); Q3Group_GetPositionObject(gCubies[x][y][z], aPos, &aFaceRotation); if (aFaceRotation) { Q3MatrixTransform_Get(aFaceRotation, &aCubieMatrix); Q3Matrix4x4_Multiply(&aCubieMatrix, &aRotationMatrix, &aCubieMatrix); Q3MatrixTransform_Set(aFaceRotation, &aCubieMatrix); Q3Object_Dispose(aFaceRotation); } } DrawCube(); // rotate cubies in gCubies switch(face) { case kFront: { if (direction == kClockwise) { aCubie = gCubies[0][0][0]; gCubies[0][0][0] = gCubies[0][2][0]; gCubies[0][2][0] = gCubies[2][2][0]; gCubies[2][2][0] = gCubies[2][0][0]; gCubies[2][0][0] = aCubie; aCubie = gCubies[1][0][0]; gCubies[1][0][0] = gCubies[0][1][0]; gCubies[0][1][0] = gCubies[1][2][0]; gCubies[1][2][0] = gCubies[2][1][0]; gCubies[2][1][0] = aCubie; } else { aCubie = gCubies[0][2][0]; gCubies[0][2][0] = gCubies[0][0][0]; gCubies[0][0][0] = gCubies[2][0][0]; gCubies[2][0][0] = gCubies[2][2][0]; gCubies[2][2][0] = aCubie; aCubie = gCubies[1][2][0]; gCubies[1][2][0] = gCubies[0][1][0]; gCubies[0][1][0] = gCubies[1][0][0]; gCubies[1][0][0] = gCubies[2][1][0]; gCubies[2][1][0] = aCubie; } break; } case kBack: { if (direction == kClockwise) { aCubie = gCubies[0][2][2]; gCubies[0][2][2] = gCubies[0][0][2]; gCubies[0][0][2] = gCubies[2][0][2]; gCubies[2][0][2] = gCubies[2][2][2]; gCubies[2][2][2] = aCubie; aCubie = gCubies[1][2][2]; gCubies[1][2][2] = gCubies[0][1][2]; gCubies[0][1][2] = gCubies[1][0][2]; gCubies[1][0][2] = gCubies[2][1][2]; gCubies[2][1][2] = aCubie; } else { aCubie = gCubies[0][0][2]; gCubies[0][0][2] = gCubies[0][2][2]; gCubies[0][2][2] = gCubies[2][2][2]; gCubies[2][2][2] = gCubies[2][0][2]; gCubies[2][0][2] = aCubie; aCubie = gCubies[1][0][2]; gCubies[1][0][2] = gCubies[0][1][2]; gCubies[0][1][2] = gCubies[1][2][2]; gCubies[1][2][2] = gCubies[2][1][2]; gCubies[2][1][2] = aCubie; } break; } case kLeft: { if (direction == kClockwise) { aCubie = gCubies[0][0][2]; gCubies[0][0][2] = gCubies[0][2][2]; gCubies[0][2][2] = gCubies[0][2][0]; gCubies[0][2][0] = gCubies[0][0][0]; gCubies[0][0][0] = aCubie; aCubie = gCubies[0][0][1]; gCubies[0][0][1] = gCubies[0][1][2]; gCubies[0][1][2] = gCubies[0][2][1]; gCubies[0][2][1] = gCubies[0][1][0]; gCubies[0][1][0] = aCubie; } else { aCubie = gCubies[0][2][2]; gCubies[0][2][2] = gCubies[0][0][2]; gCubies[0][0][2] = gCubies[0][0][0]; gCubies[0][0][0] = gCubies[0][2][0]; gCubies[0][2][0] = aCubie; aCubie = gCubies[0][2][1]; gCubies[0][2][1] = gCubies[0][1][2]; gCubies[0][1][2] = gCubies[0][0][1]; gCubies[0][0][1] = gCubies[0][1][0]; gCubies[0][1][0] = aCubie; } break; } case kRight: { if (direction == kClockwise) { aCubie = gCubies[2][2][2]; gCubies[2][2][2] = gCubies[2][0][2]; gCubies[2][0][2] = gCubies[2][0][0]; gCubies[2][0][0] = gCubies[2][2][0]; gCubies[2][2][0] = aCubie; aCubie = gCubies[2][2][1]; gCubies[2][2][1] = gCubies[2][1][2]; gCubies[2][1][2] = gCubies[2][0][1]; gCubies[2][0][1] = gCubies[2][1][0]; gCubies[2][1][0] = aCubie; } else { aCubie = gCubies[2][0][2]; gCubies[2][0][2] = gCubies[2][2][2]; gCubies[2][2][2] = gCubies[2][2][0]; gCubies[2][2][0] = gCubies[2][0][0]; gCubies[2][0][0] = aCubie; aCubie = gCubies[2][0][1]; gCubies[2][0][1] = gCubies[2][1][2]; gCubies[2][1][2] = gCubies[2][2][1]; gCubies[2][2][1] = gCubies[2][1][0]; gCubies[2][1][0] = aCubie; } break; } case kUp: { if (direction == kClockwise) { aCubie = gCubies[0][0][2]; gCubies[0][0][2] = gCubies[0][0][0]; gCubies[0][0][0] = gCubies[2][0][0]; gCubies[2][0][0] = gCubies[2][0][2]; gCubies[2][0][2] = aCubie; aCubie = gCubies[1][0][2]; gCubies[1][0][2] = gCubies[0][0][1]; gCubies[0][0][1] = gCubies[1][0][0]; gCubies[1][0][0] = gCubies[2][0][1]; gCubies[2][0][1] = aCubie; } else { aCubie = gCubies[2][0][2]; gCubies[2][0][2] = gCubies[2][0][0]; gCubies[2][0][0] = gCubies[0][0][0]; gCubies[0][0][0] = gCubies[0][0][2]; gCubies[0][0][2] = aCubie; aCubie = gCubies[1][0][2]; gCubies[1][0][2] = gCubies[2][0][1]; gCubies[2][0][1] = gCubies[1][0][0]; gCubies[1][0][0] = gCubies[0][0][1]; gCubies[0][0][1] = aCubie; } break; } case kDown: { if (direction == kClockwise) { aCubie = gCubies[2][2][2]; gCubies[2][2][2] = gCubies[2][2][0]; gCubies[2][2][0] = gCubies[0][2][0]; gCubies[0][2][0] = gCubies[0][2][2]; gCubies[0][2][2] = aCubie; aCubie = gCubies[1][2][2]; gCubies[1][2][2] = gCubies[2][2][1]; gCubies[2][2][1] = gCubies[1][2][0]; gCubies[1][2][0] = gCubies[0][2][1]; gCubies[0][2][1] = aCubie; } else { aCubie = gCubies[0][2][2]; gCubies[0][2][2] = gCubies[0][2][0]; gCubies[0][2][0] = gCubies[2][2][0]; gCubies[2][2][0] = gCubies[2][2][2]; gCubies[2][2][2] = aCubie; aCubie = gCubies[1][2][2]; gCubies[1][2][2] = gCubies[0][2][1]; gCubies[0][2][1] = gCubies[1][2][0]; gCubies[1][2][0] = gCubies[2][2][1]; gCubies[2][2][1] = aCubie; } break; } } } void RotateCube( CubeAxis axis, TurnDirection direction, short stepsToTurn ) { TQ3RotateAboutAxisTransformData aRotationdata; TQ3Matrix4x4 aCubeRotationMatrix, aTempMatrix; long i; // create a rotation object switch (axis) { case kFrontBack: { if (direction == kClockwise) Q3Vector3D_Set(&aRotationdata.orientation, 0.0, 0.0, -1.0); else Q3Vector3D_Set(&aRotationdata.orientation, 0.0, 0.0, 1.0); break; } case kLeftRight: { if (direction == kClockwise) Q3Vector3D_Set(&aRotationdata.orientation, 1.0, 0.0, 0.0); else Q3Vector3D_Set(&aRotationdata.orientation, -1.0, 0.0, 0.0); break; } case kUpDown: { if (direction == kClockwise) Q3Vector3D_Set(&aRotationdata.orientation, 0.0, -1.0, 0.0); else Q3Vector3D_Set(&aRotationdata.orientation, 0.0, 1.0, 0.0); break; } } Q3Point3D_Set(&aRotationdata.origin, 0.0, 0.0, 0.0); aRotationdata.radians = 0.0; // the cube has been rotated, rotate the orientation of the rotation Q3MatrixTransform_Get(gCubeRotation, &aCubeRotationMatrix); Q3Vector3D_Transform(&aRotationdata.orientation, &aCubeRotationMatrix, &aRotationdata.orientation); gTempCubeRotation = Q3RotateAboutAxisTransform_New(&aRotationdata); // draw and adjust the angle for (i = 1; i < stepsToTurn; i++) { Q3RotateAboutAxisTransform_SetAngle(gTempCubeRotation, (2.0 * kQ3Pi * i / gStepSize)); DrawCube(); } // set the angle to 90° and adjust the rotation object of the cube Q3RotateAboutAxisTransform_SetAngle(gTempCubeRotation, (2.0 * kQ3Pi * stepsToTurn / gStepSize)); Q3Transform_GetMatrix(gTempCubeRotation, &aTempMatrix); Q3MatrixTransform_Get(gCubeRotation, &aCubeRotationMatrix); Q3Matrix4x4_Multiply(&aCubeRotationMatrix, &aTempMatrix, &aCubeRotationMatrix); Q3MatrixTransform_Set(gCubeRotation, &aCubeRotationMatrix); // don't need gTempCubeRotation anymore, dispose it if (gTempCubeRotation) Q3Object_Dispose(gTempCubeRotation); gTempCubeRotation = 0; DrawCube(); } void TermCube(void) { long x, y, z; Q3Object_Dispose(gView); Q3Object_Dispose(gCubeModel); // object in the scene being modelled Q3Object_Dispose(gCubeRotation); for (x = 0; x < 3; x++) for (y = 0; y < 3; y++) for (z = 0; z < 3; z++) { if (gCubies[x][y][z]) Q3Object_Dispose(gCubies[x][y][z]); // object in the scene being modelled } Q3Object_Dispose(gInterpolation); // interpolation style used when rendering Q3Object_Dispose(gBackFacing); // whether to draw shapes that face away from the camera Q3Object_Dispose(gFillStyle); // whether drawn as solid filled object or decomposed to components Q3Exit(); }
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