TweetFollow Us on Twitter

Apr 97 Challenge

Volume Number: 13 (1997)
Issue Number: 4
Column Tag: Programmer's Challenge

Programmer's Challenge

By Bob Boonstra, Westford, MA

Projection

For the Challenge this month, we return to the topic of computer graphics - you'll be solving a simplified rendering problem. Your Challenge is to create the image formed by a set of polygons on a specified projection plane, as viewed from a specific viewpoint, and as illuminated from a point light source. You will need to perform hidden surface elimination, create shadows caused by the light source, and project the image as it would be seen by someone at the viewpoint. You will be performing multiple projections from a given viewpoint, so this Challenge includes an initialization routine as well as a calculation routine, both of which are included for timing purposes in determining the winner.

The prototype for the code you should write is:

#define kMAXPOINTS 10

typedef struct My2DPoint {/* point in z==0 plane */
 float x2D; /* x coordinate */
 float y2D; /* y coordinate */
} My2DPoint;

typedef struct My3DPoint {
 float x3D; /* x coordinate */
 float y3D; /* y coordinate */
 float z3D; /* z coordinate */
} My3DPoint;

typedef struct My3DDirection {
 float thetaX;   /* angle in radians */
 float thetaY;   /* angle in radians */
 float thetaZ;   /* angle in radians */
} My3DDirection;

typedef struct MyPlane {
 My3DDirection planeNormal; /* normal vector to plane */
 My3DPointplaneOrigin;  /* origin of plane in 3D space */
} MyPlane;

typedef struct MyPolygon {
 long   numPoints; /* number of points in polygon */
 My2DPointthePoint[kMAXPOINTS];  /* polygon in z==0 plane */
 MyPlanepolyPlane; /* rotate/translate z==0 plane to this plane */
 RGBColor polyColor/* the color to draw this polygon */
} MyPolygon;

void InitProjection(
 My3DPoint*viewPoint,/* viewpoint from which to project */
 My3DPoint*illumPoint,  /* viewpoint from which to draw shadow */
 void   *storage,/* auxiliary storage preallocated for your use */
 long   storageSize/* number of bytes of storage */
);

void CalcProjection(
 GWorldPtroffScreen, /* GWorld to draw projection */
 MyPolygonthePolys[],/* polygons to project */
 long   numPolys,/* number of polygons to project */
 My3DPoint*viewPoint,/* viewpoint from which to project */
 My3DPoint*illumPoint,  /* illumination point from which to draw
        shadow */
 void   *storage,/* auxiliary storage preallocated for your use */
 long   storageSize/* number of bytes of storage */
);


Your InitProjection routine will be provided with a pointer to auxiliary storage (storageSize bytes, at least 1MB) preallocated for your use, along with the viewPoint from which projections are to be made and the illumPoint location of an illumination source from which shadows are to be created. InitProjection may perform any calculations that may be useful for multiple CalcProjection calls that follow. CalcProjection will be provided the same parameters given to InitProjection, along with the number (numPolys) and location of the polygons to be projected, and the offScreen GWorld in which the projection is to be drawn. CalcProjection should calculate the way thePolys would look from viewPoint, projected onto a projection plane normal to the viewPoint vector and passing through the origin. Hidden surface elimination must be performed so that obscured polygons or parts of polygons are not seen. The image of the projection is to be rendered in the GWorld pointed to by offScreen, with the projection plane mapped to the z==0 plane in the GWorld. Polygons must be rendered in the appropriate polyColor, subject to the limitations of the GWorld. Polygons are the same color on both sides. Parts of the projection plane not filled by projections of polygons should be black.

In addition to projecting the polygon image as seen from viewPoint, you must also project the shadow of thePolys created by an illumination source at illumPoint, onto the projection plane and onto the image of other polygons, as seen from viewPoint. Shadows should be rendered in the color of the surface in shadow, using a 50% gray pattern. All polygons have a flat matte surface, creating no specular reflections of the illumination source. The illumPoint will be on the same side of the projection plane as the viewPoint.

Polygons are specified in 2-dimensional coordinates in the z==0 plane, to ensure that all points are coplanar, along with a planeNormal vector that specifies the orientation of the polygon plane and a planeOrigin that specifies the plane origin. The last vertex of a polygon is connected to the first vertex to close the polygon (i.e., a square would have four vertices, not a fifth that is the same as the first.) The true polygon coordinates to be projected are calculated by first rotating counterclockwise about the positive z axis by thetaZ (i.e., the positive x axis rotated 90 degrees maps to the positive y axis), then counterclockwise about the positive x axis by thetaX (i.e., positive y rotates to positive z), then counterclockwise about the positive y axis by thetaY (i.e., positive z rotates to positive x), and finally by translating the origin to the planeOrigin point. In matrix form, the transformation is:

 | X |   | x3D |            | x2D |
 | Y | = | y3D | + Ry Rx Rz | y2D |, where
 | Z |   | z3D |            |  0  |

      | cos(thetaZ) -sin(thetaZ)        0     | 
 Rz = | sin(thetaZ)  cos(thetaZ)        0     |
      |       0            0            1     |

      |       1            0            0     |
 Rx = |       0      cos(thetaX) -sin(thetaX) |
      |       0      sin(thetaX)  cos(thetaX) |

      | cos(thetaY)        0      sin(thetaY) | 
 Ry = |       0            1            0     |
      |-sin(thetaY)        0      cos(thetaY) |

The offScreen GWorld will have a pixelDepth of 32. The viewPoint and illumPoint will have z coordinates greater than zero, but thePolys may have coordinates with arbitrary values (after rotating and translating the polyPlane). The projection plane is opaque, meaning that any part of a polygon behind the projection plane is invisible, creating no projection and no shadow.

On average, CalcProjection will be called approximately 10 times with the same viewpoint and illumPoint, but different polygons, for each call to InitProjection. The code producing the fastest projection, including both the InitProjection and CalcProjection times, will be the winner.

This will be a native PowerPC Challenge, using the latest CodeWarrior environment. Solutions may be coded in C, C++, or Pascal.

Three Months Ago Winner

Perhaps it was the short amount of time to work with the BeOS CD-ROM bundled in the January issue of the magazine, or the fact that the BeOS required a 604 PowerMac, or some minor installation anomalies with the BeOS, or to migration of interest to a prospective NeXT-OS - whatever the reason, only two people entered the BeSort Challenge. Congratulations to Charles Higgins for submitting the fastest solution to the BeSort Challenge. The problem itself was fairly simple: write a SortWindow class that would sort a list of character strings by one of three methods, two specified by the problem statement and one of your own choosing.

Both Charles and the second contestant, Kenneth Slezak, implemented the required bubble sort and exchange sort methods, and both used the quicksort algorithm for the third method. The main difference in efficiency was in the technique used to swap list elements. Charles exchanged the pointers in the list and invalidated the list view to cause the list to be redrawn. Kenneth deleted the items to be exchanged from the list and added the items back into the list in the reverse order. On my 8500, the former was faster by 10+%. Interestingly enough, when run on a BeBox, the latter was ~5% faster. Since the problem statement called for evaluation on the Macintosh, Charles' solution is the winner.

One other interesting observation - in the winning solution, execution time was dominated by display time. I verified this by repeating the timing tests with the windows hidden. In the winning solution, this reduced execution time by almost 80%. In Ken Slezak's solution, execution time was dominated by the list additions/deletions used to swap list elements, so the difference in results is much smaller.

A straightforward optimization to the winning solution improved execution time significantly. Instead of invalidating the ListView each time two elements were exchanged, one need only invalidate the rectangles for the two items being exchanged. This change reduced execution time by some 30% when the windows were visible. (It actually hurt performance when the windows were not visible.)

The table below provides the execution times and code sizes for each two solutions submitted, plus the optimized version of the winning solution. It shows the time, in seconds, required to sort a list of 500 strings by each of the three sort methods, with either visible windows or invisible windows.

TOP 20 CONTESTANTS

Here are the Top Contestants for the Programmer's Challenge. The numbers below include points awarded over the 24 most recent contests, including points earned by this month's entrants.

RankNamePointsRankNamePoints
1.Munter, Ernst18211.Nicolle, Ludovic21
2.Gregg, Xan11412.Picao, Miguel Cruz21
3.Larsson, Gustav6713.Brown, Jorg20
4.Lengyel, Eric4014.Gundrum, Eric20
5.Lewis, Peter3215.Higgins, Charles20
6.Boring, Randy2716.Kasparian, Raffi20
7.Cooper, Greg2717.Slezak, Ken20
8.Antoniewicz, Andy2418.Studer, Thomas20
9.Beith, Gary2419.Karsh, Bill19
10.Cutts, Kevin2120.Nevard, John17

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    5th place              2 points
2nd place   10 points    finding bug            2 points
3rd place    7 points    suggesting Challenge   2 points
4th place    4 points

Here is Charles Higgins' winning solution:

SortWindow.cpp

Charles Higgins

   
#include "SortWindow.h"

void swap(BWindow *aWindow, char **s1, char **s2);
char **addlist( BWindow *aWindow, char **list, int numberOfThings);
   
SortWindow::SortWindow(BRect frame)
         : BWindow(frame, "Sort", B_TITLED_WINDOW, 0)
{
   BRect            aRect = frame;
   BListView       *aView;
   
   aRect.OffsetTo(B_ORIGIN);
   aView = new BListView(aRect, "SortView", 
                          B_FOLLOW_ALL, B_WILL_DRAW);
   this->AddChild(aView);
}

void swap(BWindow *aWindow, char **s1, char **s2)
{
   BView   *aView;
   char    *temp;
   
   aView = aWindow->FindView("SortView");
   aWindow->Lock();
   temp = *s1;
   *s1 = *s2;
   *s2 = temp;
   aView->Invalidate();
   aWindow->Unlock();
}

char **addlist( BWindow *aWindow, char **list, int numberOfThings)
{
   BListView       *aView;
   int              i;
   
   aView = (BListView*)aWindow->FindView("SortView");
   aWindow->Lock();
   for(i=0;i< numberOfThings;i++)
      aView->AddItem(list[i]);
   aWindow->Unlock();
   return((char**)aView->Items());
}

void SortWindow::DoSort(
   char *thingsToSort[], int numberOfThings, SortType sortMethod)
{
   short            i,
                    j,
                    k,
                    sorted = FALSE;
   char           **myList;
                   
   myList = addlist( this, thingsToSort, numberOfThings);
   switch(sortMethod)
   {
      case kBubbleSort:
         i = numberOfThings-1;
         while(i>0)
         {
            j=i;
            for(k=0;k<i;++k)
            {
               if (0 < strcmp(myList[k],myList[j]))
                  j = k;
            }
            swap( this, &myList[i], &myList[j]);
            i-;
         }
         break;
      case kExchange:
         while(!sorted)
         {
            sorted = TRUE;
            for(i=0;i<numberOfThings-1;i++)
            {
               if(0 < strcmp(myList[i],myList[i+1]))
               {                  
                  sorted = FALSE;
                  swap( this, &myList[i], &myList[i+1]);
               }
            }
         }
         break;
      case kMySort:
         QuickSort( myList, 0, numberOfThings);
         break;
   }
   memcpy(thingsToSort,myList,numberOfThings*sizeof(char*));
   be_app->PostMessage(B_QUIT_REQUESTED);
}

void SortWindow::QuickSort( char **list, int first, int last)
{
   int              j,i;

   while(last - first > 1)
   {
      i = first;
      j = last;
      for(;;)
      {
         while(++i < last && strcmp(list[i],list[first]) < 0)
            ;
         while(-j > first && strcmp(list[j],list[first]) > 0)
            ;
         if (i >= j)
            break;
         swap( this, &list[i], &list[j]);         
      }
      if( j == first)
      {
         ++first;
         continue;
      }
      swap( this, &list[first], &list[j]);      
      if(j - first < last - (j+1))
      {
         QuickSort( list,first,j);
         first = j + 1;
      }
      else
      {
         QuickSort( list,j+1,last);
         last = j;
      }
   }
}

SortWindow.h

typedef enum SortType {
 kBubbleSort = 1,
 kExchange = 2,
 kExchangeSort = 2,
 kMySort = 3
 } SortType;

class SortWindow : public BWindow {

public:
 SortWindow(BRect frame);

virtual void DoSort( char *thingsToSort[],
     int numberOfThings,
     SortType sortMethod);
     
virtual void QuickSort( char **list, int first, int last);

};

 

Community Search:
MacTech Search:

Software Updates via MacUpdate

Apple Digital Camera RAW Compatibility 6...
Apple Digital Camera RAW Compatibility update adds RAW image compatibility to Aperture 3 and iPhoto '11. For more information on supported RAW formats, see this page. Version 6.03: This update adds... Read more
OmniGraffle Pro 6.1.4 - Create diagrams,...
OmniGraffle Pro helps you draw beautiful diagrams, family trees, flow charts, org charts, layouts, and (mathematically speaking) any other directed or non-directed graphs. We've had people use... Read more
OmniGraffle 6.1.4 - Create diagrams, flo...
OmniGraffle helps you draw beautiful diagrams, family trees, flow charts, org charts, layouts, and (mathematically speaking) any other directed or non-directed graphs. We've had people use Graffle to... Read more
MegaSeg 5.9.5 - Professional MP3 DJ appl...
MegaSeg is a complete solution for pro audio/video DJ mixing, radio automation, and music scheduling with rock-solid performance and an easy-to-use design. Mix with visual waveforms and Magic... Read more
MarsEdit 3.6.8 - Quick and convenient bl...
MarsEdit is a blog editor for OS X that makes editing your blog like writing email, with spell-checking, drafts, multiple windows, and even AppleScript support. It works with with most blog services... Read more
BBEdit 11.0.3 - Powerful text and HTML e...
BBEdit is the leading professional HTML and text editor for the Mac. Specifically crafted in response to the needs of Web authors and software developers, this award-winning product provides a... Read more
Microsoft Office Preview 15.8 - Popular...
Welcome to the new and modern Microsoft Office for Mac. You will receive regular updates automatically until the official release in the second half of 2015. With the redesigned Ribbon and your... Read more
Yosemite Cache Cleaner 9.0.5 - Clear cac...
Yosemite Cache Cleaner is an award-winning general purpose tool for OS X. YCC makes system maintenance simple with an easy point-and-click interface to many OS X functions. Novice and expert users... Read more
ExpanDrive 4.3.2 - Access cloud storage...
ExpanDrive builds cloud storage in every application, acts just like a USB drive plugged into your Mac. With ExpanDrive, you can securely access any remote file server directly from the Finder or... Read more
RapidWeaver 6.0.8 - Create template-base...
RapidWeaver is a next-generation Web design application to help you easily create professional-looking Web sites in minutes. No knowledge of complex code is required, RapidWeaver will take care of... Read more

Take a First Look at NaturalMotion’s Daw...
NaturalMotion has released a preview of their upcoming title, Dawn of Titans. Dawn of Titans immerses you in a world of fantasy as you build your kingdom, raise an army, and capture territories. The focus on this epic action strategy game was the... | Read more »
GDC 2015 – Warfriends is Something Famil...
GDC 2015 – Warfriends is Something Familiar That’s Also a Little Different Posted by Rob Rich on March 6th, 2015 [ permalink ] About Fun‘s upcoming Warfriends is quite the interesting hybrid. | Read more »
Bored? MyLeisure FreeTime Maximizer Will...
Bored? MyLeisure FreeTime Maximizer Will Take Care of That! Posted by Jessica Fisher on March 5th, 2015 [ permalink ] iPhone App - Designed for the iPhone, compatible with the iPad | Read more »
New Publisher Allstar Games Heads West w...
Allstar Games has announced its first mobile title designed for western audiences, Allstar Heroes. The game will be a massive online battle arena (MOBA) that offers dozens of heroes for you to collect and pit against your opponents. As each hero has... | Read more »
RAD Boarding Review
RAD Boarding Review By Jennifer Allen on March 5th, 2015 Our Rating: :: NEARLY RADUniversal App - Designed for iPhone and iPad RAD Boarding isn’t quite one of the greats, but it has potential.   | Read more »
Presenting the International Mobile Gami...
11th Annual International Mobile Gaming Awards ceremony, hosted by actress Allison Haislip, gathered mobile game developers and publishers from around the world. They chose 13 winners out of the 93 nominations. British studio USTWO won the the Grand... | Read more »
AG Drive Review
AG Drive Review By Tre Lawrence on March 5th, 2015 Our Rating: :: FUTURISTIC STREET RACING.Universal App - Designed for iPhone and iPad Futuristic racing… interstellar style.   | Read more »
GDC 2015 – Nightmare Guardians is an Int...
GDC 2015 – Nightmare Guardians is an Interesting Hybrid of MOBA and Lane Defense Posted by Rob Rich on March 5th, 2015 [ permalink ] I have to say that lane defense (i.e. | Read more »
Overkill 3 Review
Overkill 3 Review By Tre Lawrence on March 5th, 2015 Our Rating: :: WHO'S NEXT?Universal App - Designed for iPhone and iPad Cover system gameplay in the third-person.   Developer: Craneballs Price: Free Version Reviewed: 1.1.6... | Read more »
Warner Bros. Interactive Entertainment A...
Warner Bros. has some exciting games coming down the pipe! | Read more »

Price Scanner via MacPrices.net

16GB iPad mini 3 on sale for $349, save $50
 Walmart has the 16GB iPad mini 3 WiFi on sale on their online store for $349.99 including free shipping or free local store pickup. Their price is $50 off MSRP, and it’s the lowest price available... Read more
Save up to 15% with Apple refurbished Time Ca...
The Apple Store has certified refurbished Time Capsules available for up to $60 off MSRP. Apple’s one-year warranty is included with each Time Capsule, and shipping is free: - 2TB Time Capsule: $255... Read more
Save up to $105 on AppleCare Protection Plans
B&H Photo has 3-Year AppleCare Warranties on sale for up to $105 off MSRP including free shipping plus NY sales tax only: - Mac Laptops 15″ and Above: $244 $105 off MSRP - Mac Laptops 13″ and... Read more
Apple restocks refurbished 15-inch Retina Mac...
The Apple Store has restocked Apple Certified Refurbished 2014 15″ Retina MacBook Pros, available for up to $400 off the cost of new models. An Apple one-year warranty is included with each model,... Read more
Roundup of MacBook Air sale prices, models up...
B&H Photo has MacBook Airs on sale for up to $100 off MSRP. Shipping is free, and B&H charges NY sales tax only: - 11″ 128GB MacBook Air: $799 100 off MSRP - 11″ 256GB MacBook Air: $999 $100... Read more
New Firstrade Mobile App Enables On-The-Go Tr...
Firstrade Securities Inc. has announced its new mobile app, which gives investors immediate access to the company’s trading platform on all mobile devices. The app was developed in-house and was... Read more
Sonnet Introduces USB 3.0 + eSATA Thunderbolt...
Sonnet has announced the launch of its new USB 3.0 + eSATA Thunderbolt Adapter for easy connectivity to USB 3.0 devices and eSATA storage, and USB 3.0 + Gigabit Ethernet Thunderbolt Adapter for easy... Read more
Apple restocks refurbished 27-inch 5K iMacs f...
The Apple Store has restocked Apple Certified Refurbished 27″ 3.5GHz 5K iMacs for $2119 including free shipping. Their price is $380 off the cost of new models, and it’s the lowest price available... Read more
Free Clean Reader Mobile App Hides Swear Word...
The new Clean Reader app, now available in the Apple App Store and Google Play, delivers the opportunity of reading any book without being exposed to profanity. By selecting how clean they want their... Read more
Kinsa Launches “Groups” App to Monitor Illnes...
Kinsa, makers of the first FDA approved app-enabled smartphone thermometer thst won the 2013 Cleveland Clinic Medical Innovation Grand Prize and recently appeared in Apple’s “Parenthood” TV... Read more

Jobs Board

*Apple* Solutions Consultant- Retail Sales -...
**Job Summary** The ASC is an Apple employee who serves as an Apple brand ambassador and influencer in a Reseller's store. The ASC's role is to grow Apple Read more
*Apple* Solutions Consultant - Retail Sales...
**Job Summary** As an Apple Solutions Consultant (ASC) you are the link between our customers and our products. Your role is to drive the Apple business in a retail Read more
*Apple* Retail - Multiple Positions (US) - A...
Sales Specialist - Retail Customer Service and Sales Transform Apple Store visitors into loyal Apple customers. When customers enter the store, you're also the Read more
*Apple* Solutions Consultant - Retail Sales...
**Job Summary** As an Apple Solutions Consultant (ASC) you are the link between our customers and our products. Your role is to drive the Apple business in a retail Read more
Position Opening at *Apple* - Apple (United...
…Summary** As a Specialist, you help create the energy and excitement around Apple products, providing the right solutions and getting products into customers' hands. You Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.