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);

};

 
AAPL
$524.94
Apple Inc.
+5.93
MSFT
$40.01
Microsoft Corpora
-0.39
GOOG
$536.10
Google Inc.
-20.44

MacTech Search:
Community Search:

Software Updates via MacUpdate

VMware Fusion 6.0.3 - Run Windows apps a...
VMware Fusion allows you to create a Virtual Machine on your Mac and run Windows (including Windows 8.1) and Windows software on your Mac. Run your favorite Windows applications alongside Mac... Read more
Tweetbot 1.5.1 - Popular iOS twitter cli...
Tweetbot is a full-featured OS X Twitter client with a lot of personality. Whether it's the meticulously-crafted interface, sounds and animation, or features like multiple timelines and column views... Read more
Mac DVDRipper Pro 4.1.7 - Copy, backup,...
Mac DVDRipper Pro is the DVD backup solution that lets you protect your DVDs from scratches, save your batteries by reading your movies from your hard disk, manage your collection with just a few... Read more
PDFpenPro 6.2 - Advanced PDF toolkit for...
PDFpenPro allows users to edit PDF's easily. Add text, images and signatures. Fill out PDF forms. Merge or split PDF documents. Reorder and delete pages. Even correct text and edit graphics! Create... Read more
PDFpen 6.2 - Edit and annotate PDFs with...
PDFpen allows users to easily edit PDF's. Add text, images and signatures. Fill out PDF forms. Merge or split PDF documents. Reorder and delete pages. Even correct text and edit graphics! Features... Read more
Monolingual 1.5.9 - Remove unwanted OS X...
Monolingual is a program for removing unnecesary language resources from OS X, in order to reclaim several hundred megabytes of disk space. It requires a 64-bit capable Intel-based Mac and at least... Read more
Maya 2015 - Professional 3D modeling and...
Maya is an award-winning software and powerful, integrated 3D modeling, animation, visual effects, and rendering solution. Because Maya is based on an open architecture, all your work can be scripted... Read more
Starcraft II: Wings of Liberty 1.1.1.180...
Download the patch by launching the Starcraft II game and downloading it through the Battle.net connection within the app. Starcraft II: Wings of Liberty is a strategy game played in real-time. You... Read more
Sibelius 7.5.0 - Music notation solution...
Sibelius is the world's best-selling music notation software for Mac. It is as intuitive to use as a pen, yet so powerful that it does most things in less than the blink of an eye. The demo includes... Read more
Typinator 5.9 - Speedy and reliable text...
Typinator turbo-charges your typing productivity. Type a little. Typinator does the rest. We've all faced projects that require repetitive typing tasks. With Typinator, you can store commonly used... Read more

Latest Forum Discussions

See All

Have a Special Dead Trigger 2 Easter Bas...
Have a Special Dead Trigger 2 Easter Basket Full of Goodies, Courtesy of Madfinger Games Posted by Rob Rich on April 18th, 2014 [ permalink ] Dead Trigger 2 | Read more »
Almost All of Playdek’s Library is on Sa...
Almost All of Playdek’s Library is on Sale Right Now, and You Should Check it Out Posted by Rob Rich on April 18th, 2014 [ permalink ] Playdek has released quite a few great iOS ports of board and card games over the years, and now most of them... | Read more »
Zynga Launches Brand New Farmville Exper...
Zynga Launches Brand New Farmville Experience with Farmville 2: Country Escape Posted by Tre Lawrence on April 18th, 2014 [ permalink ] | Read more »
David. Review
David. Review By Cata Modorcea on April 18th, 2014 Our Rating: :: MINIMALISTIC IN A DIFFERENT WAYUniversal App - Designed for iPhone and iPad David is a minimalistic game wrapped inside of a soothing atmosphere in which the hero... | Read more »
Eyefi Unveils New Eyefi Cloud Service Th...
Eyefi Unveils New Eyefi Cloud Service That Allows Users to Share Media Across Personal Devices Posted by Tre Lawrence on April 18th, 2014 [ permalink ] | Read more »
Tales from the Dragon Mountain: The Lair...
Tales from the Dragon Mountain: The Lair Review By Jennifer Allen on April 18th, 2014 Our Rating: :: STEADY ADVENTURINGiPad Only App - Designed for the iPad Treading a safe path, Tales from the Dragon Mountain: The Lair is a... | Read more »
Yahoo Updates Flickr App with Advanced E...
Yahoo Updates Flickr App with Advanced Editing Features and More Posted by Tre Lawrence on April 18th, 2014 [ permalink ] | Read more »
My Incredible Body - A Kid's App to...
My Incredible Body - A Kid's App to Learn about the Human Body 1.1.00 Device: iOS Universal Category: Education Price: $2.99, Version: 1.1.00 (iTunes) Description: Wouldn’t it be cool to look inside yourself and see what was going on... | Read more »
Trials Frontier Review
Trials Frontier Review By Carter Dotson on April 18th, 2014 Our Rating: :: A ROUGH LANDINGUniversal App - Designed for iPhone and iPad Trials Frontier finally brings the famed stunt racing franchise to mobile, but how much does its... | Read more »
Evernote Business Notebook by Moleskin I...
Evernote Business Notebook by Moleskin Introduced – Support Available in Evernote for iOS Posted by Tre Lawrence on April 18th, 2014 [ permalink ] | Read more »

Price Scanner via MacPrices.net

Free HopTo 2.2 Helps Enhance Your Productivit...
The HopTo app helps you do more on your iPad by providing more and easier adaccess to files and documents. Version 2.2 adds Egnyte and HopTo’s Mac OSX File Connector. If you already have the hopTo... Read more
National Distracted Driving Awareness Month:...
As the country recognizes National Distracted Driving Awareness Month, Sprint is reminding wireless consumers to focus on driving while behind the wheel, to not text or email while driving, and to... Read more
13-inch 2.4GHz Retina MacBook Pro available f...
Abt has the 13″ 2.4GHz 128GB Retina MacBook Pro available for $1229 including free shipping. Their price is $70 off MSRP. Read more
iMacs on sale for up to $160 off MSRP this we...
Best Buy has iMacs on sale for up to $160 off MSRP for a limited time. Choose free home shipping or free instant local store pickup (if available). Prices are valid for online orders only, in-store... Read more
iPad Airs on sale this weekend for up to $100...
Best Buy has WiFi iPad Airs on sale for $50 off MSRP and WiFi + Cellular iPad Airs on sale for $100 off MSRP on their online store for a limited time, with prices now starting at $449. Choose free... Read more
Apple restocks refurbished Mac minis starting...
The Apple Store has restocked Apple Certified Refurbished Mac minis for up to $150 off the cost of new models. Apple’s one-year warranty is included with each mini, and shipping is free: - 2.5GHz Mac... Read more
Hyundai Brings Apple CarPlay To The 2015 Sona...
Hyundai Motor America has announced it will bring Apple CarPlay functionality to the 2015 Sonata. CarPlay is pitched as a smarter, safer and easier way to use iPhone in the car and gives iPhone users... Read more
Updated iPads Coming Sooner Than We Had Thoug...
MacRumors, cites KGI securities analyst Ming Chi Kuo, well-respected as an Apple product prognisticator, saying that Apple will introduce an upgraded iPad Air and iPad mini in 2014/Q3, meaning the... Read more
Toshiba Unveils New High And Low End Laptop M...
Toshiba has announced new laptop models covering both the high-end and low-end of the notebook computer spectrum. Toshiba 4K Ultra HD Laptop Toshiba’s new Satellite P55t features one of the world’s... Read more
Save up to $270 with Apple refurbished 13-inc...
The Apple Store has Apple Certified Refurbished October 2013 13″ Retina MacBook Pros available starting at $1099, with models up to $270 off MSRP. Apple’s one-year warranty is standard, and shipping... Read more

Jobs Board

*Apple* Automotive Parts Department position...
Apple Automotive is one of the fastest growing dealer…and it shows. Consider making the switch to the Apple Automotive Group today! At Apple Automotive, we Read more
*Apple* Solutions Consultant (ASC) - Apple (...
**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* Retail - Manager - Holyoke - Apple I...
Job Summary Keeping an Apple Store thriving requires a diverse set of leadership skills, and as a Manager, you’re a master of them all. In the store’s fast-paced, Read more
*Apple* Retail - Manager - Apple (United Sta...
Job SummaryKeeping an Apple Store thriving requires a diverse set of leadership skills, and as a Manager, you're a master of them all. In the store's fast-paced, dynamic Read more
*Apple* Solutions Consultant (ASC) - Apple (...
**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
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.