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

OmniOutliner Pro 4.2 - Pro version of th...
OmniOutliner Pro is a flexible program for creating, collecting, and organizing information. Give your creativity a kick start by using an application that's actually designed to help you think. It's... Read more
VLC Media Player 2.2.1 - Popular multime...
VLC Media Player is a highly portable multimedia player for various audio and video formats (MPEG-1, MPEG-2, MPEG-4, DivX, MP3, OGG, ...) as well as DVDs, VCDs, and various streaming protocols. It... Read more
Nisus Writer Pro 2.1.1 - Multilingual wo...
Nisus Writer Pro is a powerful multilingual word processor, similar to its entry level products, but brings new features such as table of contents, indexing, bookmarks, widow and orphan control,... Read more
Tinderbox 6.2.0 - Store and organize you...
Tinderbox is a personal content management assistant. It stores your notes, ideas, and plans. It can help you organize and understand them. And Tinderbox helps you share ideas through Web journals... Read more
OmniOutliner 4.2 - Organize your ideas,...
OmniOutliner is a flexible program for creating, collecting, and organizing information. Give your creativity a kick start by using an application that's actually designed to help you think. It's... Read more
Things 2.5.4 - Elegant personal task man...
Things is a task management solution that helps to organize your tasks in an elegant and intuitive way. Things combines powerful features with simplicity through the use of tags and its intelligent... Read more
NeoOffice 2014.10 - Mac-tailored, OpenOf...
NeoOffice is a complete office suite for OS X. With NeoOffice, users can view, edit, and save OpenOffice documents, PDF files, and most Microsoft Word, Excel, and PowerPoint documents. NeoOffice 3.x... Read more
iPhoto Library Manager 4.2 - Manage mult...
iPhoto Library Manager allows you to organize your photos among multiple iPhoto libraries, rather than having to store all of your photos in one giant library. You can browse the photos in all your... Read more
Web Snapper 3.3.8 - Capture entire Web p...
Web Snapper lets you capture Web pages exactly as they appear in your browser. You can send them to a file as images or vector-based, multi-page PDFs. It captures the whole Web page - eliminating the... Read more
TeamViewer 10.0.41404 - Establish remote...
TeamViewer gives you remote control of any computer or Mac over the Internet within seconds, or can be used for online meetings. Find out why more than 200 million users trust TeamViewer! Free for... Read more

Kids Can Practice Healthy Living With Gr...
Bobaka is releasing a new interactive book called Green Riding Hood  in May. The app teaches kids about yoga and organic style of life through mini-games and a fun take on the classic Little Red Riding Hood fairy tale. | Read more »
Chainsaw Warrior: Lords of the Night has...
It's time to put the Darkness back in its place now that Chainsaw Warrior: Lords of the Night has officially made it to iOS. | Read more »
A World of Ice and Fire Lets You Stalk 2...
George R. R. Martin’s A World of Ice and Fire, by Random House, is a mobile guide to the epic series. The new update gives you the Journeys map feture that will let you track the movements of 25 different characters. But don't worry, you can protect... | Read more »
Gameloft Announces Battle Odyssey, a New...
Battle Odyssey, Gameloft's newest puzzle RPG, is coming to the App Store next week. Set in the world of Pondera, you will need to control the power of the elements to defend the world from evil. You'll be able to entlist over 500 allies to aid you... | Read more »
Here's How You Can Get 5 Free Pro D...
It's only been a couple of days since Gamevil released MLB Perfect Inning 15, so building up a decent roster could still take a little time. If you'd like to speed things up a bit, then we've got a deal for you. How does five free Pro drafts sound?... | Read more »
Fusion - HDR Camera (Photography)
Fusion - HDR Camera 1.0.0 Device: iOS Universal Category: Photography Price: $1.99, Version: 1.0.0 (iTunes) Description: Fusion creates HDR (high dynamic range) photos by capturing different exposures and then combining them into one... | Read more »
Sago Mini Toolbox (Education)
Sago Mini Toolbox 1.1 Device: iOS Universal Category: Education Price: $2.99, Version: 1.1 (iTunes) Description: Come build with the Sago Mini friends! Use a wrench, try a saw, or hammer some nails. From sewing hand puppets to... | Read more »
You Should Probably Grab Hitman GO While...
Hitman GO is a surprisingly cool (yet also incredibly drastic) departure from the Hitman series. It's well worth playing for any puzzle game fans out there, and at the moment you can get your hands - or garrotte if you will - on it for a mere $0.99... | Read more »
IFTTT is Bringing Do Button and Do Note...
IFTTT has announced Do Button and Do Note for the Apple Watch. Do Button lets you make your own personalized button that can connect to things like your Google Drive, control the temperature in your home with Nest Thermostat, or turn the lights on... | Read more »
How Many Days, Hours, and Minutes Are Le...
Countdown, by Yves Tscherry, is now available on the App Store. The app keeps track of countdowns to your favorite things such as someones birthday or days till the New Year. You can display the time in seconds, minutes, hours, days, weeks, months,... | Read more »

Price Scanner via MacPrices.net

TigerText Introduces First Secure Enterprise...
TigerText, a provider of secure, real-time messaging for the enterprise, has announced the launch of TigerText for the Apple Watch. TigerText for the Apple Watch enables users to securely send and... Read more
The Conservation Fund Partners with Apple To...
The Conservation Fund has announced that it will partner with Apple to help protect working forests in the United States. The Apple initiative will conserve more than 36,000 acres of working... Read more
Clearance 13-inch 2.6GHz Retina MacBook Pro a...
B&H Photo has clearance 2014 13″ 2.6GHz/128GB Retina MacBook Pros now available for $1099, or $200 off original MSRP. Shipping is free, and B&H charges NY sales tax only. Read more
Apple refurbished 2014 13-inch Retina MacBook...
The Apple Store has Apple Certified Refurbished 2014 13″ Retina MacBook Pros available for up to $400 off original MSRP, starting at $979. An Apple one-year warranty is included with each model, and... Read more
iMacs on sale for up to $205 off MSRP, NY tax...
B&H Photo has 21″ and 27″ iMacs on sale for up to $205 off MSRP including free shipping plus NY sales tax only: - 21″ 1.4GHz iMac: $1019 $80 off - 21″ 2.7GHz iMac: $1189 $110 off - 21″ 2.9GHz... Read more
Sale! 16GB iPhone 5S for $1 with service
Best Buy is offering 16GB iPhone 5Ss for $1.00 with 2-year activation at a participating cellular provider. Choose free home shipping and activation, or buy online and activate during in-store pickup... Read more
Apple refurbished 2014 MacBook Airs available...
The Apple Store has Apple Certified Refurbished 2014 MacBook Airs available starting at $679. An Apple one-year warranty is included with each MacBook, and shipping is free. These are currently the... Read more
27-inch 3.5GHz 5K iMac on sale for $2349, sav...
 Adorama has the 27″ 3.5GHz 5K iMac in stock today and on sale for $2349 including free shipping plus NY & NJ sales tax only. Their price is $150 off MSRP. For a limited time, Adorama will... Read more
Save up to $380 on an iMac with Apple refurbi...
The Apple Store has Apple Certified Refurbished iMacs available for up to $380 off the cost of new models. Apple’s one-year warranty is standard, and shipping is free: - 27″ 3.5GHz 5K iMac – $2119 $... Read more
iFixIt Teardown Awards 12-IInch Retina MacBoo...
iFixIt has posted its illustrated teardown of the new 12-inch MacBook Retina. They note that this new MacBook is less than half the thickness of the last Apple notebook called just “MacBook” back in... Read more

Jobs Board

Event Director, *Apple* Retail Marketing -...
…This senior level position is responsible for leading and imagining the Apple Retail Team's global engagement strategy and team. Delivering an overarching brand 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
Communication Manager - *Apple* Pay - Apple...
**Job Summary** This position works within the Apple Pay Merchant Solutions team to create, as well as oversee the development of, materials for use by Apple Pay Read more
Project Manager / Business Analyst, WW *Appl...
…a senior project manager / business analyst to work within our Worldwide Apple Fulfillment Operations and the Business Process Re-engineering team. This role will work Read more
Marketing Program Manager, *Apple* Retail O...
**Job Summary** Imagine what you could do here. At Apple , great ideas have a way of becoming great products, services, and customer experiences very quickly. Bring Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.