TweetFollow Us on Twitter

From Algorithm to Animation: the Sequel

Volume Number: 19 (2003)
Issue Number: 7
Column Tag: QuickTime

From Algorithm to Animation: the Sequel

Making QuickTime movies which illustrate abstract processes

by Jay Martin Anderson

THE ORIGINAL

In the November 1993 issue of MacTech (volume 9, number 11), I described how I made a QuickTime movie of an algorithm from computational mathematics. In the intervening ten years, QuickTime has grown and matured, the Mac OS has crossed the divide between Classic and OS X, and several generations of IDEs have come and gone.

My interest in making QuickTime movies to illustrate algorithms from computer science and mathematics has not. Consequently, I wish to present an update of the technique used to make animations of algorithms, and apply it to a theorem from beginning calculus which my colleagues challenged me to illustrate this year.

THE PROBLEM

The Department of Mathematics at Franklin and Marshall College includes both mathematics and computer science and frequently enjoys sharing problems in one area with the other. In the spring of 2003, my mathematician colleagues challenged me to construct a way to depict the Mean Value Theorem (MVT) which states that, for a suitably "nice" function f(x) on a range a <= x <= b, somewhere (some x = c, a <= c <= b) the slope of the function, f'(c) is equal to the "rise over run" of the function, (f(b)-f(a))/(b-a).

I chose to take a particular function f(x) = x3 on the range -1 <= x <= 1, trace along the function showing a line tangent to the curve at each point, and stop when the tangent line had the same slope as the "rise over run," which is 1.

THE PARADIGM

At F&M we have developed a paradigm for constructing algorithm animations. We divide the moviemaking application into three parts: the model, the view, and the controller.

The model contains the algorithm to be visualized. In this example, it is the function and its derivative. The state of the model is the value of x, along with the value of f(x) and f'(x).

The view contains the graphical elements necessary to illustrate the model. It is in the view that a single picture of a single state of the model is developed. In our work beginning in 2003, the view is developed with OpenGL. In the view we will draw the graph of the function, the tangent line at every value of x, the line which represents the "rise over run," and any tangent line with the same slope as "rise over run."

The controller does all the initialization and cleanup necessary for the moviemaking application. In particular, it does all the work necessary to pass individual views to QuickTime for the formation of a movie. Most importantly, the controller contains the timing, which signals the model to change its state and the view to generate a new picture. The controller will continue to ask the model to change its state until the value of x has spanned the entire range of interest.

Many movies are divided into "acts" and "scenes," much like a real theater piece. This provides a simple way to modularize the model and the view, and is particularly useful if the animated view of the model is more complex than simply moving an object along a path. For this simple example, acts and scenes are not necessary.

Our movies are also annotated. A view of a state of the model is also accompanied by a few sentences of text which explain what the view shows. The resulting QuickTime movie has one video track, and one text track for each (natural) language necessary. The natural language feature of QuickTime makes it particularly easy to construct movies in English, German, Italian, etc. The text annotation in this movie gives numerical values for x and f'(x).

Beginning in 2003, our development platform for algorithm animation is Apple's Developer Tools, including Project Builder and Interface Builder. The application is developed in Objective-C, using Cocoa classes. The model is a subclass of NSObject; the view is a subclass of NSOpenGLView; and the controller is also a subclass of NSObject. Since the movie, and not the application which creates it, is the object of this exercise, the graphical user interface is kept as simple as possible, often including only a button "Make Movie" and perhaps some widgets to select among choices for the movie.

The connection between the strictly object-oriented Objective-C and Cocoa classes, and the older QuickTime API is not always elegant. Nonetheless, it is that connection which is perhaps the most significant contribution of this article. Almost every time the controller has to move information between the model or the view and QuickTime, some conversion is necessary.

Using Interface Builder

We begin with Project Builder and construct a new project, a Cocoa application. Interface Builder allows us easily to construct a window and view of appropriate size, place whatever GUI widgets we need in the window, construct the model and controller objects, and generate some source code for the model-view-controller system.

Launch Interface Builder by double-clicking the MainMenu.nib icon, which is found inside the Resources folder of the Files pane of the project. Make the window an appropriate size, and drag a Custom View onto the window. Make the Custom View be an appropriate size as well. Create a subclass of NSOpenGLView, such as MyOpenGLView, and make the Custom View be an instance of MyOpenGLView.

Drop whatever widgets you need into the window. In this example, we use only a button, labeled Make Movie.

Create a subclass of NSObject called MyController and a subclass of NSObject called MyModel. Within MyController, create an Action method, for example, createMovie. Also within MyController, create Outlets, which are instances of the classes MyModel and MyOpenGLView, respectively. Likewise, in the class MyOpenGLView, create an Outlet, which is an instance of the class MyModel.

Make instances of these classes, and generate code for these classes.

Build connections as follows: from any widgets, such as the Make Movie button to the instance of MyController, with the target of the createMovie method; from the instance of MyController to the instance of MyModel; from the instance of MyController to MyOpenGLView; and finally from the instance of MyOpenGLView to the instance of MyModel. The connection from the button to the method means that the button sends the createMovie message to the controller. The connection from the controller to the model means that the controller can send messages (usually inquiries) to the model, and likewise to the view. The connection from the view to the model means that the view can send messages (again, usually inquiries) to the model.


Figure 1. Using Interface Builder. The window contains the view, a subclass of NSOpenGLView, and one button. The view is connected to the class MyModel, so that the view may inquire the state of the model.

This completes the work with interface builder; save the nib and continue with Project Builder.

The Code

The work of managing QuickTime is done with the createMovie method of the controller object. This also includes code to provide an interface, albeit awkward, between the Objective-C classes of Cocoa and the "legacy" code of QuickTime. Three points bear special mention.

First, OpenGL draws into a context, which is described by a pixel format. QuickTime accepts images from a pixMap, which is part of the GWorld data structure. The function CopyNSBitmapImageRepToGWorld accomplishes the task of copying pixels from the first to the second environment. It is based on the assumption of 32-bit pixels in each structure. Curiously, the copying of pixels requires an NSBitmapImageRep, which is four bytes wider than the context.

Second, QuickTime constructs a movie file using an FSSpec. The FSSpec must be derived from a path or file name in the "classic" Macintosh format, and it must appear as a Pascal string. The function QTUtils_ConvertCToPascalString serves to convert a C-string to a Pascal string.

Finally, the image drawn by OpenGL is inverted when it is copied to QuickTime. Given that the QuickTime movie is the object of this exercise, it seems simplest to construct the OpenGL drawings upside-down, and let the pixel copying to QuickTime invert them to the proper orientation.

The code for the class MyController, as well as for portions of the classes MyModel and MyOpenGLView, along with all header files, can be found on the website

http://eDisk.fandm.edu/~jay.anderson/mactech/example.html

The model is the simplest unit in this example. The methods f and ff serve to calculate the function and its derivative. The method changeState advances a point along the curve by equal increments in the x-direction, and computes the corresponding value of the function and its derivative. The method changeState also looks for matches between the slope of the curve and the "rise over run," and records the matches.

Listing 1: MyModel.m

MyModel

A portion of the class MyModel, which encapsulates the algorithm to be illustrated and its data 
structures.  Shown here are the method changeState, and the methods that evaluate the function and 
its derivative.  The remainder of the class, and the header file MyModel.h are found on the website.

@implementation MyModel
- (void)changeState:(int)frNo
{
   if (frNo == 0)
   {
      // beginning frame is blank, with only an annotation
      strcpy(annotation, "MEAN VALUE THEOREM.  Compare
 rise/run to slope of graph.");
   }
   else
   {
      // as frame number goes from 0 to 200, x goes from -1.0 to 1.0 in 200 steps
      x = -1.0 + frNo/100.0;
      y = [self f:x];
      slope = [self ff:x];
      sprintf(annotation, "x = %5.2f, y = %5.2f, slope =
 %5.2f", x, y, slope);
      if (fabs(slope - ror) < 0.01) 
      {
         // slope matches rise/run; record this position, append extra annotation
         match = 1;
         xMatch[nMatches++] = x;
         strcat(annotation, "\rSlope matches rise/run: mean
 value theorem!");  
      }
      else                          
         match = 0;
   }
}
- (float)f:(float)z
{ return z*z*z; }
- (float)ff:(float)z
{ return 3*z*z; }
@end

The view is responsible for drawing the curve, the "rise over run" line, a point and tangent line which moves along the curve as the state of the model changes, and any matches between the slope of the curve and the rise-over-run line. These are simple OpenGL primitives: point, line and line-strip. Colors, the point size and the line width are chosen for viewing ease.

Listing 2: MyOpenGLView.m

MyOpenGLView

The method drawRect from the class MyOpenGLView; the remainder of the class and the header file 
MyOpenGLView.h are found on the website.  This method is invoked when the display message is sent 
to the view.  It draws each frame of the movie.  

@implementation MyOpenGLView
- (void)drawRect:(NSRect)rect
{
   float x, y, slope;
   short match;
    
   glClear(GL_COLOR_BUFFER_BIT);   // clear the screen
   x = model->x;
   y = model->y;
   slope = model->slope;
   match = model->match;
   
   /* Draw the components of the frame:  the graph of the function, the rise/run line,
      the point at (x, y), and the slope of the graph at that point.
   */
   [self drawGraph];                  
   [self drawRR];
   [self drawPoint:x:y];
   [self drawSlope:x:y:slope];
 
   /* Draw a tangent line at each place where the slope of the function matches the
      rise/run line.
   */   
   if (model->nMatches > 0)
   {
      int i;
      for (i = 0; i < model->nMatches; i++)
         [self drawMatch:i];
   }
   // show it!
   glFlush();
}
@end

The text annotations are developed within the model, and left in a string. In the controller, this string is copied to the text handler, just as the image is copied to an image compressor. Color, font, and size of text can be chosen when the text handler is constructed.

Lights! CAMERA!  ACTION!

The controller runs a simple loop to construct successive frames of the movie. In particular, the controller sends the changeState message to the model, and then the display message to the view. This image is then copied to QuickTime and compressed. In addition, the controller sends a getText message to the model to acquire the annotation to be placed into the text track.

Results

The model-view-controller paradigm has been implemented for making QuickTime movies that illustrate algorithms in Java and in Cocoa/Objective-C. The Cocoa/Objective-C implementation allows the use of OpenGL with QuickTime in a workable, if awkward, marriage of Objective-C classes with "legacy" QuickTime APIs. This opens up abstract moviemaking to the standard of OpenGL, including three-dimensional graphics. The Java implementation, which is not described here, does not require the awkward connection between software components, but does not provide easy access to OpenGL.


Figure 2. One frame of the Mean Value Theorem movie. The test point has moved from x = -1.00 to x = -0.32, and has found one spot where the slope of the curve matches the rise/run line. The text track is shown in white on blue beneath the video track.

Besides the sample movie described here, our work in 2003 and beyond includes constructing animations of algorithms from computational geometry, such as the triangulation of a polygon, constructing and searching in kd-trees and range trees, and more. Our recent work includes animations of algorithms for computing the convex hull, for the intersection of many line segments and for recognizing the polygon in which a point lies. Sample movies are posted on our web site (begin at http://eDisk.fandm.edu/~jay.anderson) as they become available.

ACKNOWLEDGMENTS

Significant assistance has come from Apple Computer, from whom code to construct QuickTime movies, media, and tracks has been borrowed; and from Big Nerd Ranch and Aaron Hillegass, whose Cocoa programming book, course and advice were enormously useful.


Jay Martin Anderson is the Richard S. and Ann B. Barshinger Professor of Computer Science at Franklin and Marshall College in Lancaster, Pennsylvania. Once a physical chemist, he has been teaching computer science since 1978 and making QuickTime movies since 1992. His interests include many aspects of computer graphics, including cartography and computational geometry; opera, theatre, and bicycling. He can be reached at jay.anderson@fandm.edu.

 

Community Search:
MacTech Search:

Software Updates via MacUpdate

Lyn 1.5.11 - Lightweight image browser a...
Lyn is a lightweight and fast image browser and viewer designed for photographers, graphic artists and Web designers. Featuring an extremely versatile and aesthetically pleasing interface, it... Read more
NeoOffice 2014.11 - 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
LaunchBar 6.4 - Powerful file/URL/email...
LaunchBar is an award-winning productivity utility that offers an amazingly intuitive and efficient way to search and access any kind of information stored on your computer or on the Web. It provides... Read more
Remotix 3.1.4 - Access all your computer...
Remotix is a fast and powerful application to easily access multiple Macs (and PCs) from your own Mac. Features Complete Apple Screen Sharing support - including Mac OS X login, clipboard... Read more
DesktopLyrics 2.6.6 - Displays current i...
DesktopLyrics is an application that displays the lyrics of the song currently playing in "iTunes" right on your desktop. The lyrics for the song have to be set in iTunes; DesktopLyrics does nothing... Read more
VOX 2.5.1 - Music player that supports m...
VOX is a beautiful music player that supports many filetypes. The beauty is in its simplicity, yet behind the minimal exterior lies a powerful music player with a ton of features and support for all... Read more
NetNewsWire 4.0.0 - RSS and Atom news re...
NetNewsWire is the best way to keep up with the sites and authors you read most regularly. Let NetNewsWire pull down the latest articles, and read them in a distraction-free and Mac-like way. Native... Read more
MacUpdate Desktop 6.0.6 - Search and ins...
MacUpdate Desktop 6 brings seamless 1-click installs and version updates to your Mac. With a free MacUpdate account and MacUpdate Desktop 6, Mac users can now install almost any Mac app on macupdate.... Read more
ForkLift 2.6.5 - Powerful file manager:...
ForkLift is a powerful file manager and ferociously fast FTP client clothed in a clean and versatile UI that offers the combination of absolute simplicity and raw power expected from a well-executed... Read more
Drive Genius 4.1.0 - Powerful system uti...
Drive Genius 4 gives you faster performance from your Mac while also protecting it. The award-winning and improved DrivePulse feature alerts you to hard drive issues before they become major problems... Read more

Auroch Digital is Bringing Back Games Wo...
| Read more »
Carbo - Handwriting in the Digital Age...
Carbo - Handwriting in the Digital Age 1.0 Device: iOS Universal Category: Productivity Price: $3.99, Version: 1.0 (iTunes) Description: | Read more »
Draggy Dead (Games)
Draggy Dead 1.1 Device: iOS Universal Category: Games Price: $.99, Version: 1.1 (iTunes) Description: Ditch your dead end job and take up a rewarding career in Grave Robbing today!Guide the recently deceased to a fun filled life of... | Read more »
Bad Dinos (Games)
Bad Dinos 1.0.0 Device: iOS Universal Category: Games Price: $2.99, Version: 1.0.0 (iTunes) Description: | Read more »
The Apple Watch isn't Great as a Fi...
| Read more »
Show the World What You See With Stre.am...
Live broadcasting is getting popular on mobile devices, which is why you can now get Stre.am, by Infinite Takes. [Read more] | Read more »
PhotoTime's 2.1 Update Adds Apple W...
The latest PhotoTime update is adding even more functionality to the handy photo organizing app. Yep, including Apple Watch support. [Read more] | Read more »
Oh My Glob! Adventure Time Puzzle Quest...
Finn and Jake are taking over D3 Go!'s popular puzzle game series in the upcoming Adventure Time Puzzle Quest. [Read more] | Read more »
Earthcore: Shattered Elements - Tips, Tr...
At first glance, Earthcore: Shattered Elements seems like a rather simple card-battling game. Once you’re introduced to skills that will change quite a bit. Even more so once you start to acquire hero cards. But it’s not so complicated that we... | Read more »
Dungeon999F (Games)
Dungeon999F 1.33 Device: iOS Universal Category: Games Price: $.99, Version: 1.33 (iTunes) Description: "The game you must play at least once in your life!" "The game with potential of million downloads globally!" ...is what the... | Read more »

Price Scanner via MacPrices.net

OtterBox Maximizes Portability, Productivity...
From the kitchen recipe book to the boarsroom presentation, the OtterBox Agility Tablet System turns tablets into one of the most versatile pieces of handheld technology available. Available now, the... Read more
Launch of New Car App Gallery and Open Develo...
Automatic, a company on a mission to bring the power of the Internet into every car, has announced the launch of the Automatic App Gallery, an app store for nearly every car or truck on the road... Read more
Memorial Day Weekend Sale: 13-inch 1.6GHz Mac...
Best Buy has the new 13″ 1.6GHz/128GB MacBook Air on sale for $849 on their online store this weekend. Choose free shipping or free local store pickup (if available). Sale price for online orders... Read more
Memorial Day Weekend Sale: 27-inch 3.5GHz 5K...
Best Buy has the 27″ 3.5GHz 5K iMac on sale for $2099.99 this weekend. Choose free shipping or free local store pickup (if available). Sale price for online orders only, in-store prices may vary.... Read more
Sale! 16GB iPad mini 3 for $349, save $50
B&H Photo has the 16GB iPad mini 3 WiFi on sale for $349 including free shipping plus NY sales tax only. Their price is $50 off MSRP, and it’s the lowest price available for this model. Read more
Price drop on 2014 15-inch Retina MacBook Pro...
B&H Photo has dropped prices on 2014 15″ Retina MacBook Pros by $200. Shipping is free, and B&H charges NY sales tax only: - 15″ 2.2GHz Retina MacBook Pro: $1799.99 save $200 - 15″ 2.5GHz... Read more
With a Mission to Make Mobile Free, Scratch W...
Scratch Wireless, claiming to be the world’s first truly free mobile service, has announced the availability of a new Scratch-enabled Android smartphone, the Coolpad Arise. The smartphone is equipped... Read more
First-Ever Titanium Alloy Curved iPhone 6 Scr...
One of the most common problems with mobile phones is damage to the screens. The slightest drop can cause a dreaded spider web of gashes and cracks in the glass panel surface that can cost $hundreds... Read more
Preorder new 12-inch MacBook, $10 off, save o...
Adorama has new 12″ Retina MacBooks available for preorder for $10 off MSRP including free shipping plus NY & NJ sales tax only. For a limited time, Adorama will include a free Apple USB-C to USB... Read more
Will iOS 9 Finally Bring Productivity Friendl...
Ah, the irony. From its original announcement in 2010, Apple has doggedly insisted that the iPad remain “simple,” thus arbitrarily limiting its considerable potential as a content creation and... Read more

Jobs Board

*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
Business Development Manager - *Apple* Pay...
**Job Summary** Apple Pay is seeking an experienced Business Development professional to join the Apple Pay team to develop partnerships and strategic alliances with Read more
Project Manager, *Apple* Retail New Store O...
**Job Summary** An Apple Retail New Store Openings & Remodels Project Manager is responsible for successfully managing the openings, remodels, and small works of Read more
SW QA Engineer - *Apple* TV - Apple (United...
**Job Summary** The Apple TV team is looking for experienced Quality Assurance Engineers with a passion for delivering first in class home entertainment solutions. **Key Read more
Partner Marketing Manager - *Apple* Pay - A...
**Job Summary** The Apple Pay partner marketing team is looking for a marketing manager to develop and drive US marketing programs with our financial institution Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.