|By Mike Jacobs||
|March 9, 2005 12:00 AM EST||
Reach behind your television and yank the cable out of the wall. Do you hear that noise? Not the kids screaming about their movie. Look at the screen. What you see is white noise: random bits of white, black and gray changing constantly. What does this have to do with movie magic or Java3D? What if a spell could conjure roaring fires, fluffy clouds, rippling water, naturally grained wood, smooth marble and even realistic terrains? That spell is available to us thanks to the inventive mind of Dr. Ken Perlin.
Who Was That Math Man?
Ken Perlin is a professor in the department of computer science at New York University. In 1997 he won an Academy Award for Technical Achievement from the Academy of Motion Picture Arts and Sciences for his procedural texturing techniques, which are widely used in feature films and television. He also had a big part in the computer animation in the movie "TRON." The techniques pioneered by Dr. Perlin allow programs to generate a wide range of realistic special effects efficiently. The foundation for these effects is a mathematical function called Perlin noise.
What Was That Noise?
Procedural texturing is the art of using an algorithm to generate a texture. Procedural techniques are not limited to texturing and can be applied to geometry, motion, color or any other thing you can imagine. Procedural techniques abstract the details of a scene or sequence into an algorithm. Parameters on the algorithm allow a variety of results to be achieved with the same algorithm. An example of procedural geometry was in my last article ("When Mars Is Too Big to Download," JDJ, September 2004) where we used parameters to vary the detail and roughness of the generated terrain. The advantage of using procedural techniques is that the details are generated, saving the cost of explicitly storing and retrieving them.
To make realistic special effects, we need a way to generate natural looking randomness. You might think that random numbers would be sufficient to accomplish this, but you would only be partially right. (See Figure 1.) Random numbers are typically generated without regard to past values. This lack of correlation can lead to abrupt changes between adjacent values and an unnatural special effect. What we need is a repeatable, smooth, non-cyclic random function whose results vary with the parameters we provide. Perlin noise was designed to do just that.
While the implementation details of Perlin noise are beyond the scope of this article, we do need a conceptual model to use it. The noise function accepts a number of double parameters and returns a double value between +1 and -1. One-dimensional noise is the result of generating random numbers at regular intervals and smoothly interpolating noise values in between using a high-order polynomial. This can be represented by a smooth curve as shown in Figure 1.
Two-dimensional noise does the interpolation in two dimensions forming a wavy noise surface. The three-dimensional noise can't be depicted graphically, but its foundation is a lattice. The three parameters represent the three dimensions of the lattice from which the noise value is calculated. This lattice consists of 256 by 256 by 256 points representing random numbers between which values are smoothly interpolated to calculate the noise. The noise value at the integer lattice locations is zero, while the values between the locations follows the same high-order polynomial mentioned above. A Java reference implementation called ImprovedNoise is available from Dr. Perlin's home page and a modified version is included with the source code for this article.
This probably sounds pretty mysterious, so let's put this magic to work with a few examples.
Casting Our First Spell: Blur
In my last article, we generated terrains with colors assigned based solely on elevation. Looking closely at some of the resulting terrains, you may have noticed that the colors created a layered effect. For this article, the FractalWorld3 example uses your choice of random numbers or Perlin noise to blur the colors to eliminate the layered affect. Have a look at Figure 2 to see this example in action.
In this example, the noise function is used to blur the boundaries between colors to make the transitions less apparent. The effect is implemented by nudging the color index with the noise function as shown in part in Listing 1.
The color index is determined normally and then a delta value is calculated with the noise function. The sum of the index and the delta value is rounded and clamped to create the new color index. This method uses the row, column and elevation as arguments to the noise function. All three are scaled down to focus the noise based on trial and error. You can think of the divisors as a zoom function into the noise. Because the noise is defined in a limited-size lattice, the zoom factor focuses the range: higher zoom results in less noise range. Finding the right recipe for an effect is mostly an art but luckily others have shared their recipes.
Texturing with Noise
A popular use for noise is to generate the colors on a texture. We can apply the texture to a shape, giving the appearance of natural materials like wood or marble. Have a look at Figure 3 for an example of an image produced by the PerlinNoiseSphere.
Java3D supports texturing of a shape by setting the texture image on the appearance object. The PerlinNoiseSphere example uses a Java3D Sphere primitive as the shape and Perlin noise to generate the texture. The Sphere primitive is used in this example so some texturing details can be automatically done for us. Setting up the texture on the appearance is shown in part in Listing 2. The getImage() method is where the magic happens. The recipe is used to determine the noise values and the PerlinNoiseSphere example interprets the values as colors. Before I disclose the secret to this trick, I should mention that there's no relationship between how the recipe creates the texture and how nature creates the material. These recipes have been arrived at through trial and error and bit of luck. The results look amazingly close to the real thing, which teaches us that: In 3D graphics, there's nothing like a great fake.
The recipe for the wood texture in Listing 3 is decidedly simple.
The grain value is determined by the noise method using the image row and column as parameters. The color for the image pixel is based on the red, green and blue values calculated with the grain. Creating static texture images with noise is interesting, but the power of noise is even greater when combined with animation.
A Java3D behavior links keyboard, mouse or temporal events with changes to the scene or view. For example, the keyboard or mouse can be used to update the view allowing us to move the virtual camera through the scene. Java3D includes this support with the KeyNavigatorBehavior, MouseRotate, MouseTranslate and MouseZoom behaviors. Time can be used to animate the movement or morph the shape attributes in our scene and Java3D includes subclasses of Interpolator for this as well. While there are a number of behaviors available in Java3D, it's likely you'll eventually need to create your own behavior and Java3D is designed for that.
When a behavior is created, the constructor typically defines the triggering or wake-up condition such as a keyboard or mouse event, a number of frames or the passage of time. Behaviors are added to the scene like any other Java3D object.
When your scene is initially rendered, Java3D calls the initialize() method where your implementation should set the trigger. When Java3D detects the triggering event, it calls the processStimulus() method on your behavior. Your implementation of this method does its thing and then must reset the trigger. The documentation for the Behavior class is excellent, so refer to it for more details.
The ElapsedTimeBehavior example is the basis for the animation examples in this article. When triggered, this behavior calls the tick() method on the configured listener after the specified number of milliseconds has passed. Milliseconds are used as the trigger rather than the number of frames so it runs consistently across different computers. Let's use this behavior to recreate the animation of a movie special effect in Java3D.
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