Definitions

Amplitude The maximum absolute value that a specific coherent-noise function can output. In libnoise, a coherent-noise function with an ampltude of n generates values between +n and -n, although in some cases (for example, when generating Perlin noise), this is not guaranteed.

Coherent noise A type of smooth pseudorandom noise. Coherent noise is generated by a coherent-noise function, which has three important properties: Passing in the same input value will always return the same output value. A small change in the input value will produce a small change in the output value. A large change in the input value will produce a random change in the output value. An n-dimensional coherent-noise function requires an n-dimensional input value. Its output value is always a scalar. In libnoise, all coherent-noise functions are three-dimensional. Three-dimensional coherent noise is often called solid noise because it can be used to create solid three-dimensional textures. The following graph shows the output of a one-dimensional coherent-noise function n(x) with a frequency of 2: Compare it to the following graph that shows the output of a non-coherent-noise function n(x):

Combiner module A noise module that mathematically combines the output values from two or more source modules together. Examples of combiner modules include: noise::module::Add — Adds the two output values from two source modules.

— Adds the two output values from two source modules. noise::module::Max — Outputs the larger of the two output values from two source modules. The following image demonstrates the noise::module::Add noise module, a type of combiner module.

Control module A noise module that indicates how to combine the output values from the source modules that are connected to a selector module.

Frequency The number of cycles per unit length that a specific coherent-noise function outputs. Coherent noise has properties similar to that of a sine wave: It has periodic cycles of length 1/ f , where f is its frequency.

, where is its frequency. At the start of each cycle, it outputs a value of zero. Unlike a sine wave, the output of a coherent-noise function may or may not cross zero during the middle of a cycle. The following graph shows the output of a one-dimensional coherent-noise function n(x): In the above graph, the beginning of each cycle is shown with a circle. The following graphs show the outputs of one-dimensional coherent-noise functions n(x) with frequencies 2, 4, and 8. In these graphs, f refers to frequency.

Generator module A noise module that outputs a value generated by a coherent-noise function or some other mathematical function. If a generator module outputs coherent noise, the output of this module is often called solid noise. This is because solid noise can be used to create solid three-dimensional textures. Examples of generator modules include: noise::module::Const — Outputs a constant value.

— Outputs a constant value. noise::module::Perlin — Outputs a value generated by a Perlin-noise function.

— Outputs a value generated by a Perlin-noise function. noise::module::Voronoi — Outputs a value generated by a Voronoi-cell function. The following image demonstrates the noise::module::Perlin noise module, a type of generator module.

Lacunarity A multiplier that determines how quickly the frequency increases for each successive octave in a Perlin-noise function. The frequency of each successive octave is equal to the product of the previous octave's frequency and the lacunarity value. A similar property to lacunarity is persistence, which modifies the octaves' amplitudes in a similar way.

Modifier module A noise module that mathematically modifies the output value from a source module. Examples of modifier modules include: noise::module::Curve — Maps the output value from the source module onto an arbitrary function curve.

— Maps the output value from the source module onto an arbitrary function curve. noise::module::Invert — Inverts the output value from the source module. The following image demonstrates the noise::module::Invert noise module, a type of modifier module.

Noise Module In libnoise, an object that calculates and outputs a value given a three-dimensional input value. All noise modules are instantiations of classes derived from the base class noise::module::Module. Each noise module class uses a specific method to calculate an output value. Some of these methods include: Calculating a value using a coherent-noise function or some other mathematical function.

Changing the output value from another noise module in various ways.

Combining the output values from two noise modules in various ways. Noise modules can be chained together in near-infinite ways like LEGO® bricks. libnoise has several types of noise modules: Combiner module

Generator module

Modifier module

Selector module

Transformer module See also: Source module, Control module

Octave One of the coherent-noise functions in a series of coherent-noise functions that are added together to form Perlin noise. These coherent-noise functions are called octaves because each octave has, by default, double the frequency of the previous octave. Musical tones have this property as well; a musical C tone that is one octave higher than the previous C tone has double the frequency. The number of octaves control the amount of detail of Perlin noise. Adding more octaves increases the detail of Perlin noise, with the added drawback of increasing the calculation time. The following graphs show the outputs of one-dimensional Perlin-noise functions n(x) with 1, 2, 4, and 8 octaves. In these graphs, o refers to the octave count.

Perlin noise A type of coherent noise that is the sum of several coherent-noise functions of ever-increasing frequencies and ever-decreasing amplitudes. The following graphs show the outputs of several one-dimensional coherent-noise functions n(x). Each graph shows a function with double the frequency and one-half the amplitude of the function from the previous graph. In these graphs, f refers to frequency and a refers to amplitude. The sum of these coherent-noise functions result in Perlin noise. Each coherent-noise function that is part of a Perlin-noise function is called an octave. These functions are called octaves because each function has, by default, double the frequency of the previous function; musical tones have this property as well. Perlin noise generated with more octaves produce more detailed coherent noise, at a cost of additional calculation time. Perlin noise is fractal in nature; a zoomed-in section of Perlin noise tends to look like the original section. Natural objects also have this property; for example, a twig from a tree resembles a branch of the tree, which in turn resembles the original tree. Because of this property, Perlin noise is ideal for generating natural, self-similar textures such as granite, wood, marble, and clouds. It is also ideal for generating realistic terrain. Ken Perlin invented Perlin noise in ~1983. Because his invention is used everywhere in the special-effects industry, he won an Academy Award®. See also: Lacunarity, Persistence

Persistence A multiplier that determines how quickly the amplitudes diminish for each successive octave in a Perlin-noise function. The amplitude of each successive octave is equal to the product of the previous octave's amplitude and the persistence value. Increasing the persistence produces "rougher" Perlin noise. The following graphs show the outputs of five-octave Perlin-noise functions n(x) with persistence values of 3/4, 1/2, and 1/4. In these graphs, p refers to persistence. A similar property to persistence is lacunarity, which modifies the octaves' frequencies in a similar way.

Seed A value that changes the output of a coherent-noise function. Seeds in coherent-noise functions are used in the same way as seeds in standard random-number generators. By changing the seed of a coherent-noise function, you change its output values; however, that function's frequency and amplitude are not altered.

Solid noise A common term for three-dimensional coherent noise. Solid noise is often used as three-dimensional procedural textures. This is because one can "carve out" modeled objects from solid noise, like a sculptor carving a statue from marble. Because each point in three-dimensional space has its own coherent-noise value, the resulting texture does not have any warps or creases. An interesting consequence of this property is that if one cuts a piece out of the object, the texture inside of that object will mesh perfectly with the texture on the outside of the object. The following image shows an object that has a solid noise texture. Note that the texture does not warp anywhere on the object; it is uniform throughout the object. It would be very difficult to produce a non-warping two-dimensional texture map for this object.

Source module A noise module that is used as a source of output values for another noise module. For example, the noise module noise::module::Add outputs the sum of the two source modules connected to it. Each source module may also be connected to other source modules, and so on.