Gradient Noise

Gradient noise with a templated number of dimensions

Animation of 3D gradient noise

Image of 2D gradient noise

Image of 1D gradient noise

How it works

Gradient noise is generated by cubically interpolating pseudorandom nodes. The nodes have n-dimensional integer positions, but noise values are generated from n-dimensional floating-point positions. Generating gradient noise from a position starts with getting the unit_position and the unit_offset. The unit_position is a copy of the position, but all the axis are floored and casted to an integer. The unit_offset is the offset of the position from the unit_position. Next, the nodes are generated. Nodes are pseudorandom floating-point values between -1 and 1 which are associated with an n-dimensional position. To get a unique pseudorandom number from an n-dimensional position, a std::seed_seq is used. The std::seed_seq is initialized with each of the axis positions. After the nodes are generated, they are interpolated one dimension at a time using the cubic interpolation function. For n dimensions, 4^n nodes are required, and 4^(n - 1) cubic interpolations are required. The value returned from the final cubic interpolation is the final noise value.

Why it's useful

Gradient noise is useful for a wide variety of applications including procedural content generation, simulations, and graphical effects.

How to use it

To generate gradient noise, create a gradient_noise object, then use the operator() method to generate noise values. Returned noise values are between -1 and 1, but due to how cubic interpolation works, values slightly outside of this range are possible. gradient_noise takes two template parameters. The first template parameter, float_type, determines the return type and parameter type. The second template parameter, dimension_count, determines the number of dimensions. gradient_noise is declared inside the gnd namespace and can optionally be initialized with a seed. Construction might look like this: gnd::gradient_noise<my_float_type, my_dimension_count> my_gradient_noise(my_seed). If no seed is provided, a default seed is used. After creation, gradient_noise can be reseeded using the seed method. Example code below.

// Create a 3D gradient noise engine using 42 as a seed
gnd::gradient_noise<float, 3> gradientNoise3d(42);

// Print a gradient noise value using (123, 555, 777) as a position
std::cout << gradientNoise3d({123.0f, 555.0f, 777.0f}) << std::endl; 

// Reseed the gradient noise engine using 9001 as a new seed
gradientNoise3d.seed(9001); 

// Print a new gradient noise value using the same position as last time
std::cout << gradientNoise3d({123.0f, 555.0f, 777.0f}) << std::endl; 

// Create a 4D gradient noise engine using 1337 as a seed
gnd::gradient_noise<double, 4> gradientNoise4d(1337); 

// Print a gradient noise value using (123, 555, 777, 999) as a position
std::cout << gradientNoise4d({123.0, 555.0, 777.0, 999.0}) << std::endl;

Notes

gnd::gradient_noise is designed to be consistent with std::default_random_engine. They both use operator() overloads to generate values, they can both be reseeded with a seed method, and they can both be constructed with seeds optionally. gnd::gradient_noise uses std::default_random_engine::result_type as the seed type and std::default_random_engine::default_seed as the default seed.