Animation of 3D gradient noise
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.
Gradient noise is useful for a wide variety of applications including procedural content generation, simulations, and graphical effects.
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;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.