warp.curlnoise#

warp.curlnoise( state: uint32, xy: vec2f, octaves: uint32, lacunarity: float32, gain: float32, ) → vec2f#

Kernel

Python

Differentiable

Sample a divergence-free 2D vector field derived from Perlin noise.

Returns a rotated Perlin-noise gradient, making the field analytically divergence-free. Its continuous flow preserves area, although numerical advection may not. The 3D and 4D overloads instead return the spatial curl of three noise potentials as a warp.vec3.

Octave i uses frequency lacunarity ** i and weight gain ** i. With lacunarity > 1 and 0 < gain < 1, later octaves add finer, weaker detail. Contributions may cancel, so magnitude is not monotonic in the octave controls. Zero octaves returns zero. Scale the coordinate for feature size and the result for speed.

state selects the field and is not advanced. Results are reproducible per device, but CPU and CUDA values may differ slightly. Differentiable with respect to the coordinate; octaves, lacunarity, and gain receive no gradient.

Parameters:

state – RNG state used as a hash seed (see rand_init()), never advanced.
xy – Coordinate to sample. One swirl spans about one unit at the base frequency.
octaves – Number of noise octaves to sum. Zero returns a zero vector.
lacunarity – Frequency multiplier between successive octaves.
gain – Amplitude multiplier between successive octaves.

Returns:

A divergence-free 2D vector at xy. Not normalized.

Example

@wp.kernel
def advect(seed: int, positions: wp.array[wp.vec2], dt: float):
    tid = wp.tid()
    state = wp.rand_init(seed)
    positions[tid] = positions[tid] + wp.curlnoise(state, positions[tid]) * dt

positions = wp.array([[0.5, 0.5], [1.25, 2.0]], dtype=wp.vec2)

wp.launch(advect, dim=len(positions), inputs=[42, positions, 0.1])
print([[round(c, 3) for c in p] for p in positions.numpy().tolist()])

[[0.628, 0.514], [1.256, 2.003]]

warp.curlnoise( state: uint32, xyz: vec3f, octaves: uint32, lacunarity: float32, gain: float32, ) → vec3f

Kernel

Python

Differentiable

Sample a divergence-free 3D vector field derived from Perlin noise.

Returns the spatial curl of three Perlin-noise potentials. See curlnoise() for shared behavior, restrictions, and a usage example.

Parameters:

state – RNG state used as a hash seed (see rand_init()), never advanced.
xyz – Coordinate to sample. One swirl spans about one unit at the base frequency.
octaves – Number of noise octaves to sum. Zero returns a zero vector.
lacunarity – Frequency multiplier between successive octaves.
gain – Amplitude multiplier between successive octaves.

Returns:

A divergence-free 3D vector at xyz. Not normalized.

warp.curlnoise( state: uint32, xyzt: vec4f, octaves: uint32, lacunarity: float32, gain: float32, ) → vec3f

Kernel

Python

Differentiable

Sample a divergence-free 3D vector field that also varies along a fourth axis.

Returns a warp.vec3 spatial curl; the fourth input axis parametrizes the field and is commonly used as time. The field remains divergence-free in the first three axes. See curlnoise() for shared behavior, restrictions, and a usage example.

Parameters:

state – RNG state used as a hash seed (see rand_init()), never advanced.
xyzt – Coordinate to sample, with the fourth component usually time. One swirl spans about one unit at the base frequency.
octaves – Number of noise octaves to sum. Zero returns a zero vector.
lacunarity – Frequency multiplier between successive octaves.
gain – Amplitude multiplier between successive octaves.

Returns:

A divergence-free 3D vector at xyzt. Not normalized.