The vector field is created based on the implicit equation of a closed and differentiable implicit surface '''S = F'''(x,y,z). For every point in the space, frecuently outside or near the surface, we get a normalvector '''ng''' that is normal to the surface, this is calculatedthe gradient of S or the partial derivatives respect to x, y and z, this vector is calculatednot theunitary samebut waywe ascan theget distancea signedunitary funcion,normal using'''n''' theby partialdividing derivativeseach dividedcomponent of the point by the distancenorm toof the surface.gradient '''g'''.
Outside of the surface all these normals point away from the surface. AfterAfterwards thatwe calculate a scalar value p is calculated for that point in the space using a 3D perlin or simplex noise function. Now we create a vector field '''F''' = p'''n''' pointing outside of the surface. Then the curl of this vector field gives the direction in every point in the space where the particles should move. By construction oh this vectorsvector F will point in a tangentangent direction to a isosurface given byat the samelevel of the signed distance to the original surface and can be used to confine the movements of eachthe particleparticles to stay in that surface.
