Implicit Heart

This example generates a surface mesh of an implicit function and then performs Laplacian smoothing on it.

Defining an implicit function

Implicit functions are defined as functions of three arguments (x, y, z), which can handle vectorized inputs.

from mymesh import implicit, mesh, improvement

def heart(x, y, z):
    # Taubin's Heart Surface
    return (x**2 + 9/4*y**2 + z**2 -1)**3 - x**2*z**3 - 9/80*y**2*z**3

Creating a Surface

bounds = [-1.5, 1.5, -1.5, 1.5, -1.5, 1.5]
h = 0.05 # element size
Heart = implicit.SurfaceMesh(heart, bounds, h)
Heart.plot(bgcolor='white', color='red')

RFBOutputContext()

Smoothing

The heart surface has a bit of a ridge in the middle, this can be eliminated by smoothing the mesh. This will also improve the quality of the elements in the mesh and more evenly distribute the nodes.

Heart = improvement.LocalLaplacianSmoothing(Heart)
Heart.plot(bgcolor='white', color='red')

Identifying volume node neighbors...Done

Identifying volume node element connectivity...Done

Identifying boundary nodes...
        Identifying boundary...Done
        Done
        RFBOutputContext()