sdf.py

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import math
 
# SDF Indenter
 
# Negative level set represents interior of the indenter. 
# This normal points outside of the indenter.
 
r = 1
 
 
def sdf(t, x, y, z, tx, ty, tz):
    return 1;
 
 
def grad_sdf(t, x, y, z, tx, ty, tz):
    return [0, 0, 0]
 
 
def hess_sdf(t, x, y, z, tx, ty, tz):
    return [0, 0, 0, 0, 0, 0]
 
# Indenters
 
class yPlane:
    def sDF(shift, y):
        return y - shift
 
    def gradSdf():
        # nx, ny, nz
        return [0, 1, 0]
    
    def hessSdf():
        # xx, yx, zx, yy, zy, zz
        return [0, 0, 0, 0, 0, 0]
 
 
class CylinderZ:
    
    def sDF(r, xc, yc, x, y):
        a = pow(x-xc, 2)+pow(y-yc, 2)
        c_val = math.sqrt(a)-r
        return c_val
    
    def gradSdf(xc, yc, x, y):
        a = pow(x-xc, 2)+pow(y-yc, 2)
        c_val = math.sqrt(a)
        c_val_A = 1/c_val
        c_val_dx = c_val_A * (x-xc)
        c_val_dy = c_val_A * (y-yc)
        # x, y, z
        return [c_val_dx, c_val_dy, 0]
    
    def hessSdf(xc, yc, x, y):
        a = pow(x-xc, 2)+pow(y-yc, 2)
        c_val = math.sqrt(a)
        c_val_A = 1./c_val
        c_val_B = 1./pow(a, 3./2.)
        c_val_dx_dx = c_val_A - c_val_B * pow(x-xc, 2)
        c_val_dx_dy = -c_val_B * (x-xc)*(y-yc)
        c_val_dy_dy = c_val_A - c_val_B * pow(y-yc, 2)
        # xx, yx, zx, yy, zy, zz
        return [c_val_dx_dx, c_val_dx_dy, 0, c_val_dy_dy, 0, 0]