sdf.py

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import math
 
# SDF Indenter
 
r = 1
 
#xc = (-58.9 + 12.5)/2
#zc = (-70.5 + 0.9)/2
#yc = -58.9 - r
 
 
def sdf(t, x, y, z, tx, ty, tz):
    #return Sphere.sDF(r, xc, yc, zc, x, y, z)
    return CylinderZ.sDF(r, 0, -0.5-r, x, y)
 
 
def grad_sdf(t, x, y, z, tx, ty, tz):
    #return Sphere.gradSdf(xc, yc, zc, x, y, z)
    return CylinderZ.gradSdf(0, -0.5-r, x, y)
 
 
def hess_sdf(t, x, y, z, tx, ty, tz):
    #return Sphere.hessSdf(xc, yc, zc, x, y, z)
    return CylinderZ.hessSdf(0, -0.5-r, x, y)
 
# Indenters
 
class yPlane:
    def sDF(shift, xc, yc, x, y):
        return y-shiftl
 
    def gradSdf(xc, yc, x, y):
        # x, y, z
        return [0, 0, 0]
    
    def hessSdf(xc, yc, x, y):
        # xx, yx, zx, yy, zy, zz
        return [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]
 
class Sphere:
    
    def sDF(r, xc, yc, zc, x, y, z):
        a = pow(x-xc, 2)+pow(y-yc, 2)+pow(z-zc, 2)
        c_val = math.sqrt(a)-r
        return c_val
    
    def gradSdf(xc, yc, zc, x, y, z):
        a = pow(x-xc, 2)+pow(y-yc, 2)+pow(z-zc, 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)
        c_val_dz = c_val_A * (z-zc)
        # x, y, z
        return [c_val_dx, c_val_dy, c_val_dz]
    
    def hessSdf(xc, yc, zc, x, y, z):
        a = pow(x-xc, 2)+pow(y-yc, 2)+pow(z-zc, 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]