sdf.Sphere Class Reference

Public Member Functions
	__init__ (self, Xc, Yc, Zc, diameter)
	sDF (self, x, y, z)
	gradSdf (self, x, y, z)
	hessSdf (self, x, y, z)
	__init__ (self, Xc, Yc, Zc, diameter)
	sDF (self, x, y, z)
	gradSdf (self, x, y, z)
	hessSdf (self, x, y, z)
	__init__ (self, Xc, Yc, Zc, diameter)
	sDF (self, x, y, z)
	gradSdf (self, x, y, z)
	hessSdf (self, x, y, z)

Public Attributes
	Xc
	Yc
	Zc
	xc
	yc
	zc
	radius

Detailed Description

Definition at line 141 of file sdf.py.

Constructor & Destructor Documentation

__init__() [1/3]

sdf.Sphere.__init__	(		self,
			Xc,
			Yc,
			Zc,
			diameter
	)

Definition at line 142 of file sdf.py.

    def __init__(self, Xc, Yc, Zc, diameter):
        # Initial Centroid
        self.Xc = Xc
        self.Yc = Yc
        self.Zc = Zc
 
        # Current Centroid
        self.xc = Xc
        self.yc = Yc
        self.zc = Zc
 
        # Indenter Dimensions
        self.radius = diameter/2
    

__init__() [2/3]

sdf.Sphere.__init__	(		self,
			Xc,
			Yc,
			Zc,
			diameter
	)

Definition at line 93 of file sdf.py.

    def __init__(self, Xc, Yc, Zc, diameter):
        # Initial Centroid
        self.Xc = Xc
        self.Yc = Yc
        self.Zc = Zc
 
        # Current Centroid
        self.xc = Xc
        self.yc = Yc
        self.zc = Zc
 
        # Indenter Dimensions
        self.radius = diameter/2
    

__init__() [3/3]

sdf.Sphere.__init__	(		self,
			Xc,
			Yc,
			Zc,
			diameter
	)

Definition at line 142 of file sdf.py.

    def __init__(self, Xc, Yc, Zc, diameter):
        # Initial Centroid
        self.Xc = Xc
        self.Yc = Yc
        self.Zc = Zc
 
        # Current Centroid
        self.xc = Xc
        self.yc = Yc
        self.zc = Zc
 
        # Indenter Dimensions
        self.radius = diameter/2
    

Member Function Documentation

gradSdf() [1/3]

sdf.Sphere.gradSdf	(		self,
			x,
			y,
			z
	)

Definition at line 165 of file sdf.py.

    def gradSdf(self,x, y, z):
        a = (x-self.xc)**2 + (y-self.yc)**2 + (z-self.zc)**2
        c_val = np.sqrt(a)
        c_val_A = 1./c_val
        c_val_dx = c_val_A * (x-self.xc)
        c_val_dy = c_val_A * (y-self.yc)
        c_val_dz = c_val_A * (z-self.zc)
        # x, y, z
        #size = np.size(x)
        #grad_array = np.empty([size,3])
        c_val_dx = c_val_dx.reshape((-1,1))
        c_val_dy = c_val_dy.reshape((-1,1))
        c_val_dz = c_val_dz.reshape((-1,1))
        grad_array = np.hstack([c_val_dx,c_val_dy,c_val_dz])
        return grad_array
    

gradSdf() [2/3]

sdf.Sphere.gradSdf	(		self,
			x,
			y,
			z
	)

Definition at line 110 of file sdf.py.

    def gradSdf(self, x, y, z):
        a = (x-self.xc)**2 + (y-self.yc)**2 + (z-self.zc)**2
        c_val_A = 1./np.sqrt(a)
        c_val_dx = c_val_A * (x-self.xc)
        c_val_dy = c_val_A * (y-self.yc)
        c_val_dz = c_val_A * (z-self.zc)
        # x, y, z
        return np.hstack([c_val_dx.reshape((-1,1)), c_val_dy.reshape((-1,1)), c_val_dz.reshape((-1,1))])
    

gradSdf() [3/3]

sdf.Sphere.gradSdf	(		self,
			x,
			y,
			z
	)

Definition at line 165 of file sdf.py.

    def gradSdf(self,x, y, z):
        a = (x-self.xc)**2 + (y-self.yc)**2 + (z-self.zc)**2
        c_val = np.sqrt(a)
        c_val_A = 1./c_val
        c_val_dx = c_val_A * (x-self.xc)
        c_val_dy = c_val_A * (y-self.yc)
        c_val_dz = c_val_A * (z-self.zc)
        # x, y, z
        #size = np.size(x)
        #grad_array = np.empty([size,3])
        c_val_dx = c_val_dx.reshape((-1,1))
        c_val_dy = c_val_dy.reshape((-1,1))
        c_val_dz = c_val_dz.reshape((-1,1))
        grad_array = np.hstack([c_val_dx,c_val_dy,c_val_dz])
        return grad_array
    

hessSdf() [1/3]

sdf.Sphere.hessSdf	(		self,
			x,
			y,
			z
	)

Definition at line 181 of file sdf.py.

    def hessSdf(self,x, y, z):
        x = x-self.xc
        y = y-self.yc
        z = z-self.zc
        Hxx = -x**2/(x**2 + y**2 + z**2)**(3/2) + 1/np.sqrt(x**2 + y**2 + z**2)
        Hzx = -x*z/(x**2 + y**2 + z**2)**(3/2)
        Hxy = -x*y/(x**2 + y**2 + z**2)**(3/2)
        Hyy = -y**2/(x**2 + y**2 + z**2)**(3/2) + 1/np.sqrt(x**2 + y**2 + z**2)
        Hzy = -y*z/(x**2 + y**2 + z**2)**(3/2)
        Hzz = -z**2/(x**2 + y**2 + z**2)**(3/2) + 1/np.sqrt(x**2 + y**2 + z**2)
        # xx, yx, zx, yy, zy, zz
        Hxx = Hxx.reshape((-1,1))
        Hzx = Hzx.reshape((-1,1))
        Hxy = Hxy.reshape((-1,1))
        Hyy = Hyy.reshape((-1,1))
        Hzy = Hzy.reshape((-1,1))
        Hzz = Hzz.reshape((-1,1))
        hess_array = np.hstack([Hxx, Hxy, Hzx, Hyy, Hzy, Hzz])
 
        return hess_array
  
 
 
# Define Indenters below

hessSdf() [2/3]

sdf.Sphere.hessSdf	(		self,
			x,
			y,
			z
	)

Definition at line 119 of file sdf.py.

    def hessSdf(self, x, y, z):
        x, y, z = x-self.xc, y-self.yc, z-self.zc
        denom = (x**2 + y**2 + z**2)**(3/2)
        sqrt_denom = np.sqrt(x**2 + y**2 + z**2)
        Hxx = -x**2/denom + 1/sqrt_denom
        Hzx = -x*z/denom
        Hxy = -x*y/denom
        Hyy = -y**2/denom + 1/sqrt_denom
        Hzy = -y*z/denom
        Hzz = -z**2/denom + 1/sqrt_denom
        # xx, yx, zx, yy, zy, zz
        return np.hstack([Hxx.reshape((-1,1)), Hxy.reshape((-1,1)), Hzx.reshape((-1,1)), Hyy.reshape((-1,1)), Hzy.reshape((-1,1)), Hzz.reshape((-1,1))])
  
 
# Define Indenters below

hessSdf() [3/3]

sdf.Sphere.hessSdf	(		self,
			x,
			y,
			z
	)

Definition at line 181 of file sdf.py.

    def hessSdf(self,x, y, z):
        x = x-self.xc
        y = y-self.yc
        z = z-self.zc
        Hxx = -x**2/(x**2 + y**2 + z**2)**(3/2) + 1/np.sqrt(x**2 + y**2 + z**2)
        Hzx = -x*z/(x**2 + y**2 + z**2)**(3/2)
        Hxy = -x*y/(x**2 + y**2 + z**2)**(3/2)
        Hyy = -y**2/(x**2 + y**2 + z**2)**(3/2) + 1/np.sqrt(x**2 + y**2 + z**2)
        Hzy = -y*z/(x**2 + y**2 + z**2)**(3/2)
        Hzz = -z**2/(x**2 + y**2 + z**2)**(3/2) + 1/np.sqrt(x**2 + y**2 + z**2)
        # xx, yx, zx, yy, zy, zz
        Hxx = Hxx.reshape((-1,1))
        Hzx = Hzx.reshape((-1,1))
        Hxy = Hxy.reshape((-1,1))
        Hyy = Hyy.reshape((-1,1))
        Hzy = Hzy.reshape((-1,1))
        Hzz = Hzz.reshape((-1,1))
        hess_array = np.hstack([Hxx, Hxy, Hzx, Hyy, Hzy, Hzz])
 
        return hess_array
  
 
 
# Define Indenters below

sDF() [1/3]

sdf.Sphere.sDF	(		self,
			x,
			y,
			z
	)

Definition at line 156 of file sdf.py.

    def sDF(self, x, y, z):
        dx = np.subtract(x, self.xc)
        dy = np.subtract(y, self.yc)
        dz = np.subtract(z, self.zc)
        a = (dx)**2+(dy)**2 + (dz)**2
        gap = np.sqrt(a) - self.radius
        
        return gap
    

sDF() [2/3]

sdf.Sphere.sDF	(		self,
			x,
			y,
			z
	)

Definition at line 107 of file sdf.py.

    def sDF(self, x, y, z):
        return np.sqrt((x - self.xc)**2 + (y - self.yc)**2 + (z - self.zc)**2) - self.radius
    

sDF() [3/3]

sdf.Sphere.sDF	(		self,
			x,
			y,
			z
	)

Definition at line 156 of file sdf.py.

    def sDF(self, x, y, z):
        dx = np.subtract(x, self.xc)
        dy = np.subtract(y, self.yc)
        dz = np.subtract(z, self.zc)
        a = (dx)**2+(dy)**2 + (dz)**2
        gap = np.sqrt(a) - self.radius
        
        return gap
    

Member Data Documentation

radius

sdf.Sphere.radius

Definition at line 154 of file sdf.py.

Xc

sdf.Sphere.Xc

Definition at line 144 of file sdf.py.

xc

sdf.Sphere.xc

Definition at line 149 of file sdf.py.

Yc

sdf.Sphere.Yc

Definition at line 145 of file sdf.py.

yc

sdf.Sphere.yc

Definition at line 150 of file sdf.py.

Zc

sdf.Sphere.Zc

Definition at line 146 of file sdf.py.

zc

sdf.Sphere.zc

Definition at line 151 of file sdf.py.

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The documentation for this class was generated from the following files:

• tutorials/adv-0_plasticity/sdf.py
• tutorials/adv-1_contact/sdf_files/sdf.py
• users_modules/adolc-plasticity/sdf.py