sdf.Sphere Class Reference

Collaboration diagram for sdf.Sphere:

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

Public Attributes
	Xc = Xc
	Yc = Yc
	Zc = Zc
	xc = Xc
	yc = Yc
	zc = Zc
int	radius = diameter/2

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() [1/4]

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() [2/4]

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() [3/4]

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() [4/4]

sdf.Sphere.gradSdf	(		xc,
			yc,
			zc,
			x,
			y,
			z )

Definition at line 25 of file sdf.py.

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

hessSdf() [1/4]

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() [2/4]

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() [3/4]

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() [4/4]

sdf.Sphere.hessSdf	(		xc,
			yc,
			zc,
			x,
			y,
			z )

Definition at line 29 of file sdf.py.

    def hessSdf(xc, yc, zc, x, y, z):
        x, y, z = x-xc, y-yc, z-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))])
 
 

sDF() [1/4]

sdf.Sphere.sDF	(		r,
			xc,
			yc,
			zc,
			x,
			y,
			z )

Definition at line 22 of file sdf.py.

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

sDF() [2/4]

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() [3/4]

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() [4/4]

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

int sdf.Sphere.radius = diameter/2

Definition at line 154 of file sdf.py.

Xc

sdf.Sphere.Xc = Xc

Definition at line 144 of file sdf.py.

xc

sdf.Sphere.xc = Xc

Definition at line 149 of file sdf.py.

Yc

sdf.Sphere.Yc = Yc

Definition at line 145 of file sdf.py.

yc

sdf.Sphere.yc = Yc

Definition at line 150 of file sdf.py.

Zc

sdf.Sphere.Zc = Zc

Definition at line 146 of file sdf.py.

zc

sdf.Sphere.zc = Zc

Definition at line 151 of file sdf.py.

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

• /home/lk58p/mofem_install/vanilla_dev_release/mofem-cephas/jupyter/skel/ukmmn_summer_school_2023/sdf.py
• tutorials/adv-0/sdf.py
• tutorials/adv-1/sdf_files/sdf.py
• users_modules/adolc-plasticity/sdf.py