renamed TPMS and added more from additional references
This commit is contained in:
Philip Eisenlohr
parent
54e4943353
commit
a59e64a8e4
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@ -120,6 +120,29 @@ class Geom:
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return np.unique(self.material).size
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@staticmethod
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def load(fname):
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"""
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Read a VTK rectilinear grid.
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Parameters
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----------
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fname : str or or pathlib.Path
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Geometry file to read.
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Valid extension is .vtr, it will be appended if not given.
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"""
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v = VTK.load(fname if str(fname).endswith('.vtr') else str(fname)+'.vtr')
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comments = v.get_comments()
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grid = np.array(v.vtk_data.GetDimensions())-1
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bbox = np.array(v.vtk_data.GetBounds()).reshape(3,2).T
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return Geom(material = v.get('material').reshape(grid,order='F'),
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size = bbox[1] - bbox[0],
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origin = bbox[0],
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comments=comments)
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@staticmethod
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def load_ASCII(fname):
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"""
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@ -184,29 +207,6 @@ class Geom:
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return Geom(material.reshape(grid,order='F'),size,origin,comments)
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@staticmethod
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def load(fname):
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"""
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Read a VTK rectilinear grid.
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Parameters
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----------
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fname : str or or pathlib.Path
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Geometry file to read.
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Valid extension is .vtr, it will be appended if not given.
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"""
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v = VTK.load(fname if str(fname).endswith('.vtr') else str(fname)+'.vtr')
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comments = v.get_comments()
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grid = np.array(v.vtk_data.GetDimensions())-1
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bbox = np.array(v.vtk_data.GetBounds()).reshape(3,2).T
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return Geom(material = v.get('material').reshape(grid,order='F'),
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size = bbox[1] - bbox[0],
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origin = bbox[0],
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comments=comments)
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@staticmethod
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def _find_closest_seed(seeds, weights, point):
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return np.argmin(np.sum((np.broadcast_to(point,(len(seeds),3))-seeds)**2,axis=1) - weights)
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@ -292,10 +292,52 @@ class Geom:
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)
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_minimal_surface = \
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{'Schwarz P': lambda x,y,z: np.cos(x) + np.cos(y) + np.cos(z),
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'Double Primitive': lambda x,y,z: ( 0.5 * (np.cos(x)*np.cos(y) + np.cos(y)*np.cos(z) + np.cos(z)*np.cos(x))
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+ 0.2 * (np.cos(2*x) + np.cos(2*y) + np.cos(2*z)) ),
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'Schwarz D': lambda x,y,z: ( np.sin(x)*np.sin(y)*np.sin(z)
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+ np.sin(x)*np.cos(y)*np.cos(z)
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+ np.cos(x)*np.cos(y)*np.sin(z)
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+ np.cos(x)*np.sin(y)*np.cos(z) ),
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'Complementary D': lambda x,y,z: ( np.cos(3*x+y)*np.cos(z) - np.sin(3*x-y)*np.sin(z) + np.cos(x+3*y)*np.cos(z)
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+ np.sin(x-3*y)*np.sin(z) + np.cos(x-y)*np.cos(3*z) - np.sin(x+y)*np.sin(3*z) ),
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'Double Diamond': lambda x,y,z: 0.5 * (np.sin(x)*np.sin(y)
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+ np.sin(y)*np.sin(z)
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+ np.sin(z)*np.sin(x)
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+ np.cos(x) * np.cos(y) * np.cos(z) ),
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'Dprime': lambda x,y,z: 0.5 * ( np.cos(x)*np.cos(y)*np.cos(z)
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+ np.cos(x)*np.sin(y)*np.sin(z)
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+ np.sin(x)*np.cos(y)*np.sin(z)
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+ np.sin(x)*np.sin(y)*np.cos(z)
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- np.sin(2*x)*np.sin(2*y)
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- np.sin(2*y)*np.sin(2*z)
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- np.sin(2*z)*np.sin(2*x) ) - 0.2,
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'Gyroid': lambda x,y,z: np.cos(x)*np.sin(y) + np.cos(y)*np.sin(z) + np.cos(z)*np.sin(x),
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'Gprime': lambda x,y,z : ( np.sin(2*x)*np.cos(y)*np.sin(z)
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+ np.sin(2*y)*np.cos(z)*np.sin(x)
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+ np.sin(2*z)*np.cos(x)*np.sin(y) ) + 0.32,
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'Karcher K': lambda x,y,z: ( 0.3 * ( np.cos(x) + np.cos(y) + np.cos(z)
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+ np.cos(x)*np.cos(y) + np.cos(y)*np.cos(z) + np.cos(z)*np.cos(x) )
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- 0.4 * ( np.cos(2*x) + np.cos(2*y) + np.cos(2*z) ) ) + 0.2,
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'Lidinoid': lambda x,y,z: 0.5 * ( np.sin(2*x)*np.cos(y)*np.sin(z)
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+ np.sin(2*y)*np.cos(z)*np.sin(x)
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+ np.sin(2*z)*np.cos(x)*np.sin(y)
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- np.cos(2*x)*np.cos(2*y)
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- np.cos(2*y)*np.cos(2*z)
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- np.cos(2*z)*np.cos(2*x) ) + 0.15,
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'Neovius': lambda x,y,z: ( 3 * (np.cos(x)+np.cos(y)+np.cos(z))
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+ 4 * np.cos(x)*np.cos(y)*np.cos(z) ),
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'Fisher-Koch S': lambda x,y,z: ( np.cos(2*x)*np.sin( y)*np.cos( z)
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+ np.cos( x)*np.cos(2*y)*np.sin( z)
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+ np.sin( x)*np.cos( y)*np.cos(2*z) ),
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}
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@staticmethod
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def from_minimal_surface(grid,size,surface,threshold=0.0,periods=1,materials=(1,2)):
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"""
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Generate geometry from definition of minimal surface.
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Generate geometry from definition of triply periodic minimal surface.
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Parameters
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----------
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@ -303,7 +345,7 @@ class Geom:
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Number of grid points in x,y,z direction.
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size : list or numpy.ndarray of shape (3)
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Physical size of the geometry in meter.
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surface : {'primitive', 'gyroid', 'diamond'}
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surface : {'primitive', 'gyroid', 'lidinoid', 'neovius', 'diamond', 'doublediamond'}
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Type of the minimal surface.
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threshold : float, optional.
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Threshold of the minimal surface. Defaults to 0.0.
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@ -312,21 +354,53 @@ class Geom:
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materials : (int, int), optional
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Material IDs. Defaults to (1,2).
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References
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----------
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Surface curvature in triply-periodic minimal surface architectures as
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a distinct design parameter in preparing advanced tissue engineering scaffolds
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Sébastien B G Blanquer, Maike Werner, Markus Hannula, Shahriar Sharifi,
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Guillaume P R Lajoinie, David Eglin, Jari Hyttinen, André A Poot, and Dirk W Grijpma
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10.1088/1758-5090/aa6553
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Triply Periodic Bicontinuous Cubic Microdomain Morphologies by Symmetries
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Meinhard Wohlgemuth, Nataliya Yufa, James Hoffman, and Edwin L. Thomas
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10.1021/ma0019499
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Minisurf – A minimal surface generator for finite element modeling and additive manufacturing
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Meng-Ting Hsieh, Lorenzo Valdevit
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10.1016/j.simpa.2020.100026
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"""
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s = {'primitive': lambda x,y,z: np.cos(x)+np.cos(y)+np.cos(z),
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'gyroid': lambda x,y,z: np.sin(x)*np.cos(y)+np.sin(y)*np.cos(z)+np.cos(x)*np.sin(z),
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'diamond': lambda x,y,z: np.cos(x-y)*np.cos(z)+np.sin(x+y)*np.sin(z),
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}
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x,y,z = np.meshgrid(periods*2.0*np.pi*(np.arange(grid[0])+0.5)/grid[0],
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periods*2.0*np.pi*(np.arange(grid[1])+0.5)/grid[1],
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periods*2.0*np.pi*(np.arange(grid[2])+0.5)/grid[2],
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indexing='ij',sparse=True)
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return Geom(material = np.where(threshold < s[surface](x,y,z),materials[1],materials[0]),
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return Geom(material = np.where(threshold < Geom._minimal_surface[surface](x,y,z),materials[1],materials[0]),
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size = size,
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comments = util.execution_stamp('Geom','from_minimal_surface'),
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)
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def save(self,fname,compress=True):
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"""
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Generates vtk rectilinear grid.
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Parameters
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----------
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fname : str, optional
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Filename to write. If no file is given, a string is returned.
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Valid extension is .vtr, it will be appended if not given.
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compress : bool, optional
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Compress with zlib algorithm. Defaults to True.
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"""
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v = VTK.from_rectilinearGrid(self.grid,self.size,self.origin)
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v.add(self.material.flatten(order='F'),'material')
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v.add_comments(self.comments)
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v.save(fname if str(fname).endswith('.vtr') else str(fname)+'.vtr',parallel=False,compress=compress)
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def save_ASCII(self,fname,compress=None):
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"""
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Writes a geom file.
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@ -399,26 +473,6 @@ class Geom:
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f.write(f'{reps} of {former}\n')
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def save(self,fname,compress=True):
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"""
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Generates vtk rectilinear grid.
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Parameters
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----------
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fname : str, optional
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Filename to write. If no file is given, a string is returned.
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Valid extension is .vtr, it will be appended if not given.
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compress : bool, optional
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Compress with zlib algorithm. Defaults to True.
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"""
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v = VTK.from_rectilinearGrid(self.grid,self.size,self.origin)
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v.add(self.material.flatten(order='F'),'material')
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v.add_comments(self.comments)
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v.save(fname if str(fname).endswith('.vtr') else str(fname)+'.vtr',parallel=False,compress=compress)
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def show(self):
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"""Show on screen."""
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v = VTK.from_rectilinearGrid(self.grid,self.size,self.origin)
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@ -362,7 +362,19 @@ class TestGeom:
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assert np.all(geom.material == material)
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@pytest.mark.parametrize('surface',['primitive','gyroid','diamond'])
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@pytest.mark.parametrize('surface',['Schwarz P',
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'Double Primitive',
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'Schwarz D',
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'Complementary D',
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'Double Diamond',
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'Dprime',
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'Gyroid',
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'Gprime',
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'Karcher K',
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'Lidinoid',
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'Neovius',
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'Fisher-Koch S',
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])
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def test_minimal_surface_basic_properties(self,surface):
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grid = np.random.randint(60,100,3)
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size = np.ones(3)+np.random.rand(3)
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@ -373,8 +385,20 @@ class TestGeom:
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assert geom.material.max() == materials.max() and geom.material.min() == materials.min() \
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and (geom.size == size).all() and (geom.grid == grid).all()
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@pytest.mark.parametrize('surface',['primitive','gyroid','diamond'])
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def test_minimal_surface_volume(self,surface):
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grid = np.ones(3,dtype='i')*64
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geom = Geom.from_minimal_surface(grid,np.ones(3),surface)
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assert np.isclose(np.count_nonzero(geom.material==1)/np.prod(geom.grid),.5)
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@pytest.mark.parametrize('surface,threshold',[('Schwarz P',0),
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('Double Primitive',-1./6.),
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('Schwarz D',0),
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('Complementary D',0),
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('Double Diamond',-0.133),
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('Dprime',-0.0395),
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('Gyroid',0),
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('Gprime',0.22913),
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('Karcher K',0.17045),
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('Lidinoid',0.14455),
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('Neovius',0),
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('Fisher-Koch S',0),
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])
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def test_minimal_surface_volume(self,surface,threshold):
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grid = np.ones(3,dtype=int)*64
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geom = Geom.from_minimal_surface(grid,np.ones(3),surface,threshold)
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assert np.isclose(np.count_nonzero(geom.material==1)/np.prod(geom.grid),.5,rtol=1e-3)
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