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<h1>Defining Hypotheses and Algorithms</h1>

<h3>Defining 1D Hypotheses</h3>

<p class="whs1"><a name=bookmark>1D Arithmetic</a></p>

<p>&nbsp;</p>

<p class="whs2"><span style="font-family: 'Lucida Console', monospace;">import 
 geompy</span></p>

<p class="whs2">import smesh</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># create a box</p>

<p class="whs2">box = geompy.MakeBoxDXDYDZ(10., 
 10., 10.)</p>

<p class="whs2">geompy.addToStudy(box, 
 &quot;Box&quot;)</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># create a hexahedral 
 mesh on the box</p>

<p class="whs2">hexa = smesh.Mesh(box, 
 &quot;Box : hexahedrical mesh&quot;)</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># create a Regular 1D 
 algorithm for edges</p>

<p class="whs2">algo1D = hexa.Segment()</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># define &quot;Arithmetic1D&quot; 
 hypothesis to cut all edges in several segments with increasing arithmetic 
 length </p>

<p class="whs2">algo1D.Arithmetic1D(1, 
 4)</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># create a quadrangle 
 2D algorithm for faces</p>

<p class="whs2">hexa.Quadrangle()</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># create a hexahedron 
 3D algorithm for solids</p>

<p class="whs2">hexa.Hexahedron()</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># compute the mesh</p>

<p class="whs2">hexa.Compute() </p>

<p class="whs2">&nbsp;</p>

<h4><a name=bookmark9>Deflection 1D and Number of Segments</a></h4>

<p class="whs2"><span style="font-family: 'Lucida Console', monospace;">import 
 geompy</span></p>

<p class="whs2">import smesh</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># create a face from 
 arc and straight segment</p>

<p class="whs2">px = geompy.MakeVertex(100., 
 0. &nbsp;, 0. 
 &nbsp;)</p>

<p class="whs2">py = geompy.MakeVertex(0. 
 &nbsp;, 100., 
 0. &nbsp;)</p>

<p class="whs2">pz = geompy.MakeVertex(0. 
 &nbsp;, 0. &nbsp;, 
 100.)</p>

<p class="whs2">&nbsp;</p>

<p class="whs2">exy = geompy.MakeEdge(px, 
 py)</p>

<p class="whs2">arc = geompy.MakeArc(py, 
 pz, px)</p>

<p class="whs2">&nbsp;</p>

<p class="whs2">wire = geompy.MakeWire([exy, 
 arc])</p>

<p class="whs2">&nbsp;</p>

<p class="whs2">isPlanarFace = 1</p>

<p class="whs2">face1 = geompy.MakeFace(wire, 
 isPlanarFace)</p>

<p class="whs2">geompy.addToStudy(face1,&quot;Face1&quot;)</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># get edges from the 
 face</p>

<p class="whs2">e_straight,e_arc = 
 geompy.SubShapeAll(face1, geompy.ShapeType[&quot;EDGE&quot;])</p>

<p class="whs2">geompy.addToStudyInFather(face1, 
 e_arc, &quot;Arc Edge&quot;)</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># create hexahedral mesh</p>

<p class="whs2">hexa = smesh.Mesh(face1, 
 &quot;Face : triangle mesh&quot;)</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># define &quot;NumberOfSegments&quot; 
 hypothesis to cut a straight edge in a fixed number of segments</p>

<p class="whs2">algo1D = hexa.Segment()</p>

<p class="whs2">algo1D.NumberOfSegments(6)</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># define &quot;MaxElementArea&quot; 
 hypothesis</p>

<p class="whs2">algo2D = hexa.Triangle()</p>

<p class="whs2">algo2D.MaxElementArea(70.0)</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># define a local &quot;Deflection1D&quot; 
 hypothesis on the arc</p>

<p class="whs2">algo_local = hexa.Segment(e_arc)</p>

<p class="whs2">algo_local.Deflection1D(1.0)</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># compute the mesh</p>

<p class="whs2">hexa.Compute() </p>

<h4><a name=bookmark2>Start and End Length</a></h4>

<p class="whs2"><span style="font-family: 'Lucida Console', monospace;">from 
 geompy import *</span></p>

<p class="whs2">import smesh</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># create a box</p>

<p class="whs2">box = MakeBoxDXDYDZ(10., 
 10., 10.)</p>

<p class="whs2">addToStudy(box, &quot;Box&quot;)</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># get one edge of the 
 box to put local hypothesis on</p>

<p class="whs2">p5 = MakeVertex(5., 
 0., 0.)</p>

<p class="whs2">EdgeX = GetEdgeNearPoint(box, 
 p5)</p>

<p class="whs2">addToStudyInFather(box, 
 EdgeX, &quot;Edge [0,0,0 - 10,0,0]&quot;)</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># create a hexahedral 
 mesh on the box</p>

<p class="whs2">hexa = smesh.Mesh(box, 
 &quot;Box : hexahedrical mesh&quot;)</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># set algorithms</p>

<p class="whs2">algo1D = hexa.Segment()</p>

<p class="whs2">hexa.Quadrangle()</p>

<p class="whs2">hexa.Hexahedron()</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># define &quot;NumberOfSegments&quot; 
 hypothesis to cut an edge in a fixed number of segments</p>

<p class="whs2">algo1D.NumberOfSegments(4)</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># create a local hypothesis</p>

<p class="whs2">algo_local = hexa.Segment(EdgeX)</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># define &quot;StartEndLength&quot; 
 hypothesis to cut an edge in several segments with increasing geometric 
 length</p>

<p class="whs2">algo_local.StartEndLength(1, 
 6)</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># define &quot;Propagation&quot; 
 hypothesis that propagates all other hypothesis</p>

<p class="whs3"># on all edges on the 
 opposite side in case of quadrangular faces</p>

<p class="whs2">algo_local.Propagation()</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># compute the mesh</p>

<p class="whs2">hexa.Compute() </p>

<h4><a name=bookmark3>Average Length</a></h4>

<p class="whs2"><span style="font-family: 'Lucida Console', monospace;">from 
 geompy import *</span></p>

<p class="whs2">import smesh</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># create a box</p>

<p class="whs2">box = MakeBoxDXDYDZ(10., 
 10., 10.)</p>

<p class="whs2">addToStudy(box, &quot;Box&quot;)</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># get one edge of the 
 box to put local hypothesis on</p>

<p class="whs2">p5 = MakeVertex(5., 
 0., 0.)</p>

<p class="whs2">EdgeX = GetEdgeNearPoint(box, 
 p5)</p>

<p class="whs2">addToStudyInFather(box, 
 EdgeX, &quot;Edge [0,0,0 - 10,0,0]&quot;)</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># create a hexahedral 
 mesh on the box</p>

<p class="whs2">hexa = smesh.Mesh(box, 
 &quot;Box : hexahedrical mesh&quot;)</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># set algorithms</p>

<p class="whs2">algo1D = hexa.Segment()</p>

<p class="whs2">hexa.Quadrangle()</p>

<p class="whs2">hexa.Hexahedron()</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># define &quot;NumberOfSegments&quot; 
 hypothesis to cut all edges in a fixed number of segments</p>

<p class="whs2">algo1D.NumberOfSegments(4)</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># create a sub-mesh</p>

<p class="whs2">algo_local = hexa.Segment(EdgeX)</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># define &quot;LocalLength&quot; 
 hypothesis to cut an edge in several segments with the same length</p>

<p class="whs2">algo_local.LocalLength(2.)</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># define &quot;Propagation&quot; 
 hypothesis that propagates all other hypothesis</p>

<p class="whs3"># on all edges on the 
 opposite side in case of quadrangular faces</p>

<p class="whs2">algo_local.Propagation()</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># compute the mesh</p>

<p class="whs2">hexa.Compute() </p>

<h3>Defining 2D and 3D hypotheses</h3>

<h4><a name=bookmark4>Maximum Element Area</a></h4>

<p class="whs4"><span style="font-family: 'Lucida Console', monospace;">import 
 geompy</span></p>

<p class="whs4">import smesh</p>

<p class="whs4">import salome </p>

<p class="whs4">&nbsp;</p>

<p class="whs5"># create a face</p>

<p class="whs4">px &nbsp;&nbsp;= 
 geompy.MakeVertex(100., 0. &nbsp;, 
 0. &nbsp;)</p>

<p class="whs4">py &nbsp;&nbsp;= 
 geompy.MakeVertex(0. &nbsp;, 
 100., 0. &nbsp;)</p>

<p class="whs4">pz &nbsp;&nbsp;= 
 geompy.MakeVertex(0. &nbsp;, 
 0. &nbsp;, 100.)</p>

<p class="whs4">&nbsp;</p>

<p class="whs4">vxy = geompy.MakeVector(px, 
 py)</p>

<p class="whs4">arc = geompy.MakeArc(py, 
 pz, px)</p>

<p class="whs4">wire = geompy.MakeWire([vxy, 
 arc])</p>

<p class="whs4">&nbsp;</p>

<p class="whs4">isPlanarFace = 1</p>

<p class="whs4">face = geompy.MakeFace(wire, 
 isPlanarFace)</p>

<p class="whs4">&nbsp;</p>

<p class="whs5"># add the face in the 
 study</p>

<p class="whs4">id_face = geompy.addToStudy(face, 
 &quot;Face to be meshed&quot;)</p>

<p class="whs4">&nbsp;</p>

<p class="whs5"># create a mesh</p>

<p class="whs4">tria_mesh = smesh.Mesh(face, 
 &quot;Face : triangulation&quot;)</p>

<p class="whs4">&nbsp;</p>

<p class="whs5"># define 1D meshing:</p>

<p class="whs4">algo = tria_mesh.Segment()</p>

<p class="whs4">algo.NumberOfSegments(20)</p>

<p class="whs4">&nbsp;</p>

<p class="whs5"># define 2D meshing:</p>

<p class="whs5">&nbsp;</p>

<p class="whs5"># assign triangulation 
 algorithm</p>

<p class="whs4">algo = tria_mesh.Triangle()</p>

<p class="whs4">&nbsp;</p>

<p class="whs5"># apply &quot;Max Element 
 Area&quot; hypothesis to each triangle</p>

<p class="whs4">algo.MaxElementArea(100)</p>

<p class="whs4">&nbsp;</p>

<p class="whs5"># compute the mesh</p>

<p class="whs4">tria_mesh.Compute() 
 &nbsp;</p>

<p class="whs4">&nbsp;</p>

<h4><a name=bookmark5>Maximum Element Volume</a></h4>

<p class="whs4"><span style="font-family: 'Lucida Console', monospace;">import 
 geompy</span></p>

<p class="whs4">import smesh</p>

<p class="whs4">&nbsp;</p>

<p class="whs5"># create a cylinder</p>

<p class="whs4">cyl = geompy.MakeCylinderRH(30., 
 50.)</p>

<p class="whs4">geompy.addToStudy(cyl, 
 &quot;cyl&quot;)</p>

<p class="whs4">&nbsp;</p>

<p class="whs5"># create a mesh on 
 the cylinder</p>

<p class="whs4">tetra = smesh.Mesh(cyl, 
 &quot;Cylinder : tetrahedrical mesh&quot;)</p>

<p class="whs4">&nbsp;</p>

<p class="whs5"># assign algorithms</p>

<p class="whs4">algo1D = tetra.Segment()</p>

<p class="whs4">algo2D = tetra.Triangle()</p>

<p class="whs4">algo3D = tetra.Tetrahedron(smesh.NETGEN)</p>

<p class="whs4">&nbsp;</p>

<p class="whs5"># assign 1D and 2D 
 hypotheses</p>

<p class="whs4">algo1D.NumberOfSegments(7)</p>

<p class="whs4">algo2D.MaxElementArea(150.)</p>

<p class="whs4">&nbsp;</p>

<p class="whs5"># assign Max Element 
 Volume hypothesis</p>

<p class="whs4">algo3D.MaxElementVolume(200.)</p>

<p class="whs4">&nbsp;</p>

<p class="whs5"># compute the mesh</p>

<p class="whs4">ret = tetra.Compute()</p>

<p class="whs4">if ret == 0:</p>

<p class="whs4">&nbsp;&nbsp;&nbsp;&nbsp;print 
 &quot;probleme when computing the mesh&quot;</p>

<p class="whs4">else:</p>

<p class="whs4">&nbsp;&nbsp;&nbsp;&nbsp;print 
 &quot;Computation succeded&quot; </p>

<h4><a name=bookmark6>Length from Edges</a></h4>

<p class="whs2"><span style="font-family: 'Lucida Console', monospace;">import 
 geompy</span></p>

<p class="whs2">import smesh</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># create sketchers</p>

<p class="whs2">sketcher1 = geompy.MakeSketcher(&quot;Sketcher:F 
 0 0:TT 70 0:TT 70 70:TT 0 70:WW&quot;)</p>

<p class="whs2">sketcher2 = geompy.MakeSketcher(&quot;Sketcher:F 
 20 20:TT 50 20:TT 50 50:TT 20 50:WW&quot;)</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># create a face from 
 two wires</p>

<p class="whs2">isPlanarFace = 1</p>

<p class="whs2">face1 = geompy.MakeFaces([sketcher1, 
 sketcher2], isPlanarFace)</p>

<p class="whs2">geompy.addToStudy(face1, 
 &quot;Face1&quot;)</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># create a mesh</p>

<p class="whs2">tria = smesh.Mesh(face1, 
 &quot;Face : triangle 2D mesh&quot;)</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># Define 1D meshing</p>

<p class="whs2">algo1D = tria.Segment()</p>

<p class="whs2">algo1D.NumberOfSegments(2)</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># create and assign the 
 algorithm for 2D meshing with triangles</p>

<p class="whs2">algo2D = tria.Triangle()</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># create and assign &quot;LengthFromEdges&quot; 
 hypothesis to build triangles<span style="font-family: 'Times New Roman', serif;"> 
 based on the length of the edges taken from the wire</span></p>

<p class="whs2">algo2D.LengthFromEdges()</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># compute the mesh</p>

<p class="whs2">tria.Compute() </p>

<p class="whs2">&nbsp;</p>

<h3>Defining Additional Hypotheses</h3>

<h4><a name=bookmark7>Propagation</a></h4>

<p class="whs2">from geompy import 
 *</p>

<p class="whs2">import smesh</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># create a box</p>

<p class="whs2">box = MakeBoxDXDYDZ(10., 
 10., 10.)</p>

<p class="whs2">addToStudy(box, &quot;Box&quot;)</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># get one edge of the 
 box to put local hypothesis on</p>

<p class="whs2">p5 = MakeVertex(5., 
 0., 0.)</p>

<p class="whs2">EdgeX = GetEdgeNearPoint(box, 
 p5)</p>

<p class="whs2">addToStudyInFather(box, 
 EdgeX, &quot;Edge [0,0,0 - 10,0,0]&quot;)</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># create a hexahedral 
 mesh on the box</p>

<p class="whs2">hexa = smesh.Mesh(box, 
 &quot;Box : hexahedrical mesh&quot;)</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># set global algorithms 
 and hypotheses</p>

<p class="whs2">algo1D = hexa.Segment()</p>

<p class="whs2">hexa.Quadrangle()</p>

<p class="whs2">hexa.Hexahedron()</p>

<p class="whs2">algo1D.NumberOfSegments(4)</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># create a sub-mesh with 
 local 1D hypothesis and propagation</p>

<p class="whs2">algo_local = hexa.Segment(EdgeX)</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># define &quot;Arithmetic1D&quot; 
 hypothesis to cut an edge in several segments with increasing length</p>

<p class="whs2">algo_local.Arithmetic1D(1, 
 4)</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># define &quot;Propagation&quot; 
 hypothesis that propagates all other 1D hypotheses</p>

<p class="whs3"># from all edges on the 
 opposite side of a face in case of quadrangular faces</p>

<p class="whs2">algo_local.Propagation()</p>

<p class="whs2">&nbsp;</p>

<p class="whs3"># compute the mesh</p>

<p><span style="font-family: 'Lucida Console', monospace;">hexa.Compute()</span> 
 </p>

<h3><a name=bookmark8>Defining Meshing Algorithms</a></h3>

<p class="whs4">import geompy</p>

<p class="whs4">import smesh</p>

<p class="whs6">&nbsp;</p>

<p class="whs6"># create a box</p>

<p class="whs4">box = geompy.MakeBoxDXDYDZ(10., 
 10., 10.)</p>

<p class="whs4">geompy.addToStudy(box, 
 &quot;Box&quot;)</p>

<p class="whs4">&nbsp;</p>

<p class="whs6"># 1. Create a hexahedral 
 mesh on the box</p>

<p class="whs4">hexa = smesh.Mesh(box, 
 &quot;Box : hexahedrical mesh&quot;)</p>

<p class="whs6">&nbsp;</p>

<p class="whs6"># create a Regular 1D algorithm 
 for edges</p>

<p class="whs4">algo1D = hexa.Segment()</p>

<p class="whs6">&nbsp;</p>

<p class="whs6"># create a quadrangle 2D 
 algorithm for faces</p>

<p class="whs4">algo2D = hexa.Quadrangle()</p>

<p class="whs6">&nbsp;</p>

<p class="whs6"># create a hexahedron 3D 
 algorithm for solids</p>

<p class="whs4">algo3D = hexa.Hexahedron()</p>

<p class="whs6">&nbsp;</p>

<p class="whs6"># define hypotheses</p>

<p class="whs4">algo1D.Arithmetic1D(1, 
 4)</p>

<p class="whs6">&nbsp;</p>

<p class="whs6"># compute the mesh</p>

<p class="whs4">hexa.Compute()</p>

<p class="whs6">&nbsp;</p>

<p class="whs6"># 2. Create a tetrahedral 
 mesh on the box</p>

<p class="whs4">tetra = smesh.Mesh(box, 
 &quot;Box : tetrahedrical mesh&quot;)</p>

<p class="whs6">&nbsp;</p>

<p class="whs6"># create a Regular 1D algorithm 
 for edges</p>

<p class="whs4">algo1D = tetra.Segment()</p>

<p class="whs6">&nbsp;</p>

<p class="whs6"># create a Mefisto 2D algorithm 
 for faces</p>

<p class="whs4">algo2D = tetra.Triangle()</p>

<p class="whs6">&nbsp;</p>

<p class="whs6"># create a Netgen 3D algorithm 
 for solids</p>

<p class="whs4">algo3D = tetra.Tetrahedron(smesh.NETGEN)</p>

<p class="whs6">&nbsp;</p>

<p class="whs6"># define hypotheses</p>

<p class="whs4">algo1D.Arithmetic1D(1, 
 4)</p>

<p class="whs4">algo2D.LengthFromEdges()</p>

<p class="whs6">&nbsp;</p>

<p class="whs6"># compute the mesh</p>

<p class="whs4">tetra.Compute()</p>

<p class="whs6">&nbsp;</p>

<p class="whs6"># 3. Create a tetrahedral 
 mesh on the box with NETGEN_2D3D algorithm</p>

<p class="whs4">tetraN = smesh.Mesh(box, 
 &quot;Box : tetrahedrical mesh by NETGEN_2D3D&quot;)</p>

<p class="whs6">&nbsp;</p>

<p class="whs6"># create a Netgen_2D3D 
 algorithm for solids</p>

<p class="whs4">algo3D = tetraN.Tetrahedron(smesh.FULL_NETGEN) 
 </p>

<p class="whs6">&nbsp;</p>

<p class="whs6"># define hypotheses</p>

<p class="whs4">n23_params = algo3D.Parameters()</p>

<p class="whs6">&nbsp;</p>

<p class="whs6"># compute the mesh</p>

<p class="whs4">tetraN.Compute() 
 </p>

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