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Geometry and Mesh

Define a geometry and discretize it using a triangular or tetrahedral mesh

Reconstruct a geometry from STL or mesh data:

  • Import an STL or STEP file into MATLAB® by using importGeometry. The STL and STEP file formats are very common and supported by most CAD software. In case of a planar STL geometry, the toolbox converts it to a 2-D geometry by mapping it to the X-Y plane.

  • Reconstruct a geometry from a mesh by using geometryFromMesh. This function works with triangulated meshes, including planar, volume, and surface triangulation that bounds a closed volume.

Create a geometry:

  • Stack or nest cubes, cylinders, or spheres to create a geometry for a 3-D problem.

  • Extrude a 2-D geometry into a 3-D geometry.

  • Use the constructive solid geometry (CSG) approach, write a geometry function, or use the polyshape function to create a geometry for a 2-D problem. The CSG approach uses a set of solid building blocks (square, rectangle, circle, ellipse, and polygon) and combines them to define complex geometries.

  • Use the PDE Modeler app to create complex 2-D geometries by drawing, overlapping, and rotating basic shapes, such as circles, polygons and so on.

Mesh a geometry by using the generateMesh function. The toolbox uses the finite element method (FEM) to solve PDEs. A PDE model stores the generated mesh as an FEMesh object in its Mesh property. For details, see Mesh Data.

For details about the components of geometries and meshes and the relationships between them, see Geometry and Mesh Components.

Functions

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Creation and Visualization

importGeometryImport geometry from STL or STEP file
geometryFromMeshCreate 2-D or 3-D geometry from mesh
geometryFromEdgesCreate 2-D geometry from decomposed geometry matrix
decsgDecompose constructive solid 2-D geometry into minimal regions
multicuboidCreate geometry formed by several cubic cells
multicylinderCreate geometry formed by several cylindrical cells
multisphereCreate geometry formed by several spherical cells
pdegplotPlot PDE geometry

Modification

addCellCombine two geometries by adding one inside a cell of another
addFaceFill void regions in 2-D and split cells in 3-D geometry
addVertexAdd a vertex on a geometry boundary
addVoidCreate void regions inside 3-D geometry
rotateRotate geometry
scaleScale geometry
translateTranslate geometry
extrudeVertically extrude 2-D geometry or specified faces of 3-D geometry

Queries

cellEdgesFind edges belonging to boundaries of specified cells
cellFacesFind faces belonging to specified cells
faceEdgesFind edges belonging to specified faces
facesAttachedToEdgesFind faces attached to specified edges
nearestEdgeFind edges nearest to specified point
nearestFaceFind faces nearest to specified point

PDE Modeler App

pdecircDraw circle in PDE Modeler app
pdeellipDraw ellipse in PDE Modeler app
pdepolyDraw polygon in PDE Modeler app
pderectDraw rectangle in PDE Modeler app
generateMeshCreate triangular or tetrahedral mesh
meshQualityEvaluate shape quality of mesh elements
findElementsFind mesh elements in specified region
findNodesFind mesh nodes in specified region
areaArea of 2-D mesh elements
volumeVolume of 3-D mesh elements
pdemeshPlot PDE mesh
pdeplotPlot solution or mesh for 2-D problem
pdeplot3DPlot solution or surface mesh for 3-D problem
pdevizCreate and plot PDE visualization object

Geometry

csgdelDelete boundaries between subdomains
pdearclRepresent arc lengths as parametrized curve
wgeomWrite geometry function to file

Mesh

adaptmeshCreate adaptive 2-D mesh and solve PDE
initmeshCreate initial 2-D mesh
meshToPet[p,e,t] representation of FEMesh data
jigglemesh(Not recommended) Jiggle internal points of triangular mesh
refinemeshRefine triangular mesh

Properties

AnalyticGeometry PropertiesAnalytic 2-D geometry description
DiscreteGeometry PropertiesDiscrete 2-D or 3-D geometry description
FEMesh PropertiesMesh object
PDEVisualization PropertiesPDE visualization of mesh and nodal results

Apps

PDE ModelerCreate complex 2-D geometries by drawing, overlapping, and rotating basic shapes

Topics

Geometry

Mesh

Legacy Mesh