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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Geometry

Creation and Visualization

`importGeometry`	Import geometry from STL or STEP file
`geometryFromMesh`	Create 2-D or 3-D geometry from mesh
`geometryFromEdges`	Create 2-D geometry from decomposed geometry matrix
`decsg`	Decompose constructive solid 2-D geometry into minimal regions
`multicuboid`	Create geometry formed by several cubic cells
`multicylinder`	Create geometry formed by several cylindrical cells
`multisphere`	Create geometry formed by several spherical cells
`pdegplot`	Plot PDE geometry

Modification

`addCell`	Combine two geometries by adding one inside a cell of another
`addFace`	Fill void regions in 2-D and split cells in 3-D geometry
`addVertex`	Add a vertex on a geometry boundary
`addVoid`	Create void regions inside 3-D geometry
`rotate`	Rotate geometry
`scale`	Scale geometry
`translate`	Translate geometry
`extrude`	Vertically extrude 2-D geometry or specified faces of 3-D geometry

Queries

`cellEdges`	Find edges belonging to boundaries of specified cells
`cellFaces`	Find faces belonging to specified cells
`faceEdges`	Find edges belonging to specified faces
`facesAttachedToEdges`	Find faces attached to specified edges
`nearestEdge`	Find edges nearest to specified point
`nearestFace`	Find faces nearest to specified point

PDE Modeler App

`pdecirc`	Draw circle in PDE Modeler app
`pdeellip`	Draw ellipse in PDE Modeler app
`pdepoly`	Draw polygon in PDE Modeler app
`pderect`	Draw rectangle in PDE Modeler app

Mesh

`generateMesh`	Create triangular or tetrahedral mesh
`meshQuality`	Evaluate shape quality of mesh elements
`findElements`	Find mesh elements in specified region
`findNodes`	Find mesh nodes in specified region
`area`	Area of 2-D mesh elements
`volume`	Volume of 3-D mesh elements
`pdemesh`	Plot PDE mesh
`pdeplot`	Plot solution or mesh for 2-D problem
`pdeplot3D`	Plot solution or surface mesh for 3-D problem
`pdeviz`	Create and plot PDE visualization object

Legacy Functions

Geometry

`csgdel`	Delete boundaries between subdomains
`pdearcl`	Represent arc lengths as parametrized curve
`wgeom`	Write geometry function to file

Mesh

`adaptmesh`	Create adaptive 2-D mesh and solve PDE
`initmesh`	Create initial 2-D mesh
`meshToPet`	`[p,e,t]` representation of `FEMesh` data
`jigglemesh`	(Not recommended) Jiggle internal points of triangular mesh
`refinemesh`	Refine triangular mesh

Properties

AnalyticGeometry Properties	Analytic 2-D geometry description
DiscreteGeometry Properties	Discrete 2-D or 3-D geometry description
FEMesh Properties	Mesh object
PDEVisualization Properties	PDE visualization of mesh and nodal results

Apps

PDE Modeler

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

Topics

Geometry

Geometry and Mesh Components
Learn about the components of geometries and meshes and the relationships between them within a model object.
STL File Import
Import a 2-D or 3-D geometry from an STL file.
STEP File Import
Import a 3-D geometry from a STEP file.
Geometry from Triangulated Mesh
Reconstruct a geometry from a tetrahedral mesh and from a planar multidomain mesh.
Geometry from polyshape
Reconstruct a geometry from a triangulated mesh created by the MATLAB polyshape function.
Geometry from alphaShape
Reconstruct a geometry from a triangulated surface mesh created by the MATLAB alphaShape function.
2-D Geometry Creation at Command Line
Use constructive solid geometry (CSG) modeling approach to combine basic shapes at the command line.
Parametrized Function for 2-D Geometry Creation
Create a 2-D geometry by using a parametrized function.
Cuboids, Cylinders, and Spheres
Create a 3-D geometry by stacking or nesting three basic volumes.
3-D Multidomain Geometry from 2-D Geometry
Extrude a 2-D geometry imported as an STL file into a 3-D geometry.
Multidomain Geometry Reconstructed from Mesh
Split a single-domain block geometry into two domains.
Sphere in Cube
Create a nested multidomain geometry consisting of a unit sphere and a cube.

Mesh

Mesh Data
Recommended workflow uses FEMesh objects to represent meshes.
Generate Mesh
Adjust a mesh by using additional arguments of the generateMesh function.
Find Mesh Elements and Nodes by Location
Find mesh elements and nodes by their geometric location or proximity to a particular point or node.
Assess Quality of Mesh Elements
Evaluate the shape quality of mesh elements.

Legacy Mesh

Mesh Data as [p,e,t] Triples
Legacy workflow uses [p,e,t] triples to represent meshes.
Poisson's Equation with Point Source and Adaptive Mesh Refinement
Solve a Poisson's equation with a delta-function point source on the unit disk using the adaptmesh function.