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 file into MATLAB^® by using importGeometry. The STL file format is 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.

Functions

expand all

Geometry

Creation and Visualization

`importGeometry`	Import 2-D or 3-D geometry from STL data
`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 attached to specified cells
`cellFaces`	Find faces attached to specified cells
`faceEdges`	Find edges attached 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

STL File Import
Import a 2-D or 3-D geometry from an STL 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.