# Geometry and 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

## 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.