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

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
 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

Geometry

 csgdel Delete boundaries between subdomains pdearcl Interpolation between parametric representation and arc length 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

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.

Partial Differential Equation Toolbox Documentation 