meshes3d

The meshes3d module of the MatGeom library provides functions for the creation, manipulation, processing and vizualization of 3D polygonal meshes or polyhedra. Functions for the manipulation of more simple 3D shapes (lines, planes...) are provided in the geom3d module.

Representation

Meshes and Polyhedra are represented by a couple of variables {V, F}:

• V: Nv-by-3 array of vertices: [x1 y1 z1; ... ; xn yn zn];
• F: is either a NF-by-3 or NF-by-4 array containing reference for vertices of each face, or a NF-by-1 cell array, where each cell is an array containing a variable number of node indices.

For some functions, the array E of edges is needed. It consists in a NE-by-2 array containing indices of source and target vertices.

The library provides function to create basic polygonal meshes (the five platonic solids, plus few others), as well as functions to perform basic computations (surface area, normal angles, face centroids...). The 'MengerSponge' structure is an example of mesh that is not simply connected (multiple tunnels in the structure).

The drawMesh function is mainly a wrapper to the Matlab 'patch' function, allowing passing arguments more quickly.

Example

  % create a soccer ball mesh and display it
  [v, e, f] = createSoccerBall;
  drawMesh(v, f, 'faceColor', 'g', 'linewidth', 2);
  axis equal; view(3);

Function list

Creation and conversion

surfToMesh               - Convert surface grids into face-vertex mesh
cylinderMesh             - Create a 3D mesh representing a cylinder
sphereMesh               - Create a 3D mesh representing a sphere
ellipsoidMesh            - Convert a 3D ellipsoid to face-vertex mesh representation
torusMesh                - Create a 3D mesh representing a torus
minConvexHull            - Return the unique minimal convex hull of a set of 3D points

General processing on meshes

smoothMesh               - Smooth mesh by replacing each vertex by the average of its neighbors 
subdivideMesh            - Subdivides each face of the mesh
triangulateFaces         - Convert face array to an array of triangular faces 
removeMeshVertices       - Remove vertices and associated faces from a mesh
mergeCoplanarFaces       - Merge coplanar faces of a polyhedral mesh
meshFacePolygons         - Returns the set of polygons that constitutes a mesh
faceCentroids            - Compute centroids of a mesh faces
faceNormal               - Compute normal vector of faces in a 3D mesh
vertexNormal             - Compute normals to a mesh vertices

Geometric measures on meshes

meshSurfaceArea          - Surface area of a polyhedral mesh
trimeshSurfaceArea       - Surface area of a triangular mesh
meshVolume               - Volume of the space enclosed by a polygonal mesh
meshEdgeLength           - Lengths of edges of a polygonal or polyhedral mesh
meshDihedralAngles       - Dihedral at edges of a polyhedal mesh
polyhedronCentroid       - Compute the centroid of a 3D convex polyhedron
tetrahedronVolume        - Signed volume of a tetrahedron
polyhedronNormalAngle    - Compute normal angle at a vertex of a 3D polyhedron
polyhedronMeanBreadth    - Mean breadth of a convex polyhedron
trimeshMeanBreadth       - Mean breadth of a triangular mesh

Intersections and clipping

intersectLineMesh3d      - Intersection points of a 3D line with a mesh
intersectPlaneMesh       - Compute the polygons resulting from plane-mesh intersection
polyhedronSlice          - Intersect a convex polyhedron with a plane.
clipMeshVertices         - Clip vertices of a surfacic mesh and remove outer faces
clipConvexPolyhedronHP   - Clip a convex polyhedron by a plane

Utility functions

meshFace                 - Return the vertex indices of a face in a mesh
meshFaceEdges            - Computes edge indices of each face
meshFaceNumber           - Returns the number of faces in this mesh
meshEdges                - Computes array of edge vertex indices from face array
meshEdgeFaces            - Compute index of faces adjacent to each edge of a mesh
trimeshEdgeFaces         - Compute index of faces adjacent to each edge of a triangular mesh
trimMesh                 - Reduce memory footprint of a polygonal mesh
meshFaceAdjacency        - Compute adjacency list of face around each face
meshAdjacencyMatrix      - Compute adjacency matrix of a mesh from set of faces
checkMeshAdjacentFaces   - Check if adjacent faces of a mesh have similar orientation

Typical polyhedra

polyhedra                - Index of classical polyhedral meshes
createCube               - Create a 3D mesh representing the unit cube
createOctahedron         - Create a 3D mesh representing an octahedron
createCubeOctahedron     - Create a 3D mesh representing a cube-octahedron
createIcosahedron        - Create a 3D mesh representing an Icosahedron.
createDodecahedron       - Create a 3D mesh representing a dodecahedron
createTetrahedron        - Create a 3D mesh representing a tetrahedron
createRhombododecahedron - Create a 3D mesh representing a rhombododecahedron
createTetrakaidecahedron - Create a 3D mesh representing a tetrakaidecahedron

Less typical polyhedra

createSoccerBall         - Create a 3D mesh representing a soccer ball
createDurerPolyhedron    - Create a mesh representing Durer's polyhedron 
createMengerSponge       - Create a cube with an inside cross removed
steinerPolytope          - Create a steiner polytope from a set of vectors

Drawing functions

drawFaceNormals          - Draw normal vector of each face in a mesh
drawMesh                 - Draw a 3D mesh defined by vertices and faces

Reading from file

readMesh_off             - Read mesh data stord in OFF format