Mathematics > Computational Geometry

84 functions in MATLAB › Mathematics > Computational Geometry.

Elementary Polygons

`addboundary`	Adds a new polygonal boundary to a polyshape and returns the combined shape.
`boundingbox`	Smallest axis-aligned rectangle that contains a polyshape.
`centroid`	Center of mass of a polyshape, treated as a uniform plate.
`holes`	Returns the holes of a polyshape as an array of polyshape objects.
`inpolygon`	Tests which points lie inside or on the edge of a polygon.
`ishole`	Tells which boundaries of a polyshape are holes.
`isinterior`	Tests whether points lie inside a polyshape.
`issimplified`	Tests whether a polyshape is free of self-intersections and other defects.
`nearestvertex`	Index of the polyshape vertex closest to each query point.
`nsidedpoly`	Creates a regular polygon with a given number of sides, as a polyshape.
`numboundaries`	Number of boundaries of a polyshape, counting outer boundaries and holes.
`numsides`	Total number of sides (vertices) of a polyshape.
`overlaps`	Tests whether two polyshapes share any area.
`polyarea`	Area of a polygon given by its vertex coordinates.
`polybuffer`	Grows or shrinks a polyshape by a fixed distance.
`polyshape`	Creates a 2-D polygon, possibly with several regions and holes, that supports geometry queries and Boolean operations.
`rectint`	Area of intersection between axis-aligned rectangles.
`regions`	Splits a polyshape into its disconnected regions.
`rmboundary`	Removes selected boundaries from a polyshape.
`rmholes`	Removes holes from a polyshape, leaving solid regions.
`rmslivers`	Removes thin parts of a polyshape narrower than a given width.
`rotate`	Rotates a polyshape by an angle in degrees about a center point.
`scale`	Scales a polyshape by a factor, about a center point.
`sortboundaries`	Reorders the boundaries of a polyshape by a chosen criterion.
`sortregions`	Reorders the regions of a polyshape by a chosen criterion.
`subtract`	Boolean difference of two polyshapes: the first with the second cut out.
`translate`	Shifts a polyshape by a given offset in x and y.
`turningdist`	Turning-function distance between two polyshape boundaries.

Bounding Regions

`alphaShape`	Creates a bounding region around a set of 2-D or 3-D points, controlled by a radius alpha.
`alphaSpectrum`	Alpha values at which the alpha shape changes its set of triangles or tetrahedra.
`alphaTriangulation`	Triangles or tetrahedra that make up an alpha shape, with the point coordinates.
`area`	Area of a polyshape or a 2-D alpha shape (a 3-D alpha shape has volume instead).
`boundary`	Boundary of a set of 2-D or 3-D points, between the convex hull and a tight outline.
`boundaryFacets`	Boundary edges (2-D) or faces (3-D) of an alpha shape.
`convhull`	Convex hull of a set of 2-D or 3-D points.
`convhulln`	Convex hull of points in n dimensions, as facets of point indices.
`criticalAlpha`	Smallest alpha at which an alpha shape meets a connectivity criterion.
`inShape`	Tests whether points lie inside an alpha shape.
`numRegions`	Number of disjoint regions of an alpha shape.
`perimeter`	Perimeter length of a polyshape or a 2-D alpha shape.
`surfaceArea`	Surface area of a 3-D alpha shape.
`volume`	Volume enclosed by a 3-D alpha shape.

Triangulation Representation

`barycentricToCartesian`	Converts barycentric coordinates in given triangles or tetrahedra to Cartesian coordinates.
`baryToCart`	Legacy form of barycentricToCartesian for TriRep and DelaunayTri objects.
`boundaryshape`	Converts the boundary of a 2-D triangulation into a polyshape.
`cartesianToBarycentric`	Converts Cartesian points to barycentric coordinates relative to given triangles or tetrahedra.
`cartToBary`	Legacy form of cartesianToBarycentric for TriRep and DelaunayTri objects.
`circumcenter`	Circumcenters (and circumradii) of the triangles or tetrahedra in a triangulation.
`circumcenters`	Legacy form of circumcenter for TriRep and DelaunayTri objects.
`edgeAttachments`	Triangles or tetrahedra attached to given edges of a triangulation.
`edges`	All edges of a triangulation, as pairs of vertex indices.
`faceNormal`	Unit normal vector of each triangle of a triangulated surface.
`faceNormals`	Legacy form of faceNormal for TriRep and DelaunayTri objects.
`featureEdges`	Sharp edges of a triangulated surface, selected by the angle between adjacent faces.
`freeBoundary`	Boundary facets of a triangulation: edges of a 2-D mesh or faces of a 3-D one that touch only one simplex.
`incenter`	Incenters and inscribed-circle radii of the triangles or tetrahedra of a triangulation.
`incenters`	Legacy form of incenter for TriRep and DelaunayTri objects.
`isConnected`	Tests whether pairs of vertices are joined by an edge in a triangulation.
`isEdge`	Tests whether pairs of vertices form an edge of a legacy DelaunayTri or TriRep triangulation.
`nearestNeighbor`	Nearest vertex of a triangulation or alpha shape to each query point.
`pointLocation`	Finds the triangle or tetrahedron of a triangulation that contains each query point.
`stlread`	Reads a triangulated surface from an STL file.
`stlwrite`	Writes a triangulation to an STL file.
`tetramesh`	Draws a tetrahedral mesh as semi-transparent solid elements.
`triangulation`	Stores a 2-D or 3-D triangulation and answers queries about it.
`trimesh`	Plots a triangular mesh as wireframe edges.
`triplot`	Plots a 2-D triangulation as line edges.
`TriRep`	Legacy triangulation representation class, replaced by triangulation.
`trisurf`	Plots a triangular surface with shaded faces.
`vertexAttachments`	Lists the triangles or tetrahedra attached to given vertices.
`vertexNormal`	Unit normal vector at the vertices of a triangulated surface.

Delaunay Triangulation

`convexHull`	Convex hull of the points of a Delaunay triangulation, as point indices.
`delaunay`	Delaunay triangulation of 2-D or 3-D points, as a matrix of triangle or tetrahedron indices.
`delaunayn`	Delaunay triangulation of points in n dimensions.
`DelaunayTri`	Legacy class that builds and stores the Delaunay triangulation of a point set.
`delaunayTriangulation`	Creates a Delaunay triangulation object from 2-D or 3-D points.
`inOutStatus`	Flags which triangles of a constrained Delaunay triangulation lie inside the constrained region.
`isInterior`	Flags the triangles of a constrained Delaunay triangulation that lie inside the constrained region.
`voronoiDiagram`	Returns vertices and cells of the Voronoi diagram of a delaunayTriangulation.

Spatial Search

`dsearchn`	Index of the nearest point in a set, for each query point.
`tsearchn`	Finds the enclosing simplex of query points in an n-D triangulation.

Voronoi Diagram

`patch`	Draws one or more filled polygons from vertex coordinates or from faces and vertices.
`voronoi`	Computes or plots the Voronoi diagram of 2-D points.
`voronoin`	Voronoi vertices and cells for points in n dimensions.