Most efficient way of looking up values in an array.

triangulation Triangulation in 2-D or 3-D triangulation supports topological and geometric queries for triangulations in 2D and 3D space. For example, you can query triangles attached to a vertex, triangle neighbor information, circumcenters, etc. You can create a triangulation directly using existing triangulation data in matrix format. Alternatively, you can create a delaunayTriangulation, which provides access to the triangulation functions. TR = triangulation(TRI, X, Y) creates a 2D triangulation from the triangulation connectivity matrix TRI and the points (X, Y). TRI is an m-by-3 matrix where m is the number of triangles. Each row of TRI is a triangle defined by vertex IDs - the row numbers of the points (X, Y). The point coordinates (X, Y) are column vectors representing the points in the triangulation. TR = triangulation(TRI, X, Y, Z) creates a 3D triangulation from the triangulation connectivity matrix TRI and the points (X, Y, Z). TRI is an m-by-3 or m-by-4 matrix that represents m triangles or tetrahedra that have 3 or 4 vertices respectively. Each row of TRI is a triangle or tetrahedron defined by vertex IDs - the row numbers of the points (X, Y, Z). The point coordinates (X, Y, Z) are column vectors representing the points in the triangulation. TR = triangulation(TRI, P) creates a triangulation from the triangulation connectivity matrix TRI and the points P. TRI is an m-by-3 or m-by-4 matrix that represents m triangles or tetrahedra that have 3 or 4 vertices respectively. Each row of TRI is a triangle or tetrahedron defined by vertex IDs - the row numbers of the points P. P is a mpts-by-ndim matrix where mpts is the number of points and ndim is the number of dimensions, 2 <= ndim <= 3. Example 1: % Load a 2D triangulation in matrix format and use the triangulation % to query the free boundary edges. load trimesh2d % This loads triangulation tri and vertex coordinates x, y trep = triangulation(tri, x,y); fe = freeBoundary(trep)'; triplot(trep); % Add the free edges in red hold on; plot(x(fe), y(fe), 'r','LineWidth',2); hold off; axis([-50 350 -50 350]); axis equal; Example 2: % Load a 3D tetrahedral triangulation in matrix format and use the % triangulation to compute the free boundary. load tetmesh % This loads triangulation tet and vertex coordinates X trep = triangulation(tet, X); [tri, Xb] = freeBoundary(trep); %Plot the surface mesh trisurf(tri, Xb(:,1), Xb(:,2), Xb(:,3), 'FaceColor', 'cyan', 'FaceAlpha', 0.8); Example 3: % Direct query of a 3D Delaunay triangulation created using % delaunayTriangulation. Compute the free boundary as in Example 2 Points = rand(50,3); dt = delaunayTriangulation(Points); [tri, Xb] = freeBoundary(dt); %Plot the surface mesh trisurf(tri, Xb(:,1), Xb(:,2), Xb(:,3), 'FaceColor', 'cyan','FaceAlpha', 0.8); triangulation methods: barycentricToCartesian - Converts the coordinates of a point from Barycentric to Cartesian cartesianToBarycentric - Converts the coordinates of a point from Cartesian to Barycentric circumcenter - Circumcenter of triangle or tetrahedron edgeAttachments - Triangles or tetrahedra attached to an edge edges - Triangulation edges faceNormal - Triangulation face normal featureEdges - Triangulation sharp edges freeBoundary - Triangulation facets referenced by only one triangle or tetrahedron incenter - Incenter of triangle or tetrahedron isConnected - Test if a pair of vertices is connected by an edge neighbors - Neighbors to a triangle or tetrahedron vertexAttachments - Triangles or tetrahedra attached to a vertex vertexNormal - Triangulation vertex normal size - Size of the triangulation ConnectivityList nearestNeighbor - Vertex closest to a specified point pointLocation - Triangle or tetrahedron containing a specified point triangulation properties: Points - The coordinates of the points in the triangulation ConnectivityList - The triangulation connectivity list See also delaunayTriangulation. Documentation for triangulation doc triangulation Other uses of triangulation polyshape/triangulation

Methods for class triangulation: barycentricToCartesian edgeAttachments featureEdges isConnected pointLocation vertexAttachments cartesianToBarycentric edges freeBoundary nearestNeighbor size vertexNormal circumcenter faceNormal incenter neighbors triangulation

pointLocation Triangle or tetrahedron containing specified point TI = pointLocation(T, QP) returns the index of the triangle/tetrahedron enclosing the query point QP. The matrix QP contains the coordinates of the query points. QP is a mpts-by-ndim matrix where mpts is the number of query points and 2 <= ndim <= 3. TI is a column vector of triangle or tetrahedron IDs corresponding to the row numbers of the triangulation connectivity matrix T.ConnectivityList. The triangle/tetrahedron enclosing the point QP(k,:) is TI(k). Returns NaN for points not located in a triangle or tetrahedron of T. TI = pointLocation(T, QX,QY) and TI = pointLocation (T, QX,QY,QZ) allow the query points to be specified in alternative column vector format when working in 2D and 3D. [TI, BC] = pointLocation(T,...) returns, in addition, the Barycentric coordinates BC. BC is a mpts-by-ndim matrix, each row BC(i,:) represents the Barycentric coordinates of QP(i,:) with respect to the enclosing TI(i). Example 1: % Point Location in 2D T = triangulation([1 2 4; 1 4 3; 2 4 5],[0 0; 2 0; 0 1; 1 1; 2 1]); % Find the triangle that contains the following query point QP = [1, 0.5]; triplot(T,'-b*'), hold on plot(QP(:,1),QP(:,2),'ro') % The query point QP is located in a triangle with index TI = 1 TI = pointLocation(T, QP) Example 2: % Point Location in 3D plus barycentric coordinate evaluation % for a Delaunay triangulation x = rand(10,1); y = rand(10,1); z = rand(10,1); DT = delaunayTriangulation(x,y,z); % Find the tetrahedra that contain the following query points QP = [0.25 0.25 0.25; 0.5 0.5 0.5] [TI, BC] = pointLocation(DT, QP) See also triangulation, triangulation.nearestNeighbor, delaunayTriangulation. Documentation for triangulation/pointLocation doc triangulation/pointLocation