MATLAB Mathematics - SERC - Index of

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2 Polynomials and Interpolation −48 −48.05 −48.1 Latitude −48.15 −48.2 −48.25 −48.3 −48.35 −48.4 210.9 211 211.1 211.2 211.3 211.4 211.5 211.6 Longitude Note See the voronoi function for an example that uses the vertices of the edges to plot a Voronoi diagram. Tessellation and Interpolation of Scattered Data in Higher Dimensions Many applications in science, engineering, statistics, and mathematics require structures like convex hulls, Voronoi diagrams, and Delaunay tessellations. Using Qhull [1], MATLAB functions enable you to geometrically analyze data sets in any dimension. 2-26
Interpolation Functions for Multidimensional Geometrical Analysis Function convhulln delaunayn dsearchn griddatan tsearchn voronoin Description N-dimensional convex hull. N-dimensional Delaunay tessellation. N-dimensional nearest point search. N-dimensional data gridding and hypersurface fitting. N-dimensional closest simplex search. N-dimensional Voronoi diagrams. This section demonstrates these geometric analysis techniques: • Convex hulls • Delaunay triangulations • Voronoi diagrams • Interpolation of scattered multidimensional data Convex Hulls The convex hull of a data set in n-dimensional space is defined as the smallest convex region that contains the data set. Computing a Convex Hull. The convhulln function returns the indices of the points in a data set that comprise the facets of the convex hull for the set. For example, suppose X is an 8-by-3 matrix that consists of the 8 vertices of a cube. The convex hull of X then consists of 12 facets: d = [-1 1]; [x,y,z] = meshgrid(d,d,d); X = [x(:),y(:),z(:)]; C = convhulln(X) % 8 corner points of a cube C = 4 2 1 3 4 1 2-27
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MATLAB® The Language of Technical
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Revision History June 2004 First pr
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2 Polynomials and Interpolation Pol
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Introduction to Initial Value ODE P
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1 Matrices and Linear Algebra Funct
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5 Differential Equations Initial Va
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5 Differential Equations y0, yp0 Ve
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5 Differential Equations 1 0.8 0.6
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6 Sparse Matrices Function Summary
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6 Sparse Matrices Function Summary
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6 Sparse Matrices This matrix requi
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6 Sparse Matrices S = (3,1) 1 (2,2)
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6 Sparse Matrices Now F = full(S) d
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6 Sparse Matrices Importing Sparse
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6 Sparse Matrices west0479 west0479
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6 Sparse Matrices The find Function
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6 Sparse Matrices of the rows and c
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6 Sparse Matrices 0 500 1000 1500 2
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6 Sparse Matrices simply sparse(m,n
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6 Sparse Matrices Similarly, S(:,p)
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6 Sparse Matrices QR Factorization
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Index comparing sparse and full mat
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Index H hb1dae demo 5-35 hb1ode dem
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Index LU factorization 6-30 minimum
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Index twobvp demo 5-63 two-dimensio
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