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Qo%'"{ ōMQ<\$#J,Z6SݠӋlibrary(geometry) ## 2D example ps1 <- rbind(c(0, sqrt(3)), c(3/2, -sqrt(3)/2), c(-3/2, -sqrt(3)/2)) ps2 <- ps1 ps2[,2] <- -ps2[,2] is <- intersectn(ps1, ps2) plot(is, asp=1) ## 3D example ps1a <- rbox(2, C=0.5) dt1a <- delaunayn(ps1a) ps1b <- rbox(2, C=0.5) + 2 dt1b <- delaunayn(ps1b) ps1 <- rbind(ps1a, ps1b) dt1 <- rbind(dt1a, dt1b + nrow(ps1a)) tetramesh(dt1, ps1, alpha=0.5, col="yellow") ps2 <- rbox(2, C=0.5) + 0.5 dt2 <- delaunayn(ps2) tetramesh(dt2, ps2, alpha=0.5, col="red", clear=FALSE) vol <- 0 for (i in 1:nrow(dt1)) { for (j in 1:nrow(dt2)) { is <- intersectn(ps1[dt1[i,],], ps2[dt2[j,],]) vol <- vol + is$ch$vol } } message(paste("Volume of overlap should be 0.125. It is:", vol)) Qhull manual

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[random-fixed] Qhull manual

Qhull is a general dimension code for computing convex hulls, Delaunay triangulations, halfspace intersections about a point, Voronoi diagrams, furthest-site Delaunay triangulations, and furthest-site Voronoi diagrams. These structures have applications in science, engineering, statistics, and mathematics. See Fukuda's introduction to convex hulls, Delaunay triangulations, Voronoi diagrams, and linear programming. For a detailed introduction, see O'Rourke ['94], Computational Geometry in C.

There are six programs. Except for rbox, they use the same code. Each program includes instructions and examples.

  • qconvex -- convex hulls
  • qdelaunay -- Delaunay triangulations and furthest-site Delaunay triangulations
  • qhalf -- halfspace intersections about a point
  • qhull -- all structures with additional options
  • qvoronoi -- Voronoi diagrams and furthest-site Voronoi diagrams
  • rbox -- generate point distributions for qhull

Qhull implements the Quickhull algorithm for computing the convex hull. Qhull includes options for hull volume, facet area, multiple output formats, and graphical output. It can approximate a convex hull.

Qhull handles roundoff errors from floating point arithmetic. It generates a convex hull with "thick" facets. A facet's outer plane is clearly above all of the points; its inner plane is clearly below the facet's vertices. Any exact convex hull must lie between the inner and outer plane.

Qhull uses merged facets, triangulated output, or joggled input. Triangulated output triangulates non-simplicial, merged facets. Joggled input also guarantees simplicial output, but it is less accurate than merged facets. For merged facets, Qhull reports the maximum outer and inner plane.

Brad Barber, Arlington, MA

Copyright © 1995-2020 C.B. Barber


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