convexHull: Find the convex hull of a set of points.

In gMOIP: Tools for 2D and 3D Plots of Single and Multi-Objective Linear/Integer Programming Models

Find the convex hull of a set of points.

Description

Find the convex hull of a set of points.

Usage

convexHull(
  pts,
  addRays = FALSE,
  useRGLBBox = FALSE,
  direction = 1,
  tol = mean(mean(abs(pts))) * sqrt(.Machine$double.eps) * 2,
  m = apply(pts, 2, min) - 5,
  M = apply(pts, 2, max) + 5
)

Arguments

pts	A matrix with a point in each row.
addRays	Add the ray defined by direction.
useRGLBBox	Use the RGL bounding box when add rays.
direction	Ray direction. If i'th entry is positive, consider the i'th column of pts plus a value greater than on equal zero (minimize objective $i$). If negative, consider the i'th column of pts minus a value greater than on equal zero (maximize objective $i$).
tol	Tolerance on standard deviation if using PCA.
m	Minimum values of the bounding box.
M	Maximum values of the bounding box.

Value

A list with hull equal a matrix with row indices of the vertices defining each facet in the hull and pts equal the input points (and dummy points) and columns: pt, true if a point in the original input; false if a dummy point (a point on a ray). vtx, TRUE if a vertex in the hull.

Examples

## 1D
pts<-matrix(c(1,2,3), ncol = 1, byrow = TRUE)
dimFace(pts) # a line
convexHull(pts)
convexHull(pts, addRays = TRUE)

## 2D
pts<-matrix(c(1,1, 2,2), ncol = 2, byrow = TRUE)
dimFace(pts) # a line
convexHull(pts)
plotHull2D(pts, drawPoints = TRUE)
convexHull(pts, addRays = TRUE)
plotHull2D(pts, addRays = TRUE, drawPoints = TRUE)
pts<-matrix(c(1,1, 2,2, 0,1), ncol = 2, byrow = TRUE)
dimFace(pts) # a polygon
convexHull(pts)
plotHull2D(pts, drawPoints = TRUE)
convexHull(pts, addRays = TRUE, direction = c(-1,1))
plotHull2D(pts, addRays = TRUE, direction = c(-1,1), addText = "coord")

## 3D
pts<-matrix(c(1,1,1), ncol = 3, byrow = TRUE)
dimFace(pts) # a point
convexHull(pts)
pts<-matrix(c(0,0,0,1,1,1,2,2,2,3,3,3), ncol = 3, byrow = TRUE)
dimFace(pts) # a line
convexHull(pts)
pts<-matrix(c(0,0,0,0,1,1,0,2,2,0,0,2), ncol = 3, byrow = TRUE)
dimFace(pts) # a polygon
convexHull(pts)
convexHull(pts, addRays = TRUE)
pts<-matrix(c(1,0,0,1,1,1,1,2,2,3,1,1), ncol = 3, byrow = TRUE)
dimFace(pts) # a polygon
convexHull(pts) # a polyhedron
pts<-matrix(c(1,1,1,2,2,1,2,1,1,1,1,2), ncol = 3, byrow = TRUE)
dimFace(pts) # a polytope (polyhedron)
convexHull(pts)

ini3D(argsPlot3d = list(xlim = c(0,3), ylim = c(0,3), zlim = c(0,3)))
pts<-matrix(c(1,1,1,2,2,1,2,1,1,1,1,2), ncol = 3, byrow = TRUE)
plotPoints3D(pts)
plotHull3D(pts, argsPolygon3d = list(color = "red"))
convexHull(pts)
plotHull3D(pts, addRays = TRUE)
convexHull(pts, addRays = TRUE)
finalize3D()

gMOIP documentation built on Oct. 25, 2024, 5:06 p.m.