PolygonSoup (version 1.0.1)

Mesh: Make a 3D mesh

Description

Make a 3D mesh from given vertices and faces; the returned faces are coherently oriented, normals are computed if desired, and triangulation is performed if desired. The mesh is also cleaned: duplicated vertices or faces are merged, and isolated vertices are removed.

Usage

Mesh(vertices, faces, mesh = NULL, triangulate = FALSE, normals = FALSE)

Value

A list giving the vertices, the edges, the faces of the mesh, the exterior edges, the exterior vertices and optionally the normals. If triangulate=TRUE, this list has two additional components

edges0 and normals0 giving the edges and the normals before the triangulation, unless the mesh is already triangulated, in which case the triangulate option is ignored.

Arguments

vertices

a numeric matrix with three columns, or a bigq matrix with three columns

faces

either an integer matrix (each row provides the vertex indices of the corresponding face) or a list of integer vectors, each one providing the vertex indices of the corresponding face

mesh

if not NULL, this argument takes precedence over vertices and faces, and must be either a list containing the fields vertices and faces (objects as described above), otherwise a rgl mesh (i.e. a mesh3d object)

triangulate

Boolean, whether to triangulate the faces

normals

Boolean, whether to compute the normals

See Also

See plotEdges for more details about the edges returned by this function.

Examples

library(PolygonSoup)
library(rgl)

# a tetrahedron with ill-oriented faces ####
vertices <- rbind(
  c(-1, -1, -1),
  c(1, 1, -1),
  c(1, -1, 1),
  c(-1, 1, 1)
)
faces <- rbind(
  c(1, 2, 3),
  c(3, 4, 2),
  c(4, 2, 1),
  c(4, 3, 1)
)

# plot the tetrahedron, hiding the back of the faces
# then some faces do not appear, as their orientation is not correct
tmesh1 <- tmesh3d(
  vertices = t(vertices),
  indices = t(faces),
  homogeneous = FALSE
)
open3d(windowRect = c(50, 50, 562, 562))
shade3d(tmesh1, color = "green", back = "cull")

# now run the `Mesh` function
mesh2 <- Mesh(vertices, faces, normals = FALSE)
# plot the tetrahedron, hiding the back of the faces
# then all faces appear now
tmesh2 <- toRGL(mesh2)
open3d(windowRect = c(50, 50, 562, 562))
shade3d(tmesh2, color = "blue", back = "cull")

# illustration of the cleaning feature ####
# we construct a mesh with a lot of duplicated vertices
library(misc3d) # to compute a mesh of an isosurface
a <- 0.94; mu <- 0.56; c <- 0.34 # cyclide parameters
f <- function(x, y, z, a, c, mu){ # implicit equation of the cyclide
  b <- sqrt(a^2 - c^2)
  (x^2 + y^2 + z^2 - mu^2 + b^2)^2 - 4*(a*x - c*mu)^2 - 4*b^2*y^2
}
x <- seq(-c - mu - a, abs(mu - c) + a, length.out = 45)
y <- seq(-mu - a, mu + a, length.out = 45)
z <- seq(-mu - c, mu + c, length.out = 30)
g <- expand.grid(x = x, y = y, z = z)
voxel <- array(with(g, f(x, y, z, a, c, mu)), c(45, 45, 30))
cont <- computeContour3d(voxel, level = 0, x = x, y = y, z = z)
ids <- matrix(1:nrow(cont), ncol = 3, byrow = TRUE)
# run the `Mesh` function 
mesh <- Mesh(cont, ids, normals = TRUE)
# plot the cyclide
tmesh <- toRGL(mesh)
open3d(windowRect = c(50, 50, 562, 562), zoom = 0.9)
shade3d(tmesh, color = "green")

# illustration of the `triangulate` option ####
# the faces of the truncated icosahedron are hexagonal or pentagonal:
truncatedIcosahedron[["faces"]]
# so we triangulate them:
mesh <- Mesh(
  mesh = truncatedIcosahedron,
  triangulate = TRUE, normals = FALSE
)
# now we can plot the truncated icosahedron
tmesh <- toRGL(mesh)
open3d(windowRect = c(50, 50, 562, 562), zoom = 0.9)
shade3d(tmesh, color = "orange")