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Transforms

using Meshes # hide
import CairoMakie as Mke # hide

Geometric (e.g. coordinates) transforms are implemented according to the TransformsBase.jl interface. Please read their documentation for more details.

GeometricTransform
CoordinateTransform

Rotate

Rotate

using Rotations: Angle2d

grid = CartesianGrid(10, 10)

mesh = grid |> Rotate(Angle2d(π/4))

fig = Mke.Figure(size = (800, 400))
viz(fig[1,1], grid)
viz(fig[1,2], mesh)
fig

Translate

Translate

grid = CartesianGrid(10, 10)

mesh = grid |> Translate(10., 20.)

fig = Mke.Figure(size = (800, 400))
viz(fig[1,1], grid)
viz(fig[1,2], mesh)
fig

Affine

Affine

grid = CartesianGrid(10, 10)

mesh = grid |> Affine(Angle2d(π/4), [10., 20.])

fig = Mke.Figure(size = (800, 400))
viz(fig[1,1], grid)
viz(fig[1,2], mesh)
fig

Scale

Scale

grid = CartesianGrid(10, 10)

mesh = grid |> Scale(2., 3.)

fig = Mke.Figure(size = (800, 400))
viz(fig[1,1], grid)
viz(fig[1,2], mesh)
fig

Stretch

Stretch

grid = CartesianGrid(10, 10)

mesh = grid |> Stretch(2., 3.)

fig = Mke.Figure(size = (800, 400))
viz(fig[1,1], grid)
viz(fig[1,2], mesh)
fig

StdCoords

StdCoords

# Cartesian grid with coordinates [0,10] x [0,10]
grid = CartesianGrid(10, 10)

# scale coordinates to [-1,1] x [-1,1]
mesh = grid |> StdCoords()

fig = Mke.Figure(size = (800, 400))
viz(fig[1,1], grid)
viz(fig[1,2], mesh)
fig

Repair

Repair

# mesh with unreferenced point
points = [(0, 0, 0), (0, 0, 1), (5, 5, 5), (0, 1, 0), (1, 0, 0)]
connec = connect.([(1, 2, 4), (1, 2, 5), (1, 4, 5), (2, 4, 5)])
mesh   = SimpleMesh(points, connec)

rmesh = mesh |> Repair{1}()

Bridge

Bridge

# polygon with two holes
outer = [(0, 0), (1, 0), (1, 1), (0, 1)]
hole1 = [(0.2, 0.2), (0.4, 0.2), (0.4, 0.4), (0.2, 0.4)]
hole2 = [(0.6, 0.2), (0.8, 0.2), (0.8, 0.4), (0.6, 0.4)]
poly = PolyArea([outer, hole1, hole2])

# polygon with single outer ring
bpoly = poly |> Bridge(0.01)

fig = Mke.Figure(size = (800, 400))
viz(fig[1,1], poly)
viz(fig[1,2], bpoly)
fig

Smoothing

LambdaMuSmoothing
LaplaceSmoothing
TaubinSmoothing

using PlyIO

# helper function to read *.ply files
function readply(fname)
  ply = load_ply(fname)
  x = ply["vertex"]["x"]
  y = ply["vertex"]["y"]
  z = ply["vertex"]["z"]
  points = Point.(x, y, z)
  connec = [connect(Tuple(c.+1)) for c in ply["face"]["vertex_indices"]]
  SimpleMesh(points, connec)
end

# download mesh from the web
file = download(
  "https://raw.githubusercontent.com/juliohm/JuliaCon2021/master/data/beethoven.ply"
)

# read mesh from disk
mesh = readply(file)

# smooth mesh with 30 iterations
smesh = mesh |> TaubinSmoothing(30)

fig = Mke.Figure(size = (800, 1200))
viz(fig[1,1], mesh)
viz(fig[2,1], smesh)
fig