# Make triangulation of 2D point mesh Function for creating Delaunay type-I triangulation (see Schumaker 2007) with consistent oriented edges adapted for a regular point mesh created by `point_mesh` function. See Details for more information. ```r make_triangulation(mesh) ``` ## Arguments - `mesh`: A data frame or tibble with named columns: `x`, `y` (required) and `index` (optionally, if missing, it will be generated internally). It should optimally be a `D2` element of a `"mesh"` object or a list with the same structure of uniformly spaced grid. ## Returns A three column matrix with indices of the vertices of the triangles. Each row represents one triangle, defined by three vertex indices pointing to rows in the input mesh. ## Details The type-I Delaunay triangulation is a triangulation obtained by drawing in the north-east diagonals in all subrectangles of the triangulated area. Due to the regularity of the input mesh (in the sense of distances between mesh points), a simplified procedure is used: The triangulation is created within the individual strips and then bound together. The order of the vertices is chosen to maintain a consistent orientation of the triangles (for more details see Schneider 2003). If the input mesh has not regular grid spacing, the result triangulation may not be meaningful and will not meet the Delaunay triangulation criteria. ## Examples ```r # a) Create small mesh for triangulation example # using 204 electrodes from epochdata M <- point_mesh(n = 500, template = "HCGSN256", sensor_select = unique(epochdata$sensor)) # b) Make triangulation on this mesh TRI <- make_triangulation(M$D2) head(TRI) # c) plot triangulation in 2D # prepare empty plot plot(M$D2, type = "n", main = "Triangulation plot", xlab = "", ylab = "", asp = 1, axes = FALSE) # create a structure for plotting x0 <- c() y0 <- c() x1 <- c() y1 <- c() for (i in 1:nrow(TRI)) { v_indices <- TRI[i, ] v_coords <- M$D2[v_indices, ] x0 <- c(x0, v_coords[1, "x"], v_coords[2, "x"], v_coords[3, "x"]) y0 <- c(y0, v_coords[1, "y"], v_coords[2, "y"], v_coords[3, "y"]) x1 <- c(x1, v_coords[2, "x"], v_coords[3, "x"], v_coords[1, "x"]) y1 <- c(y1, v_coords[2, "y"], v_coords[3, "y"], v_coords[1, "y"]) } # plot triangulation using segments segments(x0, y0, x1, y1) ## Note: this code opens a rgl 3D viewer # d) Plot the result triangulation as 3D wire model using rgl rgl::open3d() rgl::wire3d(rgl::mesh3d(M$D3$x, M$D3$y, M$D3$z, triangles = t(TRI))) ``` ## References Lai M-J, Schumaker LL. **Spline functions on triangulations.** Cambridge University Press; 2007. Schneider PJ, Eberly DH. **Geometric Tools for Computer Graphics.** The Morgan Kaufmann Series in Computer Graphics. San Francisco: Morgan Kaufmann, 2003.

make_triangulation function