# Interpolate values on a 3d mesh The function takes a reconstructed `mesh3d` object (`sur`) with some related `values` (to either triangles or vertices of the mesh) and transfers such values to the real mesh (`refsur`) from which `sur` was derived. ```r interpolMesh(sur,values,refsur,refmat,element=c("triangles","vertices"),k=4) ``` ## Arguments - `sur`: a reconstructed `mesh3d` object with vertices matching to `refmat`. - `values`: the vector of values related to `sur` to be interpolated. `values` can be related to either triangles or vertices (see `element`). - `refsur`: the reference mesh (`mesh3d` object) to interpolate the `values` on. - `refmat`: the landmark set related to `refsur`. - `element`: one of `"triangles"` or `"vertices"`, depending on which of them `values` is related to. - `k`: the number of nearest neighbor vertices used for interpolation (see details). ## Returns The vector of values related to each vertex of `refsur`. ## Details The function starts by locating a set of points (NNps) on `refsur`, each being the single nearest neighbor for each vertex of `sur` (or barycenter if `element="triangles"`). Then, interpolation is performed by identifying the `k` points among NNps being the closest to each vertex of `refsur` and computing the mean of their `values` weighted by their distance. ## Examples ```r da<-"https://github.com/pasraia/RRmorph_example_data/raw/refs/heads/main/RRmorphdata.rda" download.file(url=da,destfile = paste0(tempdir(),"/RRmorphdata.rda")) load(paste0(tempdir(),"/RRmorphdata.rda")) require(rgl) require(Morpho) require(Rvcg) pca<-procSym(endo.set) ldm<-endo.set[,,"Homo_sapiens"] sur<-endo.sur[["Homo_sapiens"]] rec<- vcgBallPivoting(pca$mshape, radius = 0) rec$vb[1:3,]<-t(ldm) val1<-rnorm(ncol(rec$vb)) # Interpolate values associated to vertices val1<-rnorm(ncol(rec$vb)) interp1<-interpolMesh(sur = rec,refsur = sur,refmat = ldm, values = val1,element ="vertices",k = 4) colmesh1<-col2mesh(mesh = sur,values = interp1,pal = heat.colors(5)) open3d() shade3d(colmesh1,specular="black") # Interpolate values associated to triangles val2<-rnorm(ncol(rec$it)) interp2<-interpolMesh(sur = rec,refsur = sur,refmat = ldm, values = val2,element ="triangles",k = 4) colmesh2<-col2mesh(mesh = sur,values = interp2,pal = heat.colors(5)) open3d() shade3d(colmesh2,specular="black") ``` ## Author(s) Marina Melchionna, Silvia Castiglione

interpolMesh function