Quads vs Triangles

Two-minute explanation of https://twitter.com/mdsumner/status/1264039295947431936/photo/1

Referring to the pic at twitter above:

(the coloured primitives are triangles, anchored to pixel centre at each x,y the wire traverses each pixel boundary - a quad)

The matrix values "are at" the triangle corners (the quad corners use a defensible and simple trick)

Here looking in 2D:

  ## mesh3d way (with a quad interpretation)
  z <- matrix(c(1:6, 6:1), 4)
  x <- 1:4
  y <- 1:3
  library(anglr)
  ## surface3d way
  rr <- raster::raster(list(x = x, y = y, z = z))
  tmesh <- quadmesh::triangmesh(rr, triangles = TRUE)  ## triangles in dev-only
  ## mesh3d way
  qmesh <- as.mesh3d(rr, triangles = FALSE)  ## triangles in dev-only
  
 
op <-   par(mfrow = c(2, 2), mar = par("mar")/1, xaxs = "i", yaxs = "i", xpd = F)
  plot(t(qmesh$vb[1:2, ]), asp = 1, main = "triangle mesh", axes = FALSE)
  mesh_plot(tmesh, add = TRUE, col = viridis::viridis(length(z)))
  abline(h = qmesh$vb[2, ], v = qmesh$vb[1, ])
  plot(t(qmesh$vb[1:2, ]), asp = 1, main = "quadmesh", axes = FALSE)
  mesh_plot(qmesh, add = TRUE)
  abline(h = qmesh$vb[2, ], v = qmesh$vb[1, ])
  axis(2)
  plot(t(qmesh$vb[1:2, ]), asp = 1, main = "image", axes = FALSE)
  image(x, y, z, add = TRUE)
  abline(h = qmesh$vb[2, ], v = qmesh$vb[1, ])
  axis(1)
  plot(t(qmesh$vb[1:2, ]), asp = 1, main = "matrix cell centres", axes = FALSE)
  points(expand.grid(x, y), pch = "+") 
  abline(h = qmesh$vb[2, ], v = qmesh$vb[1, ])
  axis(1);axis(2)

^{Created on 2020-05-23 by the reprex package (v0.3.0)}