Generating Planar Terrain Mesh
Given a gray scale heightmap, I need a planar triangulated mesh to serve as the base for a terrain object + shader to be used in the above webapp.
I already have some tools to abstract a heightmap from an image. I’m going to start with a smaller version of the terrain image file which I’ve converted to grayscale:
if (file.exists("data/terrain-small.png")) {
small_input <- "data/terrain-small.png"
} else {
small_input <- file.choose()
}
image <- data.frame(png::readPNG(small_input))
cat(paste0('<img src="/post/', small_input, '" style="float: right; width:256px; padding: 1%;" />'))
## [1] 128## [1] 128## 'data.frame': 128 obs. of 128 variables:
## $ X1 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X2 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X3 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X4 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X5 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X6 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X7 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X8 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X9 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X10 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X11 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X12 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X13 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X14 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X15 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X16 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X17 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X18 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X19 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X20 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X21 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X22 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X23 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X24 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X25 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X26 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X27 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X28 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X29 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X30 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X31 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X32 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X33 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X34 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X35 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X36 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X37 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X38 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X39 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X40 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X41 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X42 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X43 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X44 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X45 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X46 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X47 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X48 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X49 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X50 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X51 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X52 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X53 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X54 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X55 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X56 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X57 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X58 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X59 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X60 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X61 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X62 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X63 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X64 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X65 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X66 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X67 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X68 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X69 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X70 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X71 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X72 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X73 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X74 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X75 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X76 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X77 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X78 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X79 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X80 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X81 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X82 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X83 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X84 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X85 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X86 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X87 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X88 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X89 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X90 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X91 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X92 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X93 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X94 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X95 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X96 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X97 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X98 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X99 : num 0 0 0 0 0 0 0 0 0 0 ...
## [list output truncated]Now for every point in the image, I need to create coordinates for a 3d vertex (x, y, z), a normal for each vertex and texture coordinates (s, t) for each vertex:
mapHeight <- function (image_map, image_width, image_height) {
# make a 1.0 x 1.0 plane starting at (0, 0, 0)... z is up
heights <- matrix(nrow = image_width, ncol = image_height)
for (y in 1:image_height) {
for (x in 1:image_width) {
heights[y, x] <- round(image_map[y, x], 6)
}
}
for (y in 1:image_height) {
for (x in 1:image_width) {
# vertices (x, y, z)
# z is "up", and png y coordinate system is reverse of WebGL
print(paste0(round((x / image_width), 6), ", ", round(y / image_height, 6), ", ", heights[(image_width + 1) - y, x]))
# normals
print(paste0(0.0, ", ", 0.0, ", ", 1.0)) # z is "up"
# texture coordinates (s, t)
print(paste0(round((x / image_width), 6), ", ", round(y / image_height, 6)))
}
}
heights
}## [1] "0.007812, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.007812, 0.007812"
## [1] "0.015625, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.015625, 0.007812"
## [1] "0.023438, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.023438, 0.007812"
## [1] "0.03125, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.03125, 0.007812"
## [1] "0.039062, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.039062, 0.007812"
## [1] "0.046875, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.046875, 0.007812"
## [1] "0.054688, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.054688, 0.007812"
## [1] "0.0625, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.0625, 0.007812"
## [1] "0.070312, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.070312, 0.007812"
## [1] "0.078125, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.078125, 0.007812"
## [1] "0.085938, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.085938, 0.007812"
## [1] "0.09375, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.09375, 0.007812"
## [1] "0.101562, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.101562, 0.007812"
## [1] "0.109375, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.109375, 0.007812"
## [1] "0.117188, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.117188, 0.007812"
## [1] "0.125, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.125, 0.007812"
## [1] "0.132812, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.132812, 0.007812"
## [1] "0.140625, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.140625, 0.007812"
## [1] "0.148438, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.148438, 0.007812"
## [1] "0.15625, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.15625, 0.007812"
## [1] "0.164062, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.164062, 0.007812"
## [1] "0.171875, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.171875, 0.007812"
## [1] "0.179688, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.179688, 0.007812"
## [1] "0.1875, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.1875, 0.007812"
## [1] "0.195312, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.195312, 0.007812"
## [1] "0.203125, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.203125, 0.007812"
## [1] "0.210938, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.210938, 0.007812"
## [1] "0.21875, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.21875, 0.007812"
## [1] "0.226562, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.226562, 0.007812"
## [1] "0.234375, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.234375, 0.007812"
## [1] "0.242188, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.242188, 0.007812"
## [1] "0.25, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.25, 0.007812"
## [1] "0.257812, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.257812, 0.007812"
## [1] "0.265625, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.265625, 0.007812"
## [1] "0.273438, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.273438, 0.007812"
## [1] "0.28125, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.28125, 0.007812"
## [1] "0.289062, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.289062, 0.007812"
## [1] "0.296875, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.296875, 0.007812"
## [1] "0.304688, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.304688, 0.007812"
## [1] "0.3125, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.3125, 0.007812"
## [1] "0.320312, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.320312, 0.007812"
## [1] "0.328125, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.328125, 0.007812"
## [1] "0.335938, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.335938, 0.007812"
## [1] "0.34375, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.34375, 0.007812"
## [1] "0.351562, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.351562, 0.007812"
## [1] "0.359375, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.359375, 0.007812"
## [1] "0.367188, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.367188, 0.007812"
## [1] "0.375, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.375, 0.007812"
## [1] "0.382812, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.382812, 0.007812"
## [1] "0.390625, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.390625, 0.007812"
## [1] "0.398438, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.398438, 0.007812"
## [1] "0.40625, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.40625, 0.007812"
## [1] "0.414062, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.414062, 0.007812"
## [1] "0.421875, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.421875, 0.007812"
## [1] "0.429688, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.429688, 0.007812"
## [1] "0.4375, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.4375, 0.007812"
## [1] "0.445312, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.445312, 0.007812"
## [1] "0.453125, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.453125, 0.007812"
## [1] "0.460938, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.460938, 0.007812"
## [1] "0.46875, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.46875, 0.007812"
## [1] "0.476562, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.476562, 0.007812"
## [1] "0.484375, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.484375, 0.007812"
## [1] "0.492188, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.492188, 0.007812"
## [1] "0.5, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.5, 0.007812"
## [1] "0.507812, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.507812, 0.007812"
## [1] "0.515625, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.515625, 0.007812"
## [1] "0.523438, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.523438, 0.007812"
## [1] "0.53125, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.53125, 0.007812"
## [1] "0.539062, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.539062, 0.007812"
## [1] "0.546875, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.546875, 0.007812"
## [1] "0.554688, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.554688, 0.007812"
## [1] "0.5625, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.5625, 0.007812"
## [1] "0.570312, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.570312, 0.007812"
## [1] "0.578125, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.578125, 0.007812"
## [1] "0.585938, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.585938, 0.007812"
## [1] "0.59375, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.59375, 0.007812"
## [1] "0.601562, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.601562, 0.007812"
## [1] "0.609375, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.609375, 0.007812"
## [1] "0.617188, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.617188, 0.007812"
## [1] "0.625, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.625, 0.007812"
## [1] "0.632812, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.632812, 0.007812"
## [1] "0.640625, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.640625, 0.007812"
## [1] "0.648438, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.648438, 0.007812"
## [1] "0.65625, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.65625, 0.007812"
## [1] "0.664062, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.664062, 0.007812"
## [1] "0.671875, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.671875, 0.007812"
## [1] "0.679688, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.679688, 0.007812"
## [1] "0.6875, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.6875, 0.007812"
## [1] "0.695312, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.695312, 0.007812"
## [1] "0.703125, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.703125, 0.007812"
## [1] "0.710938, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.710938, 0.007812"
## [1] "0.71875, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.71875, 0.007812"
## [1] "0.726562, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.726562, 0.007812"
## [1] "0.734375, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.734375, 0.007812"
## [1] "0.742188, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.742188, 0.007812"
## [1] "0.75, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.75, 0.007812"
## [1] "0.757812, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.757812, 0.007812"
## [1] "0.765625, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.765625, 0.007812"
## [1] "0.773438, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.773438, 0.007812"
## [1] "0.78125, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.78125, 0.007812"
## [1] "0.789062, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.789062, 0.007812"
## [1] "0.796875, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.796875, 0.007812"
## [1] "0.804688, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.804688, 0.007812"
## [1] "0.8125, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.8125, 0.007812"
## [1] "0.820312, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.820312, 0.007812"
## [1] "0.828125, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.828125, 0.007812"
## [1] "0.835938, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.835938, 0.007812"
## [1] "0.84375, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.84375, 0.007812"
## [1] "0.851562, 0.007812, 0"
## [1] "0, 0, 1"
## [1] "0.851562, 0.007812"
## [1] "0.859375, 0.007812, 0"
## [1] "0, 0, 1"
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## [1] "0, 0, 1"
## [1] "0.234375, 1"
## [1] "0.242188, 1, 0"
## [1] "0, 0, 1"
## [1] "0.242188, 1"
## [1] "0.25, 1, 0"
## [1] "0, 0, 1"
## [1] "0.25, 1"
## [1] "0.257812, 1, 0"
## [1] "0, 0, 1"
## [1] "0.257812, 1"
## [1] "0.265625, 1, 0"
## [1] "0, 0, 1"
## [1] "0.265625, 1"
## [1] "0.273438, 1, 0"
## [1] "0, 0, 1"
## [1] "0.273438, 1"
## [1] "0.28125, 1, 0"
## [1] "0, 0, 1"
## [1] "0.28125, 1"
## [1] "0.289062, 1, 0"
## [1] "0, 0, 1"
## [1] "0.289062, 1"
## [1] "0.296875, 1, 0"
## [1] "0, 0, 1"
## [1] "0.296875, 1"
## [1] "0.304688, 1, 0"
## [1] "0, 0, 1"
## [1] "0.304688, 1"
## [1] "0.3125, 1, 0"
## [1] "0, 0, 1"
## [1] "0.3125, 1"
## [1] "0.320312, 1, 0"
## [1] "0, 0, 1"
## [1] "0.320312, 1"
## [1] "0.328125, 1, 0"
## [1] "0, 0, 1"
## [1] "0.328125, 1"
## [1] "0.335938, 1, 0"
## [1] "0, 0, 1"
## [1] "0.335938, 1"
## [1] "0.34375, 1, 0"
## [1] "0, 0, 1"
## [1] "0.34375, 1"
## [1] "0.351562, 1, 0"
## [1] "0, 0, 1"
## [1] "0.351562, 1"
## [1] "0.359375, 1, 0"
## [1] "0, 0, 1"
## [1] "0.359375, 1"
## [1] "0.367188, 1, 0"
## [1] "0, 0, 1"
## [1] "0.367188, 1"
## [1] "0.375, 1, 0"
## [1] "0, 0, 1"
## [1] "0.375, 1"
## [1] "0.382812, 1, 0"
## [1] "0, 0, 1"
## [1] "0.382812, 1"
## [1] "0.390625, 1, 0"
## [1] "0, 0, 1"
## [1] "0.390625, 1"
## [1] "0.398438, 1, 0"
## [1] "0, 0, 1"
## [1] "0.398438, 1"
## [1] "0.40625, 1, 0"
## [1] "0, 0, 1"
## [1] "0.40625, 1"
## [1] "0.414062, 1, 0"
## [1] "0, 0, 1"
## [1] "0.414062, 1"
## [1] "0.421875, 1, 0"
## [1] "0, 0, 1"
## [1] "0.421875, 1"
## [1] "0.429688, 1, 0"
## [1] "0, 0, 1"
## [1] "0.429688, 1"
## [1] "0.4375, 1, 0"
## [1] "0, 0, 1"
## [1] "0.4375, 1"
## [1] "0.445312, 1, 0"
## [1] "0, 0, 1"
## [1] "0.445312, 1"
## [1] "0.453125, 1, 0"
## [1] "0, 0, 1"
## [1] "0.453125, 1"
## [1] "0.460938, 1, 0"
## [1] "0, 0, 1"
## [1] "0.460938, 1"
## [1] "0.46875, 1, 0"
## [1] "0, 0, 1"
## [1] "0.46875, 1"
## [1] "0.476562, 1, 0"
## [1] "0, 0, 1"
## [1] "0.476562, 1"
## [1] "0.484375, 1, 0"
## [1] "0, 0, 1"
## [1] "0.484375, 1"
## [1] "0.492188, 1, 0"
## [1] "0, 0, 1"
## [1] "0.492188, 1"
## [1] "0.5, 1, 0"
## [1] "0, 0, 1"
## [1] "0.5, 1"
## [1] "0.507812, 1, 0"
## [1] "0, 0, 1"
## [1] "0.507812, 1"
## [1] "0.515625, 1, 0"
## [1] "0, 0, 1"
## [1] "0.515625, 1"
## [1] "0.523438, 1, 0"
## [1] "0, 0, 1"
## [1] "0.523438, 1"
## [1] "0.53125, 1, 0"
## [1] "0, 0, 1"
## [1] "0.53125, 1"
## [1] "0.539062, 1, 0"
## [1] "0, 0, 1"
## [1] "0.539062, 1"
## [1] "0.546875, 1, 0"
## [1] "0, 0, 1"
## [1] "0.546875, 1"
## [1] "0.554688, 1, 0"
## [1] "0, 0, 1"
## [1] "0.554688, 1"
## [1] "0.5625, 1, 0"
## [1] "0, 0, 1"
## [1] "0.5625, 1"
## [1] "0.570312, 1, 0"
## [1] "0, 0, 1"
## [1] "0.570312, 1"
## [1] "0.578125, 1, 0"
## [1] "0, 0, 1"
## [1] "0.578125, 1"
## [1] "0.585938, 1, 0"
## [1] "0, 0, 1"
## [1] "0.585938, 1"
## [1] "0.59375, 1, 0"
## [1] "0, 0, 1"
## [1] "0.59375, 1"
## [1] "0.601562, 1, 0"
## [1] "0, 0, 1"
## [1] "0.601562, 1"
## [1] "0.609375, 1, 0"
## [1] "0, 0, 1"
## [1] "0.609375, 1"
## [1] "0.617188, 1, 0"
## [1] "0, 0, 1"
## [1] "0.617188, 1"
## [1] "0.625, 1, 0"
## [1] "0, 0, 1"
## [1] "0.625, 1"
## [1] "0.632812, 1, 0"
## [1] "0, 0, 1"
## [1] "0.632812, 1"
## [1] "0.640625, 1, 0"
## [1] "0, 0, 1"
## [1] "0.640625, 1"
## [1] "0.648438, 1, 0"
## [1] "0, 0, 1"
## [1] "0.648438, 1"
## [1] "0.65625, 1, 0"
## [1] "0, 0, 1"
## [1] "0.65625, 1"
## [1] "0.664062, 1, 0"
## [1] "0, 0, 1"
## [1] "0.664062, 1"
## [1] "0.671875, 1, 0"
## [1] "0, 0, 1"
## [1] "0.671875, 1"
## [1] "0.679688, 1, 0"
## [1] "0, 0, 1"
## [1] "0.679688, 1"
## [1] "0.6875, 1, 0"
## [1] "0, 0, 1"
## [1] "0.6875, 1"
## [1] "0.695312, 1, 0"
## [1] "0, 0, 1"
## [1] "0.695312, 1"
## [1] "0.703125, 1, 0"
## [1] "0, 0, 1"
## [1] "0.703125, 1"
## [1] "0.710938, 1, 0"
## [1] "0, 0, 1"
## [1] "0.710938, 1"
## [1] "0.71875, 1, 0"
## [1] "0, 0, 1"
## [1] "0.71875, 1"
## [1] "0.726562, 1, 0"
## [1] "0, 0, 1"
## [1] "0.726562, 1"
## [1] "0.734375, 1, 0"
## [1] "0, 0, 1"
## [1] "0.734375, 1"
## [1] "0.742188, 1, 0"
## [1] "0, 0, 1"
## [1] "0.742188, 1"
## [1] "0.75, 1, 0"
## [1] "0, 0, 1"
## [1] "0.75, 1"
## [1] "0.757812, 1, 0"
## [1] "0, 0, 1"
## [1] "0.757812, 1"
## [1] "0.765625, 1, 0"
## [1] "0, 0, 1"
## [1] "0.765625, 1"
## [1] "0.773438, 1, 0"
## [1] "0, 0, 1"
## [1] "0.773438, 1"
## [1] "0.78125, 1, 0"
## [1] "0, 0, 1"
## [1] "0.78125, 1"
## [1] "0.789062, 1, 0"
## [1] "0, 0, 1"
## [1] "0.789062, 1"
## [1] "0.796875, 1, 0"
## [1] "0, 0, 1"
## [1] "0.796875, 1"
## [1] "0.804688, 1, 0"
## [1] "0, 0, 1"
## [1] "0.804688, 1"
## [1] "0.8125, 1, 0"
## [1] "0, 0, 1"
## [1] "0.8125, 1"
## [1] "0.820312, 1, 0"
## [1] "0, 0, 1"
## [1] "0.820312, 1"
## [1] "0.828125, 1, 0"
## [1] "0, 0, 1"
## [1] "0.828125, 1"
## [1] "0.835938, 1, 0"
## [1] "0, 0, 1"
## [1] "0.835938, 1"
## [1] "0.84375, 1, 0"
## [1] "0, 0, 1"
## [1] "0.84375, 1"
## [1] "0.851562, 1, 0"
## [1] "0, 0, 1"
## [1] "0.851562, 1"
## [1] "0.859375, 1, 0"
## [1] "0, 0, 1"
## [1] "0.859375, 1"
## [1] "0.867188, 1, 0"
## [1] "0, 0, 1"
## [1] "0.867188, 1"
## [1] "0.875, 1, 0"
## [1] "0, 0, 1"
## [1] "0.875, 1"
## [1] "0.882812, 1, 0"
## [1] "0, 0, 1"
## [1] "0.882812, 1"
## [1] "0.890625, 1, 0"
## [1] "0, 0, 1"
## [1] "0.890625, 1"
## [1] "0.898438, 1, 0"
## [1] "0, 0, 1"
## [1] "0.898438, 1"
## [1] "0.90625, 1, 0"
## [1] "0, 0, 1"
## [1] "0.90625, 1"
## [1] "0.914062, 1, 0"
## [1] "0, 0, 1"
## [1] "0.914062, 1"
## [1] "0.921875, 1, 0"
## [1] "0, 0, 1"
## [1] "0.921875, 1"
## [1] "0.929688, 1, 0"
## [1] "0, 0, 1"
## [1] "0.929688, 1"
## [1] "0.9375, 1, 0"
## [1] "0, 0, 1"
## [1] "0.9375, 1"
## [1] "0.945312, 1, 0"
## [1] "0, 0, 1"
## [1] "0.945312, 1"
## [1] "0.953125, 1, 0"
## [1] "0, 0, 1"
## [1] "0.953125, 1"
## [1] "0.960938, 1, 0"
## [1] "0, 0, 1"
## [1] "0.960938, 1"
## [1] "0.96875, 1, 0"
## [1] "0, 0, 1"
## [1] "0.96875, 1"
## [1] "0.976562, 1, 0"
## [1] "0, 0, 1"
## [1] "0.976562, 1"
## [1] "0.984375, 1, 0"
## [1] "0, 0, 1"
## [1] "0.984375, 1"
## [1] "0.992188, 1, 0"
## [1] "0, 0, 1"
## [1] "0.992188, 1"
## [1] "1, 1, 0"
## [1] "0, 0, 1"
## [1] "1, 1"## [1] 128## [1] 128The following line will convert the heightmap frame into JavaScript or JSON data and optionally print the results within HTML tags:
require(jsonlite)## Loading required package: jsonlitejsonHeightmap <- toJSON(heightmap)
# print without tabs so R markdown will add
# it to the DOM tree of the resulting page
cat(paste0(
'<div id="data_in_html">\n',
'<script type="application/json">\n', jsonHeightmap, '\n', '</script>\n',
'</div>'
))
The input and output test looks good, so time to work on a larger (medium sized) terrain image.
if (file.exists("data/terrain-medium.png")) {
medium_input <- "data/terrain-medium.png"
} else {
medium_input <- file.choose()
}
image <- data.frame(png::readPNG(medium_input))length(image[1,]) # width of the map## [1] 512length(image[,1]) # height of the map## [1] 512str(image)## 'data.frame': 512 obs. of 512 variables:
## $ X1 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X2 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X3 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X4 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X5 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X6 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X7 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X8 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X9 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X10 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X11 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X12 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X13 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X14 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X15 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X16 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X17 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X18 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X19 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X20 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X21 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X22 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X23 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X24 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X25 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X26 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X27 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X28 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X29 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X30 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X31 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X32 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X33 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X34 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X35 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X36 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X37 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X38 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X39 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X40 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X41 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X42 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X43 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X44 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X45 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X46 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X47 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X48 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X49 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X50 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X51 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X52 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X53 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X54 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X55 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X56 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X57 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X58 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X59 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X60 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X61 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X62 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X63 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X64 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X65 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X66 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X67 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X68 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X69 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X70 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X71 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X72 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X73 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X74 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X75 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X76 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X77 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X78 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X79 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X80 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X81 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X82 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X83 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X84 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X85 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X86 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X87 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X88 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X89 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X90 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X91 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X92 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X93 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X94 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X95 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X96 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X97 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X98 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ X99 : num 0 0 0 0 0 0 0 0 0 0 ...
## [list output truncated]Once the vertices, the normals, and the texture coordinates have been built for this new map, I will need indices to tie everything together. The sequence of the indices will trace the vertices into triangular faces:
mapTerrainCoords <- function (image_map, image_width, image_height) {
# make a 2.0 x 2.0 plane, starting from at (-1, -1, 0) ... z is up
heights <- matrix(nrow = image_width, ncol = image_height)
height_array <- array(dim = c(image_height, image_width))
vertices <- list()
normals <- list()
normal_array <- array(dim = c(image_height, image_width, 3))
textureCoords <- list()
# map heights
for (y in 1:image_height) {
for (x in 1:image_width) {
heights[y, x] <- round(image_map[y, x], 6)
}
}
# map vetices, normals, texture
i <- 0
for (y in 1:image_height) {
height_array_x <- c()
for (x in 1:image_width) {
i <- i + 1 # increment before to start on 1
height_array_x <- c(height_array_x , heights[y, x])
# vertices (x, y, z)
# png y-coordinate system is reverse of WebGL
vertices[[i]] <- c(2.0 * round((x / image_width - (1.0 / image_width) - 0.5), 6), 2.0 * round((y / image_height - (1.0 / image_height) - 0.5), 6), heights[(image_width + 1) - y, x] * DISPLACE_MULTIPLY) # z is up
# normals
normals[[i]] <- c(0.0, 0.0, 1.0)
# texture coordinates (s, t)
textureCoords[[i]] <- c(round((x / image_width - ((image_width - x) / (image_width * image_width))), 6), round(1.0 - (y / image_height - ((image_height - y) / (image_height * image_height))), 6)) # go to flip the y
}
# start mapping z normals
for (x in 1:image_width) {
normal_array[y, x,] <- c(0.0, 0.0, round(height_array_x[x], 6))
}
height_array[y,] <- height_array_x
}
total_points <- i
print(total_points)
print("heights:")
print(length(height_array[1,]) * length(height_array[,1]))
print(length(height_array[1,]))
print("vertices:")
print(length(vertices))
print(length(vertices[[1]]))
print("textureCoords:")
print(length(textureCoords))
print(length(textureCoords[[1]]))
# Now re-calculate x and y normals based on neighboring heightmap coords
i <- 0
for (y in 1:image_height) {
for (x in 1:image_width) {
i <- i + 1 # increment before to start on 1
# png y-coordinate system is reverse of WebGL
if (x < image_width) {
za <- normal_array[(image_width + 1) - y, x, 3]
zb <- normal_array[(image_width + 1) - y, x + 1, 3]
xa <- (za - zb) # / image_width
# print(paste0(za, " - ", zb, " = ", xa))
# normal_array[y, x,] <- c(round(xa, 6), 0.0, 0.0)
normal_array[(image_width + 1) - y, x,] <- c(round(xa, 6), normal_array[(image_width + 1) - y, x, 2], normal_array[(image_width + 1) - y, x, 3])
normals[[i]] <- normal_array[(image_width + 1) - y, x,]
}
if (y < image_height) {
za <- normal_array[(image_width + 1) - y, x, 3]
zb <- normal_array[(image_width + 1) - (y + 1), x, 3]
ya <- (za - zb) # / image_height
# print(paste0(za, " - ", zb, " = ", ya))
# normal_array[y, x,] <- c(0.0, round(ya, 6), 0.0)
normal_array[(image_width + 1) - y, x,] <- c(normal_array[(image_width + 1) - y, x, 1], round(ya, 6), normal_array[(image_width + 1) - y, x, 3])
normals[[i]] <- normal_array[(image_width + 1) - y, x,]
}
}
}
print("normals:")
print(length(normals))
print(length(normals[[1]]))
print(length(normal_array[,,1])) # total sets of normal coords
print(length(normal_array[,1,1])) # normal coords per image row
print(length(normal_array[1,1,])) # normal coordinate dimensions
list(
heights = height_array,
vertices = vertices,
normals = normals,
normal_array = normal_array,
textureCoords = textureCoords
)
}
image_width <- length(image[1,])
image_height <- length(image[, 1])
map <- mapTerrainCoords(image, image_width, image_height)## [1] 262144
## [1] "heights:"
## [1] 262144
## [1] 512
## [1] "vertices:"
## [1] 262144
## [1] 3
## [1] "textureCoords:"
## [1] 262144
## [1] 2
## [1] "normals:"
## [1] 262144
## [1] 3
## [1] 262144
## [1] 512
## [1] 3
Now I have some idea of what this is supposed to look like, so I can verify whether my indexing algorithm works…
currentRow <- 1
indices <- c()
indices <- c(indices, (image_width - 2))
indices <- c(indices, (image_width - 1 + image_width))
indices <- c(indices, (image_width - 1 + (image_width - 1)))
indices <- c(indices, (image_width - 1 + image_width))
indices <- c(indices, (image_width - 2))
indices <- c(indices, (image_width - 1))
print(indices)## [1] 510 1023 1022 1023 510 511
knitTriangleIndices <- function(img_width, img_height) {
ind <- c()
width <- img_width - 1
row <- 1
...
knitTriangleIndices(..., ...)
...
}
Hours later, I decide my force powers are not strong enough for recursion in R, hence the following for-loop.
knitTriangleIndices <- function(img_width, img_height) {
indices <- c()
width <- img_width - 1
row <- 1
for (r in 1:(img_height - 1)) {
offset <- (img_width * (row - 1))
while (width > 0) {
idx1 <- (width - 1) + offset
idx2 <- (width + img_width) + offset
idx3 <- (width + (img_width - 1)) + offset
idx4 <- (width + img_width) + offset
idx5 <- (width - 1) + offset
idx6 <- (width) + offset
indices <- c(indices, idx1, idx2, idx3, idx4, idx5, idx6)
width <- (width - 1)
}
width <- img_width - 1
row <- row + 1
}
indices
}terrain (heightmap) object that can be imported by @sveltejs/gl, with the form:
new Geometry({
position: {
data: new Float32Array([ /* array of vertices ... */ ]
.flat(Infinity)),
size: 3
},
normal: {
data: new Float32Array([ /* array of normals ... */ ]
.flat(Infinity)),
size: 3
},
uv: {
data: new Float32Array([ /* array of textureCoords ... */ ]
.flat(Infinity)),
size: 2
}
}, {
index: new Uint32Array([ /* array of indices returned by knitTriangleIndices */ ]
)
});
Now this turns out to be a ginormous MJS file (~ 20MB), so I will ultimately use the smaller heightmap as the basis of terrain object imported by @sveltejs/gl. However, I will use the higher density height data exported by the normalmap (the blue PNG above) as well as create a json file for reference and use it to place the markers on the terrain later:
jsonlite::write_json(heights, "data/planar-terrain-heights.json")
jsonlite::write_json(vertices, "data/planar-terrain-verts.json")
jsonlite::write_json(normals, "data/planar-terrain-norms.json")
jsonlite::write_json(textureCoords, "data/planar-terrain-uvs.json")
jsonlite::write_json(knitTriangleIndices(image_width, image_height), "data/planar-terrain-idx.json")