# R/utils-d20.R In trevorld/piecepack: Board Game Graphics

#### Defines functions write_d20_texturesave_d20_objd20_xyzd20_rot_to_topd20_rot_from_topd20TopGrob

```# https://mathworld.wolfram.com/RegularIcosahedron.html
# https://www.blocklayer.com/pyramid-calculator gives us pyramid side angle 37.4 degrees
# a = from vertex to adjacent vertex
# inradius = (3 * sqrt(3) + sqrt(15)) / 12) * a ~=  0.75576 * a

## d20 Top
d20TopGrob <- function(piece_side, suit, rank, cfg=pp_cfg(),
x=unit(0.5, "npc"), y=unit(0.5, "npc"), z=unit(0, "npc"),
angle=0, type="normal",
width=NA, height=NA, depth=NA,
op_scale=0, op_angle=45) {
cfg <- as_pp_cfg(cfg)

x <- convertX(x, "in", valueOnly = TRUE)
y <- convertY(y, "in", valueOnly = TRUE)
z <- convertX(z, "in", valueOnly = TRUE)
width <- convertX(width, "in", valueOnly = TRUE)
height <- convertY(height, "in", valueOnly = TRUE)
depth <- convertX(depth, "in", valueOnly = TRUE)

#### allow limited 3D rotation #281
axis_x <- 0
axis_y <- 0

xyz <- d20_xyz(suit, rank, cfg, x, y, z, angle, axis_x, axis_y, width, height, depth)
l_xyz <- list()
dfc <- data.frame(x = numeric(0), y = numeric(0), z = numeric(0))
for (i in 1:20) {
idx <- seq.int(3 * i - 2, length.out = 3)
dfc <- rbind(dfc, as.data.frame(xyz[idx]\$c))
}

op_ref <- Point2D\$new(as.data.frame(xyz\$c))\$translate_polar(op_angle + 180, 10 * xyz\$width)
xy_dists <- purrr::pmap_dbl(dfc, function(x, y, z) Point2D\$new(x, y)\$distance_to(op_ref))
dfc\$rank <- 1:20
dfc\$xy_dists <- xy_dists
dfc <- dfc[order(round(dfc\$z, 2), -xy_dists), ]

gl <- gList()
for (i in 1:nrow(dfc)) {
edge_rank <- dfc\$rank[i]
edge <- paste("d20_", edge_rank)
opt <- cfg\$get_piece_opt("die_face", suit, edge_rank)
gp <- gpar(col = opt\$border_color, lex = opt\$border_lex, fill = opt\$background_color)
idx <- seq.int(3 * edge_rank - 2, length.out = 3)
xyz_polygon <- xyz[idx]
xy_polygon <- xyz_polygon\$project_op(op_angle, op_scale)
xy_vp <- xy_vp_convex(xyz_polygon, op_scale, op_angle)
gl[[i]] <- at_ps_grob("die_face", suit, edge_rank, cfg, xy_vp, xy_polygon, name = edge)
}

# pre-compute grobCoords
coords_xyl <- as.list(as.data.frame(xyz\$project_op(op_angle, op_scale)\$convex_hull))

gTree(scale = 1,
coords_xyl = coords_xyl,
children=gl, cl=c("projected_rpg_die", "coords_xyl"))
}

# if `rank` on top figure out rotation so one on top instead
# currently just a fixed arrangement
d20_rot_from_top <- function(rank) {
a1 <- 180 - to_degrees(arccos(-sqrt(5)/3)) # 180 - dihedral angle
a2 <- 37.4 # equilateral pentagonal pyramid side (face) angle
# a <- 50
stopifnot(rank <= 20)
switch(rank,
diag(3), # 01
R_x(180) %*% R_z(180) %*% R_x(a1) %*% R_z(120), # 02
R_z(-120) %*% R_x(a2) %*% R_z(144) %*% R_x(-a2), # 03
R_z(120) %*% R_x(180) %*% R_z(-120) %*% R_x(a2) %*% R_z(-144) %*% R_x(-a2), # 04
R_z(120) %*% R_x(a2) %*% R_z(-144) %*% R_x(-a2) %*% R_z(120), # 05
R_x(180) %*% R_z(-120) %*% R_x(a2) %*% R_z(144) %*% R_x(-a2) %*% R_z(120), # 06
R_z(180) %*% R_x(a1) %*% R_z(-120), # 07
R_x(180) %*% R_z(180) %*% R_x(a1), # 08
R_z(120) %*% R_x(a2) %*% R_z(-144) %*% R_x(-a2) %*% R_z(-120), # 09
R_z(120) %*% R_x(a2) %*% R_z(-144) %*% R_x(-a2) %*% R_z(120) %*% R_x(180), # 10
R_z(-120) %*% R_x(a2) %*% R_z(144) %*% R_x(-a2) %*% R_z(-120), # 11
R_z(-120) %*% R_x(a2) %*% R_z(144) %*% R_x(-a2) %*% R_z(120) %*% R_x(180), # 12
R_z(180) %*% R_x(a1), # 13
R_x(180) %*% R_z(180) %*% R_x(a1) %*% R_z(-120), # 14
R_z(-120) %*% R_x(a2) %*% R_z(144) %*% R_x(-a2) %*% R_z(120), # 15
R_x(180) %*% R_z(120) %*% R_x(a2) %*% R_z(-144) %*% R_x(-a2) %*% R_z(120), # 16
R_z(120) %*% R_x(a2) %*% R_z(-144) %*% R_x(-a2), # 17
R_x(180) %*% R_z(-120) %*% R_x(a2) %*% R_z(144) %*% R_x(-a2), # 18
R_z(180) %*% R_x(a1) %*% R_z(120), # 19
R_x(180)) # 20
}

# if one on top figure out rotation so `rank` on top instead
d20_rot_to_top <- function(rank) {
a1 <- 180 - to_degrees(arccos(-sqrt(5)/3)) # 180 - dihedral angle
a2 <- 37.4 # equilateral pentagonal pyramid side (face) angle
stopifnot(rank <= 20)
switch(rank,
diag(3), # 01
R_z(-120) %*% R_x(-a1) %*% R_z(-180) %*% R_x(-180), # 02
R_x(a2) %*% R_z(-144) %*% R_x(-a2) %*% R_z(120), # 03
R_x(a2) %*% R_z(144) %*% R_x(-a2) %*% R_z(120) %*% R_x(-180) %*% R_z(-120), # 04
R_z(-120) %*% R_x(a2) %*% R_z(144) %*% R_x(-a2) %*% R_z(-120), # 05
R_z(-120) %*% R_x(a2) %*% R_z(-144) %*% R_x(-a2) %*% R_z(120) %*% R_x(-180), # 06
R_z(120) %*% R_x(-a1) %*% R_z(-180), # 07
R_x(-a1) %*% R_z(-180) %*% R_x(-180), # 08
R_z(120) %*% R_x(a2) %*% R_z(144) %*% R_x(-a2) %*% R_z(-120), # 09
R_x(-180) %*% R_z(-120) %*% R_x(a2) %*% R_z(144) %*% R_x(-a2) %*% R_z(-120), # 10
R_z(120) %*% R_x(a2) %*% R_z(-144) %*% R_x(-a2) %*% R_z(120), # 11
R_x(-180) %*% R_z(-120) %*% R_x(a2) %*% R_z(-144) %*% R_x(-a2) %*% R_z(120), # 12
R_x(-a1) %*% R_z(180), # 13
R_z(120) %*% R_x(-a1) %*% R_z(-180) %*% R_x(-180), # 14
R_z(-120) %*% R_x(a2) %*% R_z(-144) %*% R_x(-a2) %*% R_z(120), # 15
R_z(-120) %*% R_x(a2) %*% R_z(144) %*% R_x(-a2) %*% R_z(-120) %*% R_x(-180), # 16
R_x(a2) %*% R_z(144) %*% R_x(-a2) %*% R_z(-120), # 17
R_x(a2) %*% R_z(-144) %*% R_x(-a2) %*% R_z(120) %*% R_x(-180), # 18
R_z(-120) %*% R_x(-a1) %*% R_z(-180), # 19
R_x(-180)) # 20
}

d20_xyz <- function(suit, rank, cfg,
x, y, z,
angle, axis_x, axis_y,
width, height, depth) {
pc <- Point3D\$new(x, y, z)
R_rank <- d20_rot_to_top(rank)
xs <- numeric(0)
ys <- numeric(0)
zs <- numeric(0)
xyz_t <- Point3D\$new(convex_xy(3, 90), z = 0.0)\$translate(-0.5, -0.5, 0.5)\$dilate(width, height, depth)
for (i in 1:20) {
R_i <- d20_rot_from_top(i)
xyz_i <- xyz_t\$clone()\$rotate(R_i %*% R_rank)
xs <- append(xs, xyz_i\$x)
ys <- append(ys, xyz_i\$y)
zs <- append(zs, xyz_i\$z)
}

R <- AA_to_R(angle, axis_x, axis_y)
Point3D\$new(xs, ys, zs)\$rotate(R)\$translate(pc)
}

save_d20_obj <- function(piece_side, suit, rank, cfg,
x, y, z, angle, axis_x, axis_y,
width, height, depth,
filename, scale, res) {
cfg <- as_pp_cfg(cfg)
opt <- cfg\$get_piece_opt(piece_side, suit, rank)

xyz <- d20_xyz(suit, rank, cfg,
x, y, z,
angle, axis_x, axis_y,
width, height, depth)

cxy <- convex_xy(3, 90)
xy_vt <- list(x = rep(cxy\$x / 4, 20) + rep(rep(0:3/4, each = 3), 5),
y = rep(cxy\$y / 5, 20) + rep(rep(4:0/5, each = 3), each = 4))

# textured face elements
f <- list()
for (i in 1:20) {
idx <- seq.int(3 * i - 2, length.out = 3)
f[[i]] <- list(v = idx, vt = idx)
}

ext <- tools::file_ext(filename)
mtl_filename <- gsub(paste0("\\.", ext, "\$"), ".mtl", filename)
png_filename <- gsub(paste0("\\.", ext, "\$"), ".png", filename)

write_obj(filename, v = xyz, vt = xy_vt, f = f)
write_d20_texture("die_face", suit, rank, cfg, filename = png_filename, res = res)

invisible(list(obj = filename, mtl = mtl_filename, png = png_filename))
}

write_d20_texture <- function(piece_side = "die_face", suit = 1, rank = 1, cfg = pp_cfg(),
..., filename = tempfile(fileext = ".png"), res = 72) {

current_dev <- grDevices::dev.cur()
if (current_dev > 1) on.exit(grDevices::dev.set(current_dev))
width <- cfg\$get_width("die_face", suit, rank)

args <- list(filename = filename, height = 5 * width, width = 4 * width,
units = "in", res = res, bg = "transparent")
if (capabilities("cairo"))
args\$type <- "cairo"
do.call(grDevices::png, args)

xs <- rep(1:4 / 4 - 1/8, 5)
ys <- rep(5:1 / 5 - 1/10, each = 4)
for (i in 1:20) {
pushViewport(viewport(x = xs[i], width = 1/4, y = ys[i], height = 1/5))
draw_piece_and_bleed("die_face", suit, i, cfg)
popViewport()
}

grDevices::dev.off()
invisible(filename)
}
```
trevorld/piecepack documentation built on May 20, 2024, 4:31 a.m.