Calculate axis-aligned bounding box for set of game pieces

Calculate axis-aligned bounding box (AABB) for set of game pieces with and without an “oblique projection”.

Usage

aabb_piece(
  df,
  cfg = getOption("piecepackr.cfg", pp_cfg()),
  envir = getOption("piecepackr.envir"),
  op_scale = getOption("piecepackr.op_scale", 0),
  op_angle = getOption("piecepackr.op_angle", 45),
  ...
)

Arguments

df: A data frame of game piece information with (at least) the named columns “piece_side”, “x”, and “y”.
cfg: Piecepack configuration list or pp_cfg object, a list of pp_cfg objects, or a character vector referring to names in envir or a character vector referring to object names that can be retrieved by base::dynGet().
envir: Environment (or named list) containing configuration list(s).
op_scale: How much to scale the depth of the piece in the oblique projection (viewed from the top of the board). 0 (the default) leads to an “orthographic” projection, 0.5 is the most common scale used in the “cabinet” projection, and 1.0 is the scale used in the “cavalier” projection.
op_angle: What is the angle of the oblique projection? Has no effect if op_scale is 0.
...: Ignored

Value

A named list of ranges with five named elements x, y, and z for the axis-aligned bounding cube in xyz-space plus x_op and y_op for the axis-aligned bounding box of the “oblique projection” onto the xy plane.

Details

The “oblique projection” of a set of \((x,y,z)\) points onto the xy-plane is \((x + \lambda * z * cos(\alpha), y + \lambda * z * sin(\alpha))\) where \(\lambda\) is the scale factor and \(\alpha\) is the angle.

Examples

 df_tiles <- data.frame(piece_side="tile_back", x=0.5+c(3,1,3,1), y=0.5+c(3,3,1,1),
                        suit=NA, angle=NA, z=NA, stringsAsFactors=FALSE)
 df_coins <- data.frame(piece_side="coin_back", x=rep(4:1, 4), y=rep(4:1, each=4),
                        suit=1:16%%2+rep(c(1,3), each=8),
                        angle=rep(c(180,0), each=8), z=1/4+1/16, stringsAsFactors=FALSE)
 df <- rbind(df_tiles, df_coins)

 aabb_piece(df, op_scale = 0)
#> $x
#> [1] 0.5 4.5
#> 
#> $y
#> [1] 0.5 4.5
#> 
#> $z
#> [1] 0.000 0.375
#> 
#> $x_op
#> [1] 0.5 4.5
#> 
#> $y_op
#> [1] 0.5 4.5
#> 
 aabb_piece(df, op_scale = 1, op_angle = 45)
#> $x
#> [1] 0.5 4.5
#> 
#> $y
#> [1] 0.5 4.5
#> 
#> $z
#> [1] 0.000 0.375
#> 
#> $x_op
#> [1] 0.500000 4.676777
#> 
#> $y_op
#> [1] 0.500000 4.676777
#> 
 aabb_piece(df, op_scale = 1, op_angle = -90)
#> $x
#> [1] 0.5 4.5
#> 
#> $y
#> [1] 0.5 4.5
#> 
#> $z
#> [1] 0.000 0.375
#> 
#> $x_op
#> [1] 0.5 4.5
#> 
#> $y_op
#> [1] 0.25 4.50
#>