In {affiner} angles are represented by the angle() class:
Supports the following angular units (note we ignore any punctuation and space characters as well as any trailing s’s e.g. “half turns” will be treated as equivalent to “halfturn”):
degrees(), gradians(), pi_radians(), radians(), turns() are convenience wrappers around as_angle.() that specifies the angular unit.
One can use the affiner_angular_unit global option to set the default angular unit used by this package from “degrees” to “gradians”, (multiples of) “pi-radians”, “radians”, or “turns”.
Use is_congruent() to check if two angles are congruent modulo full turns.
library("affiner")
as_angle(90, "degrees") + turns(1)## <angle<degrees>[1]>
## [1] 450°is_congruent(degrees(180), radians(pi))## [1] TRUEas.numeric(turns(1/3), "radians")## [1] 2.094395{affiner} provides several angle() class aware trigonometric functions:
sine(), cosine(), tangent(), secant(), cosecant(), cotangent(),arcsine(), arccosine(), arctangent(), arcsecant(), arccosecant(), and arccotangent(). arcsine() and arccosine() also feature a tolerance value so that values that exceed the 1 / -1 cutoffs by a small tolerance are rounded to those values.sin(), cos(), and tan() on angle() objects.library("affiner")
sin(2 * pi)## [1] -2.449294e-16sine(degrees(360))## [1] 0arctangent(x = 0, y = 1)## <angle<degrees>[1]>
## [1] 90°In {affiner} 2D Coordinates are represented by a Coord2D R6 class:
Create Coord2D objects with as_coord2d()
Coord2D R6 objects supports several affine transformation methods that can be chained:
permute()project()reflect()rotate()scale()shear()translate()transform(){affiner} affine transformations are post-multiplied so affine transformations can be applied in an intuitive order.abs() computes Euclidean norm and distance2d() computes Euclidean distancesconvex_hull2d() computes the convex hull.range() computes the axis-aligned bounding box ranges.# Cartesian coordinates
library("affiner")
p <- as_coord2d(x = 1:10, y = 1:10)
print(p)## <Coord2D[10]>
## x y w
## [1,] 1 1 1
## [2,] 2 2 1
## [3,] 3 3 1
## [4,] 4 4 1
## [5,] 5 5 1
## [6,] 6 6 1
## [7,] 7 7 1
## [8,] 8 8 1
## [9,] 9 9 1
## [10,] 10 10 1p2 <- p$
clone()$
scale(x = 0.5)$
rotate(degrees(90))$
reflect(as_line2d("y-axis"))$
translate(as_coord2d(x = 0.5, y = 0.5))$
print()## <Coord2D[10]>
## x y w
## [1,] 1.0 1.0 1
## [2,] 1.5 1.5 1
## [3,] 2.0 2.0 1
## [4,] 2.5 2.5 1
## [5,] 3.0 3.0 1
## [6,] 3.5 3.5 1
## [7,] 4.0 4.0 1
## [8,] 4.5 4.5 1
## [9,] 5.0 5.0 1
## [10,] 5.5 5.5 1# Polar coordinates
theta <- degrees(seq(0, 300, by = 60))
radius <- 1
p <- as_coord2d(theta, radius = radius)
is_congruent(as_angle(p), theta) |> all()## [1] TRUEis_congruent(abs(p), radius) |> all()## [1] TRUEIn {affiner} 3D Coordinates are represented by a Coord3D R6 class:
Create Coord3D objects with as_coord3d()
Coord3D R6 objects supports several affine transformation methods that can be chained:
permute()project()reflect()rotate()scale()shear()translate()transform(){affiner} affine transformations are post-multiplied so affine transformations can be applied in an intuitive order.abs() computes Euclidean norm and distance3d() computes Euclidean distancesrange() computes the axis-aligned bounding box ranges.cross_product3d() computes cross products (* computes inner products).# Cartesian coordinates
library("affiner")
p <- as_coord3d(x = 1:10, y = 1:10, z = 1:10)
print(p)## <Coord3D[10]>
## x y z w
## [1,] 1 1 1 1
## [2,] 2 2 2 1
## [3,] 3 3 3 1
## [4,] 4 4 4 1
## [5,] 5 5 5 1
## [6,] 6 6 6 1
## [7,] 7 7 7 1
## [8,] 8 8 8 1
## [9,] 9 9 9 1
## [10,] 10 10 10 1p2 <- p$
clone()$
scale(z = 0.5)$
rotate(axis = as_coord3d("z-axis"), theta = degrees(90))$
reflect(as_plane3d("yz-plane"))$
shear(xy_shear = 0.5)$
translate(as_coord3d(x = 0.5, y = 0.5, z = 0.5))$
print()## <Coord3D[10]>
## x y z w
## [1,] 2.0 1.5 1.0 1
## [2,] 3.5 2.5 1.5 1
## [3,] 5.0 3.5 2.0 1
## [4,] 6.5 4.5 2.5 1
## [5,] 8.0 5.5 3.0 1
## [6,] 9.5 6.5 3.5 1
## [7,] 11.0 7.5 4.0 1
## [8,] 12.5 8.5 4.5 1
## [9,] 14.0 9.5 5.0 1
## [10,] 15.5 10.5 5.5 1# Spherical coordinates
inclination <- as_angle(p, type = "inclination")
azimuth <- as_angle(p, type = "azimuth")
radius <- abs(p)
ps <- as_coord3d(azimuth, radius = radius, inclination = inclination)
all.equal(p, ps)## [1] TRUE# Cylindrical coordinates
radius <- as_coord2d(p, plane = "xy-plane") |> abs()
pc <- as_coord3d(azimuth, radius = radius, z = p$z)
all.equal(p, pc)## [1] TRUE{affiner} can project Coord3D objects to Coord2D objects using orthographic/axonometric and oblique projections:
For a multiview/primary orthographic projection onto the xy-plane use as_coord2d(x)
For a multiview/primary orthographic projection onto the xz-plane use as_coord2d(x, permutation = "xzy")
For a “cabinet” oblique projection onto the xy-plane use as_coord2d(x, scale = 0.5)
For a “cabinet” oblique projection onto the xz-plane use as_coord2d(x, permutation = "xzy", scale = 0.5)
For other oblique projections manipulate the scale parameter (usually from 0.5 to 1.0) and the alpha angle parameter (usually from 30° to 45°).
For one “isometric” axonometric projection one can use
x$
clone()$
translate(-mean(x)$
rotate("z-axis", degrees(45))$
rotate("x-axis", degrees(-90 + 35.264)) |>
as_coord2d()Other axonometric projections can be achieved with the right 3D rotations
See vignette("affiner", package = "affiner") for some visual examples
Recall one can use “scale” affine transformation to flip signs of x/y/z axes and “permute” affine transformation to switch order of x/y/z coordinates