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Type:	Package
Title:	A Finer Way to Render 3D Illustrated Objects in 'grid' UsingAffine Transformations
Version:	0.1.3
Description:	Dilate, permute, project, reflect, rotate, shear, and translate 2D and 3D points. Supports parallel projections including oblique projections such as the cabinet projection as well as axonometric projections such as the isometric projection. Use 'grid's "affine transformation" feature to render illustrated flat surfaces.
URL:	https://trevorldavis.com/R/affiner/
BugReports:	https://github.com/trevorld/affiner/issues
License:	MIT + file LICENSE
Imports:	graphics, grDevices, grid, R6, utils
Suggests:	aRtsy, ggplot2, gridpattern, gtable, knitr, ragg (≥ 1.3.3),rgl, rlang, rmarkdown, stats, testthat (≥ 3.0.0), vdiffr,withr
VignetteBuilder:	knitr, ragg, rmarkdown
Encoding:	UTF-8
RoxygenNote:	7.3.1
Config/testthat/edition:	3
NeedsCompilation:	no
Packaged:	2024-12-02 06:12:41 UTC; trevorld
Author:	Trevor L. Davis [aut, cre]
Maintainer:	Trevor L. Davis <trevor.l.davis@gmail.com>
Repository:	CRAN
Date/Publication:	2024-12-02 06:40:02 UTC

affiner: A Finer Way to Render 3D Illustrated Objects in 'grid' Using Affine Transformations

Description

Dilate, permute, project, reflect, rotate, shear, and translate 2D and 3D points. Supports parallel projections including oblique projections such as the cabinet projection as well as axonometric projections such as the isometric projection. Use 'grid's "affine transformation" feature to render illustrated flat surfaces.

Package options

The following affiner function arguments may be set globally viabase::options():

affiner_angular_unit

The default for theunit argument used byangle() andas_angle().The default for this option is "degrees".

affiner_grid_unit

The default for theunit argument used byaffine_settings().The default for this option is "inches".

The followingcli options may also be of interest:

cli.unicode

Whether UTF-8 character support should be assumed.Along withl10n_info() used to determine the default of theuse_unicode argument offormat.angle() andprint.angle().

Author(s)

Maintainer: Trevor L. Davistrevor.l.davis@gmail.com (ORCID)

See Also

Useful links:

• https://trevorldavis.com/R/affiner/

• Report bugs athttps://github.com/trevorld/affiner/issues

1D coordinate vector R6 Class

Description

Coord1D is anR6::R6Class() object representing two-dimensional pointsrepresented by Cartesian Coordinates.

Active bindings

Methods

Public methods

• Coord1D$new()

• Coord1D$print()

• Coord1D$project()

• Coord1D$reflect()

• Coord1D$scale()

• Coord1D$translate()

• Coord1D$transform()

• Coord1D$clone()

Methodnew()

Usage

Coord1D$new(xw)

Arguments

Methodprint()

Usage

Coord1D$print(n = NULL, ...)

Arguments

Methodproject()

Usage

Coord1D$project(point = as_point1d("origin"), ...)

Arguments

Methodreflect()

Usage

Coord1D$reflect(point = as_point1d("origin"), ...)

Arguments

Methodscale()

Usage

Coord1D$scale(x_scale = 1)

Arguments

Methodtranslate()

Usage

Coord1D$translate(x = as_coord1d(0), ...)

Arguments

Methodtransform()

Usage

Coord1D$transform(mat = transform1d())

Arguments

Methodclone()

The objects of this class are cloneable with this method.

Usage

Coord1D$clone(deep = FALSE)

Arguments

Examples

p <- as_coord1d(x = rnorm(100, 2))print(p, n = 10L)pc <- mean(p) # Centroid# method chained affine transformation matrices are auto-pre-multipliedp$  translate(-pc)$  reflect("origin")$  print(n = 10L)

2D coordinate vector R6 Class

Description

Coord2D is anR6::R6Class() object representing two-dimensional pointsrepresented by Cartesian Coordinates.

Active bindings

Methods

Public methods

• Coord2D$new()

• Coord2D$permute()

• Coord2D$print()

• Coord2D$project()

• Coord2D$reflect()

• Coord2D$rotate()

• Coord2D$scale()

• Coord2D$shear()

• Coord2D$translate()

• Coord2D$transform()

• Coord2D$clone()

Methodnew()

Usage

Coord2D$new(xyw)

Arguments

Methodpermute()

Usage

Coord2D$permute(permutation = c("xy", "yx"))

Arguments

Methodprint()

Usage

Coord2D$print(n = NULL, ...)

Arguments

Methodproject()

Usage

Coord2D$project(line = as_line2d("x-axis"), ..., scale = 0)

Arguments

Methodreflect()

Usage

Coord2D$reflect(line = as_line2d("x-axis"), ...)

Arguments

Methodrotate()

Usage

Coord2D$rotate(theta = angle(0), ...)

Arguments

Methodscale()

Usage

Coord2D$scale(x_scale = 1, y_scale = x_scale)

Arguments

Methodshear()

Usage

Coord2D$shear(xy_shear = 0, yx_shear = 0)

Arguments

Methodtranslate()

Usage

Coord2D$translate(x = as_coord2d(0, 0), ...)

Arguments

Methodtransform()

Usage

Coord2D$transform(mat = transform2d())

Arguments

Methodclone()

The objects of this class are cloneable with this method.

Usage

Coord2D$clone(deep = FALSE)

Arguments

Examples

p <- as_coord2d(x = rnorm(100, 2), y = rnorm(100, 2))print(p, n = 10)pc <- mean(p) # Centroid# method chained affine transformation matrices are auto-pre-multipliedp$  translate(-pc)$  shear(x = 1, y = 0)$  reflect("x-axis")$  rotate(90, "degrees")$  print(n = 10)

3D coordinate vector R6 Class

Description

Coord3D is anR6::R6Class() object representing three-dimensional pointsrepresented by Cartesian Coordinates.

Active bindings

Methods

Public methods

• Coord3D$new()

• Coord3D$permute()

• Coord3D$print()

• Coord3D$project()

• Coord3D$reflect()

• Coord3D$rotate()

• Coord3D$scale()

• Coord3D$shear()

• Coord3D$translate()

• Coord3D$transform()

• Coord3D$clone()

Methodnew()

Usage

Coord3D$new(xyzw)

Arguments

Methodpermute()

Usage

Coord3D$permute(permutation = c("xyz", "xzy", "yxz", "yzx", "zyx", "zxy"))

Arguments

Methodprint()

Usage

Coord3D$print(n = NULL, ...)

Arguments

Methodproject()

Usage

Coord3D$project(  plane = as_plane3d("xy-plane"),  ...,  scale = 0,  alpha = angle(45, "degrees"))

Arguments

Methodreflect()

Usage

Coord3D$reflect(plane = as_plane3d("xy-plane"), ...)

Arguments

Methodrotate()

Usage

Coord3D$rotate(axis = as_coord3d("z-axis"), theta = angle(0), ...)

Arguments

Methodscale()

Usage

Coord3D$scale(x_scale = 1, y_scale = x_scale, z_scale = x_scale)

Arguments

Methodshear()

Usage

Coord3D$shear(  xy_shear = 0,  xz_shear = 0,  yx_shear = 0,  yz_shear = 0,  zx_shear = 0,  zy_shear = 0)

Arguments

Methodtranslate()

Usage

Coord3D$translate(x = as_coord3d(0, 0, 0), ...)

Arguments

Methodtransform()

Usage

Coord3D$transform(mat = transform3d())

Arguments

Methodclone()

The objects of this class are cloneable with this method.

Usage

Coord3D$clone(deep = FALSE)

Arguments

Examples

p <- as_coord3d(x = rnorm(100, 2), y = rnorm(100, 2), z = rnorm(100, 2))print(p, n = 10)pc <- mean(p) # Centroid# method chained affine transformation matrices are auto-pre-multipliedp$  translate(-pc)$  reflect("xy-plane")$  rotate("z-axis", degrees(90))$  print(n = 10)

2D lines R6 Class

Description

Line2D is anR6::R6Class() object representing two-dimensional lines.

Public fields

Methods

Public methods

• Line2D$new()

• Line2D$print()

• Line2D$clone()

Methodnew()

Usage

Line2D$new(a, b, c)

Arguments

Methodprint()

Usage

Line2D$print(n = NULL, ...)

Arguments

Methodclone()

The objects of this class are cloneable with this method.

Usage

Line2D$clone(deep = FALSE)

Arguments

Examples

p1 <- as_coord2d(x = 5, y = 10)p2 <- as_coord2d(x = 7, y = 12)theta <- degrees(45)as_line2d(theta, p1)as_line2d(p1, p2)

3D planes R6 Class

Description

Plane3D is anR6::R6Class() object representing three-dimensional planes.

Public fields

Methods

Public methods

• Plane3D$new()

• Plane3D$print()

• Plane3D$clone()

Methodnew()

Usage

Plane3D$new(a, b, c, d)

Arguments

Methodprint()

Usage

Plane3D$print(n = NULL, ...)

Arguments

Methodclone()

The objects of this class are cloneable with this method.

Usage

Plane3D$clone(deep = FALSE)

Arguments

1D points R6 Class

Description

Point1D is anR6::R6Class() object representing one-dimensional points.

Public fields

Methods

Public methods

• Point1D$new()

• Point1D$print()

• Point1D$clone()

Methodnew()

Usage

Point1D$new(a, b)

Arguments

Methodprint()

Usage

Point1D$print(n = NULL, ...)

Arguments

Methodclone()

The objects of this class are cloneable with this method.

Usage

Point1D$clone(deep = FALSE)

Arguments

Examples

p1 <- as_point1d(a = 1, b = 5)

Compute Euclidean norm

Description

abs() computes the Euclidean norm forCoord2D class objects andCoord3D class objects.

Usage

## S3 method for class 'Coord1D'abs(x)## S3 method for class 'Coord2D'abs(x)## S3 method for class 'Coord3D'abs(x)

Arguments

Value

A numeric vector

Examples

  z <- complex(real = 1:4, imaginary = 1:4)  p <- as_coord2d(z)  abs(p) # Euclidean norm  # Less efficient ways to calculate same Euclidean norms  sqrt(p * p) # `*` dot product  distance2d(p, as_coord2d(0, 0, 0))  # In {base} R `abs()` calculates Euclidean norm of complex numbers  all.equal(abs(p), abs(z))  all.equal(Mod(p), Mod(z))  p3 <- as_coord3d(x = 1:4, y = 1:4, z = 1:4)  abs(p3)

Affine transformation grob

Description

affineGrob() is a grid grob function to facilitateusing the group affine transformation features introduced in R 4.2.

Usage

affineGrob(  grob,  vp_define = NULL,  transform = NULL,  vp_use = NULL,  name = NULL,  gp = grid::gpar(),  vp = NULL)grid.affine(...)

Arguments

Details

Not all graphics devices provided bygrDevices or other R packages support theaffine transformation feature introduced in R 4.2.IfisTRUE(getRversion() >= '4.2.0') then the active graphics device should support this feature ifisTRUE(grDevices::dev.capabilities()$transformations).In particular the following graphics devices should support the affine transformation feature:

• R'sgrDevices::pdf() device

• R's 'cairo' devices e.g.grDevices::cairo_pdf(),grDevices::png(type = 'cairo'),grDevices::svg(),grDevices::x11(type = 'cairo'), etc. IfisTRUE(capabilities('cairo')) then R was compiled with support for the 'cairo' devices .

• R's 'quartz' devices (since R 4.3.0) e.g.grDevices::quartz(),grDevices::png(type = 'quartz'), etc. IfisTRUE(capabilities('aqua')) then R was compiled with support for the 'quartz' devices (generally onlyTRUE on macOS systems).

• ragg's devices (since v1.3.0) e.g.ragg::agg_png(),ragg::agg_capture(), etc.

Value

Agrid::gTree() (grob) object of class "affine".As a side effectgrid.affine() draws to the active graphics device.

See Also

Seeaffine_settings() for computing goodtransform andvp_use settings.Seehttps://www.stat.auckland.ac.nz/~paul/Reports/GraphicsEngine/groups/groups.htmlfor more information about the group affine transformation feature.SeeisocubeGrob() which wraps this function to render isometric cubes.

Examples

if (require("grid")) {  grob <- grobTree(rectGrob(gp = gpar(fill = "blue", col = NA)),                   circleGrob(gp=gpar(fill="yellow", col = NA)),                   textGrob("RSTATS", gp=gpar(fontsize=32)))  grid.newpage()  pushViewport(viewport(width=unit(4, "in"), height=unit(2, "in")))  grid.draw(grob)  popViewport()}if (require("grid") &&    getRversion() >= "4.2.0" &&    isTRUE(dev.capabilities()$transformations)) {  # Only works if active graphics device supports affine transformations  # such as `png(type="cairo")` on R 4.2+  vp_define <- viewport(width=unit(2, "in"), height=unit(2, "in"))  affine <- affineGrob(grob, vp_define=vp_define)  grid.newpage()  pushViewport(viewport(width=unit(4, "in"), height=unit(2, "in")))  grid.draw(affine)  popViewport()}if (require("grid") &&    getRversion() >= "4.2.0" &&    isTRUE(dev.capabilities()$transformations)) {  # Only works if active graphics device supports affine transformations  # such as `png(type="cairo")` on R 4.2+  settings <- affine_settings(xy = list(x = c(3/3, 2/3, 0/3, 1/3),                                        y = c(2/3, 1/3, 1/3, 2/3)),                              unit = "snpc")  affine <- affineGrob(grob,                       vp_define = vp_define,                       transform = settings$transform,                       vp_use = settings$vp)  grid.newpage()  grid.draw(affine)}

Computegrid affine transformation feature viewports and transformation functions

Description

affine_settings() computesgrid group affine transformation feature viewport and transformationfunction settings given the (x,y) coordinates of the corners of theaffine transformed "viewport" one wishes to draw in.

Usage

affine_settings(  xy = data.frame(x = c(0, 0, 1, 1), y = c(1, 0, 0, 1)),  unit = getOption("affiner_grid_unit", "inches"))

Arguments

Value

A named list with the following group affine transformation feature viewportand functions settings:

transform

An affine transformation function to pass toaffineGrob() oruseGrob().IfgetRversion() is less than"4.2.0" will instead beNULL.

vp

Agrid::viewport() object to pass toaffineGrob() oruseGrob().

sx

x-axis sx factor

flipX

whether the affine transformed "viewport" is "flipped" horizontally

x

x-coordinate for viewport

y

y-coordinate for viewport

width

Width of viewport

height

Height of viewport

default.units

Defaultgrid::unit() for viewport

angle

angle for viewport

Usage in other packages

To avoid taking a dependency onaffiner you may copy the source ofaffine_settings()into your own package under the permissive Unlicense. Either useusethis::use_standalone("trevorld/affiner", "standalone-affine-settings.r") orcopy the filestandalone-affine-settings.r into yourR directory and addgridto theImports of yourDESCRIPTION file.

See Also

Intended for use withaffineGrob() andgrid::useGrob().Seehttps://www.stat.auckland.ac.nz/~paul/Reports/GraphicsEngine/groups/groups.htmlfor more information about the group affine transformation feature.

Examples

if (require("grid")) {  grob <- grobTree(rectGrob(gp = gpar(fill = "blue", col = NA)),                   circleGrob(gp=gpar(fill="yellow", col = NA)),                   textGrob("RSTATS", gp=gpar(fontsize=32)))  grid.newpage()  pushViewport(viewport(width=unit(4, "in"), height=unit(2, "in")))  grid.draw(grob)  popViewport()}if (require("grid") &&    getRversion() >= "4.2.0" &&    isTRUE(dev.capabilities()$transformations)) {  # Only works if active graphics device supports affine transformations  # such as `png(type="cairo")` on R 4.2+  vp_define <- viewport(width=unit(2, "in"), height=unit(2, "in"))  settings <- affine_settings(xy = list(x = c(1/3, 0/3, 2/3, 3/3),                                        y = c(2/3, 1/3, 1/3, 2/3)),                              unit = "snpc")  affine <- affineGrob(grob,                       vp_define=vp_define,                       transform = settings$transform,                       vp_use = settings$vp)  grid.newpage()  grid.draw(affine)}if (require("grid") &&    getRversion() >= "4.2.0" &&    isTRUE(dev.capabilities()$transformations)) {  # Only works if active graphics device supports affine transformations  # such as `png(type="cairo")` on R 4.2+  settings <- affine_settings(xy = list(x = c(3/3, 2/3, 0/3, 1/3),                                        y = c(2/3, 1/3, 1/3, 2/3)),                              unit = "snpc")  affine <- affineGrob(grob,                       vp_define=vp_define,                       transform = settings$transform,                       vp_use = settings$vp)  grid.newpage()  grid.draw(affine)}

Get affiner options

Description

affiner_options() returns theaffiner package's global options.

Usage

affiner_options(..., default = FALSE)

Arguments

Value

A list of option values.Note this functiondoes not set option values itself butthis list can be passed tooptions(),withr::local_options(), orwithr::with_options().

See Also

affiner for a high-level description of relevant global options.

Examples

  affiner_options()  affiner_options(default = TRUE)  affiner_options(affiner_angular_unit = "pi-radians")

Angle vectors

Description

angle() creates angle vectors with user specified angular unit.aroundas_angle() for those angular units.

Usage

angle(x = numeric(), unit = getOption("affiner_angular_unit", "degrees"))degrees(x)gradians(x)pi_radians(x)radians(x)turns(x)

Arguments

Value

A numeric vector of class "angle".Its "unit" attribute is a standardized string of the specified angular unit.

See Also

as_angle(),angular_unit(), andangle-methods.https://en.wikipedia.org/wiki/Angle#Units for more information about angular units.

Examples

  # Different representations of the "same" angle  angle(180, "degrees")  angle(pi, "radians")  angle(0.5, "turns")  angle(200, "gradians")  pi_radians(1)  a1 <- angle(180, "degrees")  angular_unit(a1)  is_angle(a1)  as.numeric(a1, "radians")  cos(a1)  a2 <- as_angle(a1, "radians")  angular_unit(a2)  is_congruent(a1, a2)

Implemented base methods for angle vectors

Description

We implemented methods for several base generics for theangle() vectors.

Usage

## S3 method for class 'angle'as.double(x, unit = angular_unit(x), ...)## S3 method for class 'angle'as.complex(x, modulus = 1, ...)## S3 method for class 'angle'format(x, unit = angular_unit(x), ..., use_unicode = is_utf8_output())## S3 method for class 'angle'print(x, unit = angular_unit(x), ..., use_unicode = is_utf8_output())## S3 method for class 'angle'abs(x)

Arguments

Details

• MathematicalOps (in particular+ and-)for two angle vectors will (if necessary)set the second vector'sangular_unit() to match the first.

• as.numeric() takes aunit argument which can be used to convert angles into other angular unitse.g.angle(x, "degrees") |> as.numeric("radians") to cast a numeric vectorx from degrees to radians.

• abs() will calculate the angle modulo full turns.

• Useis_congruent() to test if two angles are congruent instead of== orall.equal().

• Not all implemented methods are documented here and sinceangle() is anumeric() class many other S3 genericsbesides the explicitly implemented ones should also work with it.

Value

Typical values as usually returned by these base generics.

Examples

  # Two "congruent" angles  a1 <- angle(180, "degrees")  a2 <- angle(pi, "radians")  print(a1)  print(a1, unit = "radians")  print(a1, unit = "pi-radians")  cos(a1)  sin(a1)  tan(a1)  # mathematical operations will coerce second `angle()` object to  # same `angular_unit()` as the first one  a1 + a2  a1 - a2  as.numeric(a1)  as.numeric(a1, "radians")  as.numeric(a1, "turns")  # Use `is_congruent()` to check if two angles are "congruent"  a1 == a2  isTRUE(all.equal(a1, a2))  is_congruent(a1, a2)  is_congruent(a1, a2, mod_turns = FALSE)  a3 <- angle(-180, "degrees") # Only congruent modulus full turns  a1 == a3  isTRUE(all.equal(a1, a2))  is_congruent(a1, a3)  is_congruent(a1, a3, mod_turns = FALSE)

Get/set angular unit of angle vectors

Description

angular_unit() gets/sets the angular unit ofangle() vectors.

Usage

angular_unit(x)angular_unit(x) <- value

Arguments

Value

angular_unit() returns a string ofx's angular unit.

Examples

a <- angle(seq(0, 360, by = 90), "degrees")angular_unit(a)print(a)angular_unit(a) <- "turns"angular_unit(a)print(a)

Cast to angle vector

Description

as_angle() casts to anangle() vector

Usage

as_angle(x, unit = getOption("affiner_angular_unit", "degrees"), ...)## S3 method for class 'angle'as_angle(x, unit = getOption("affiner_angular_unit", "degrees"), ...)## S3 method for class 'character'as_angle(x, unit = getOption("affiner_angular_unit", "degrees"), ...)## S3 method for class 'complex'as_angle(x, unit = getOption("affiner_angular_unit", "degrees"), ...)## S3 method for class 'Coord2D'as_angle(x, unit = getOption("affiner_angular_unit", "degrees"), ...)## S3 method for class 'Coord3D'as_angle(  x,  unit = getOption("affiner_angular_unit", "degrees"),  type = c("azimuth", "inclination"),  ...)## S3 method for class 'Line2D'as_angle(x, unit = getOption("affiner_angular_unit", "degrees"), ...)## S3 method for class 'Plane3D'as_angle(  x,  unit = getOption("affiner_angular_unit", "degrees"),  type = c("azimuth", "inclination"),  ...)## S3 method for class 'numeric'as_angle(x, unit = getOption("affiner_angular_unit", "degrees"), ...)

Arguments

Value

Anangle() vector

Examples

as_angle(angle(pi, "radians"), "pi-radians")as_angle(complex(real = 0, imaginary = 1), "degrees")as_angle(as_coord2d(x = 0, y = 1), "turns")as_angle(200, "gradians")

Cast to coord1d object

Description

as_coord1d() casts to aCoord1D class object

Usage

as_coord1d(x, ...)## S3 method for class 'character'as_coord1d(x, ...)## S3 method for class 'Coord2D'as_coord1d(  x,  permutation = c("xy", "yx"),  ...,  line = as_line2d("x-axis"),  scale = 0)## S3 method for class 'data.frame'as_coord1d(x, ...)## S3 method for class 'list'as_coord1d(x, ...)## S3 method for class 'matrix'as_coord1d(x, ...)## S3 method for class 'numeric'as_coord1d(x, ...)## S3 method for class 'Coord1D'as_coord1d(x, ...)## S3 method for class 'Point1D'as_coord1d(x, ...)

Arguments

Value

ACoord1D class object

Examples

as_coord1d(x = rnorm(10))

Cast to coord2d object

Description

as_coord2d() casts to aCoord2D class object

Usage

as_coord2d(x, ...)## S3 method for class 'angle'as_coord2d(x, radius = 1, ...)## S3 method for class 'character'as_coord2d(x, ...)## S3 method for class 'complex'as_coord2d(x, ...)## S3 method for class 'Coord3D'as_coord2d(  x,  permutation = c("xyz", "xzy", "yxz", "yzx", "zyx", "zxy"),  ...,  plane = as_plane3d("xy-plane"),  scale = 0,  alpha = angle(45, "degrees"))## S3 method for class 'data.frame'as_coord2d(x, ...)## S3 method for class 'list'as_coord2d(x, ...)## S3 method for class 'matrix'as_coord2d(x, ...)## S3 method for class 'numeric'as_coord2d(x, y = rep_len(0, length(x)), ...)## S3 method for class 'Coord2D'as_coord2d(x, ...)

Arguments

Value

ACoord2D class object

Examples

df <- data.frame(x = sample.int(10, 3),                 y = sample.int(10, 3))as_coord2d(df)as_coord2d(complex(real = 3, imaginary = 2))as_coord2d(angle(90, "degrees"), radius = 2)as_coord2d(as_coord3d(1, 2, 2), alpha = degrees(90), scale = 0.5)

Cast to coord3d object

Description

as_coord3d() casts to aCoord3D class object

Usage

as_coord3d(x, ...)## S3 method for class 'angle'as_coord3d(x, radius = 1, inclination = NULL, z = NULL, ...)## S3 method for class 'character'as_coord3d(x, ...)## S3 method for class 'data.frame'as_coord3d(x, ..., z = NULL)## S3 method for class 'list'as_coord3d(x, ..., z = NULL)## S3 method for class 'matrix'as_coord3d(x, ...)## S3 method for class 'numeric'as_coord3d(x, y = rep_len(0, length(x)), z = rep_len(0, length(x)), ...)## S3 method for class 'Coord3D'as_coord3d(x, ...)## S3 method for class 'Coord2D'as_coord3d(x, z = rep_len(0, length(x)), ...)

Arguments

Value

ACoord3D class object

Examples

as_coord3d(x = 1, y = 2, z = 3)df <- data.frame(x = sample.int(10, 3),                 y = sample.int(10, 3),                 z = sample.int(10, 3))as_coord3d(df)# Cylindrical coordinatesas_coord3d(degrees(90), z = 1, radius = 1)# Spherical coordinatesas_coord3d(degrees(90), inclination = degrees(90), radius = 1)

Cast to Line2D object

Description

as_line2d() casts to aLine2D object.

Usage

as_line2d(...)## S3 method for class 'numeric'as_line2d(a, b, c, ...)## S3 method for class 'angle'as_line2d(theta, p1 = as_coord2d("origin"), ...)## S3 method for class 'character'as_line2d(x, ...)## S3 method for class 'Coord2D'as_line2d(normal, p1 = as_coord3d("origin"), p2, ...)## S3 method for class 'Line2D'as_line2d(line, ...)## S3 method for class 'Point1D'as_line2d(point, b = 0, ...)

Arguments

Examples

p1 <- as_coord2d(x = 5, y = 10)p2 <- as_coord2d(x = 7, y = 12)theta <- degrees(45)as_line2d(theta, p1)as_line2d(p1, p2)

Cast to Plane3D object

Description

as_plane3d() casts to aPlane3D object.

Usage

as_plane3d(...)## S3 method for class 'numeric'as_plane3d(a, b, c, d, ...)## S3 method for class 'character'as_plane3d(x, ...)## S3 method for class 'Coord3D'as_plane3d(normal, p1 = as_coord3d("origin"), p2, p3, ...)## S3 method for class 'Plane3D'as_plane3d(plane, ...)## S3 method for class 'Point1D'as_plane3d(point, b = 0, c = 0, ...)## S3 method for class 'Line2D'as_plane3d(line, c = 0, ...)

Arguments

Cast to Point1D object

Description

as_point1d() casts to aPoint1D object.

Usage

as_point1d(...)## S3 method for class 'numeric'as_point1d(a, b, ...)## S3 method for class 'character'as_point1d(x, ...)## S3 method for class 'Coord1D'as_point1d(normal, ...)## S3 method for class 'Point1D'as_point1d(point, ...)

Arguments

Examples

p1 <- as_point1d(a = 1, b = 0)

Cast to 1D affine transformation matrix

Description

as_transform1d() casts to atransform1d() affine transformation matrix

Usage

as_transform1d(x, ...)## S3 method for class 'transform1d'as_transform1d(x, ...)## Default S3 method:as_transform1d(x, ...)

Arguments

Value

Atransform1d() object

Examples

m <- diag(2L)as_transform1d(m)

Cast to 2D affine transformation matrix

Description

as_transform2d() casts to atransform2d() affine transformation matrix

Usage

as_transform2d(x, ...)## S3 method for class 'transform2d'as_transform2d(x, ...)## Default S3 method:as_transform2d(x, ...)

Arguments

Value

Atransform2d() object

Examples

m <- diag(3L)as_transform2d(m)

Cast to 3D affine transformation matrix

Description

as_transform3d() casts to atransform3d() affine transformation matrix

Usage

as_transform3d(x, ...)## S3 method for class 'transform3d'as_transform3d(x, ...)## Default S3 method:as_transform3d(x, ...)

Arguments

Value

Atransform3d() object

Examples

m <- diag(4L)as_transform3d(m)

Compute axis-aligned ranges

Description

range() computes axis-aligned ranges forCoord1D,Coord2D, andCoord3D class objects.

Usage

## S3 method for class 'Coord1D'range(..., na.rm = FALSE)## S3 method for class 'Coord2D'range(..., na.rm = FALSE)## S3 method for class 'Coord3D'range(..., na.rm = FALSE)

Arguments

Value

Either aCoord1D,Coord2D, orCoord3D object of length two.The first element will have the minimum x/y(/z) coordinatesand the second element will have the maximum x/y(/z) coordinatesof the axis-aligned ranges.

Examples

range(as_coord2d(rnorm(5), rnorm(5)))range(as_coord3d(rnorm(5), rnorm(5), rnorm(5)))

Compute centroids of coordinates

Description

mean()computes centroids forCoord1D,Coord2D, andCoord3D class objects

Usage

## S3 method for class 'Coord1D'mean(x, ...)## S3 method for class 'Coord2D'mean(x, ...)## S3 method for class 'Coord3D'mean(x, ...)

Arguments

Value

ACoord1D,Coord2D, orCoord3D class object of length one

Examples

p <- as_coord2d(x = 1:4, y = 1:4)print(mean(p))print(sum(p) / length(p)) # less efficient alternativep <- as_coord3d(x = 1:4, y = 1:4, z = 1:4)print(mean(p))

Compute 2D convex hulls

Description

convex_hull2d() is a S3 generic for computing the convex hull of an object.There is an implemented method supportingCoord2D class objectsusinggrDevices::chull() to compute the convex hull.

Usage

convex_hull2d(x, ...)## S3 method for class 'Coord2D'convex_hull2d(x, ...)

Arguments

Value

An object of same class asx representing just the subset of points on the convex hull.The method forCoord2D class objects returns these points in counter-clockwise order.

Examples

p <- as_coord2d(x = rnorm(25), y = rnorm(25))print(convex_hull2d(p))# Equivalent to following caculation using `grDevices::chull()`all.equal(convex_hull2d(p),          p[rev(grDevices::chull(as.list(p)))])

Compute 3D vector cross product

Description

cross_product3d() computes the cross product of twoCoord3D class vectors.

Usage

cross_product3d(x, y)

Arguments

Value

ACoord3D class vector

Examples

x <- as_coord3d(2, 3, 4)y <- as_coord3d(5, 6, 7)cross_product3d(x, y)

1D Euclidean distances

Description

distance1d() computes 1D Euclidean distances.

Usage

distance1d(x, y)

Arguments

Examples

p <- as_coord1d(x = 1:4)distance1d(p, as_coord1d(0))

2D Euclidean distances

Description

distance2d() computes 2D Euclidean distances.

Usage

distance2d(x, y)

Arguments

Examples

p <- as_coord2d(x = 1:4, y = 1:4)distance2d(p, as_coord2d(0, 0))

3D Euclidean distances

Description

distance3d() computes 3D Euclidean distances.

Usage

distance3d(x, y)

Arguments

Examples

p <- as_coord3d(x = 1:4, y = 1:4, z = 1:4)distance3d(p, as_coord3d("origin"))

Plot coordinates, points, lines, and planes

Description

plot() plotsCoord1D andCoord2D class objects whilepoints() drawsCoord1D andCoord2D class objectsandlines() drawsPoint1D andLine2D class objects to an existing plot.If the suggestedggplot2 andrgl packages are available we also registerggplot2::autolayer() methods forCoord1D,Coord2D,Point1D, andLine2D class objects and argl::plot3d() method forCoord3D class objects.

Usage

## S3 method for class 'Coord1D'plot(x, ...)## S3 method for class 'Coord1D'points(x, ...)## S3 method for class 'Point1D'lines(x, ...)## S3 method for class 'Coord2D'plot(x, ...)## S3 method for class 'Coord2D'points(x, ...)## S3 method for class 'Line2D'lines(x, ...)

Arguments

Value

Used for its side effect of drawing to the graphics device.

Examples

c1 <- as_coord2d(x = 0, y = 1:10)l <- as_line2d(a = 1, b = -1, c = 0) # y = xc2 <- c1$clone()$reflect(l)plot(c1, xlim = c(-1, 11), ylim = c(-1, 11),     main = "2D reflection across a line")lines(l)points(c2, col = "red")c1 <- as_coord2d(x = 1:10, y = 1:10)l <- as_line2d(a = -1, b = 0, c = 0) # x = 0c2 <- c1$clone()$project(l)if (require("ggplot2", quietly = TRUE,            include.only = c("ggplot", "autolayer", "labs"))) {  ggplot() +      autolayer(c1) +      autolayer(l) +      autolayer(c2, color = "red") +      labs(title = "2D projection onto a line")}c1 <- as_coord1d(x = seq.int(-4, -1))pt <- as_point1d(a = 1, b = 0) # x = 0c2 <- c1$clone()$reflect(pt)plot(c1, xlim = c(-5, 5), main = "1D reflection across a point")lines(pt)points(c2, col = "red")# 3D reflection across a planec1 <- as_coord3d(x = 1:10, y = 1:10, z = 1:10)pl <- as_plane3d(a = 0, b = 0, c = -1, d = 2) # z = 2c2 <- c1$clone()$reflect(pl)if (require("rgl", quietly = TRUE,             include.only = c("plot3d", "planes3d", "points3d"))) {  plot3d(c1, size = 8)  planes3d(as.data.frame(pl), d =  pl$d, color = "grey", alpha = 0.6)  points3d(as.data.frame(c2), col = "red", size = 8)}

Angle vector aware inverse trigonometric functions

Description

arcsine(),arccosine(),arctangent(),arcsecant(),arccosecant(), andarccotangent() areinverse trigonometric functions that returnangle() vectorswith a user chosen angular unit.

Usage

arcsine(  x,  unit = getOption("affiner_angular_unit", "degrees"),  tolerance = sqrt(.Machine$double.eps))arccosine(  x,  unit = getOption("affiner_angular_unit", "degrees"),  tolerance = sqrt(.Machine$double.eps))arctangent(x, unit = getOption("affiner_angular_unit", "degrees"), y = NULL)arcsecant(x, unit = getOption("affiner_angular_unit", "degrees"))arccosecant(x, unit = getOption("affiner_angular_unit", "degrees"))arccotangent(x, unit = getOption("affiner_angular_unit", "degrees"))

Arguments

Value

Anangle() vector

Examples

arccosine(-1, "degrees")arcsine(0, "turns")arctangent(0, "gradians")arccosecant(-1, "degrees")arcsecant(1, "degrees")arccotangent(1, "half-turns")# `base::atan2(y, x)` computes the angle of the vector from origin to (x, y)as_angle(as_coord2d(x = 1, y = 1), "degrees")

Test whether an object is an angle vector

Description

is_angle() tests whether an object is an angle vector

Usage

is_angle(x)

Arguments

Value

A logical value

Examples

a <- angle(180, "degrees")is_angle(a)is_angle(pi)

Test whether two objects are congruent

Description

is_congruent() is a S3 generic that tests whether two different objects are “congruent”.Theis_congruent() method forangle() classes tests whether two angles are congruent.

Usage

is_congruent(x, y, ...)## S3 method for class 'numeric'is_congruent(x, y, ..., tolerance = sqrt(.Machine$double.eps))## S3 method for class 'angle'is_congruent(  x,  y,  ...,  mod_turns = TRUE,  tolerance = sqrt(.Machine$double.eps))

Arguments

Value

A logical vector

Examples

  # Use `is_congruent()` to check if two angles are "congruent"  a1 <- angle(180, "degrees")  a2 <- angle(pi, "radians")  a3 <- angle(-180, "degrees") # Only congruent modulus full turns  a1 == a2  isTRUE(all.equal(a1, a2))  is_congruent(a1, a2)  is_congruent(a1, a2, mod_turns = FALSE)  a1 == a3  isTRUE(all.equal(a1, a3))  is_congruent(a1, a3)  is_congruent(a1, a3, mod_turns = FALSE)

Test whether an object has a Coord1D class

Description

is_coord1d() tests whether an object has a "Coord1D" class

Usage

is_coord1d(x)

Arguments

Value

A logical value

Examples

p <- as_coord1d(x = sample.int(10, 3))is_coord1d(p)

Test whether an object has a Coord2D class

Description

is_coord2d() tests whether an object has a "Coord2D" class

Usage

is_coord2d(x)

Arguments

Value

A logical value

Examples

p <- as_coord2d(x = sample.int(10, 3), y = sample.int(10, 3))is_coord2d(p)

Test whether an object has a Coord3D class

Description

is_coord3d() tests whether an object has a "Coord3D" class

Usage

is_coord3d(x)

Arguments

Value

A logical value

Examples

p <- as_coord3d(x = sample.int(10, 3),                y = sample.int(10, 3),                z = sample.int(10, 3))is_coord3d(p)

Test whether an object has a Line2D class

Description

is_line2d() tests whether an object has a "Line2D" class

Usage

is_line2d(x)

Arguments

Value

A logical value

Examples

l <- as_line2d(a = 1, b = 2, c = 3)is_line2d(l)

Test whether an object has a Plane3D class

Description

is_plane3d() tests whether an object has a "Plane3D" class

Usage

is_plane3d(x)

Arguments

Value

A logical value

Examples

p <- as_plane3d(a = 1, b = 2, c = 3, 4)is_plane3d(p)

Test whether an object has a Point1D class

Description

is_point1d() tests whether an object has a "Point1D" class

Usage

is_point1d(x)

Arguments

Value

A logical value

Examples

p <- as_point1d(a = 1, b = 5)is_point1d(p)

Test if 1D affine transformation matrix

Description

is_transform1d() tests if object is atransform1d() affine transformation matrix

Usage

is_transform1d(x)

Arguments

Value

A logical value

Examples

m <- transform1d(diag(2L))is_transform1d(m)is_transform1d(diag(2L))

Test if 2D affine transformation matrix

Description

is_transform2d() tests if object is atransform2d() affine transformation matrix

Usage

is_transform2d(x)

Arguments

Value

A logical value

Examples

m <- transform2d(diag(3L))is_transform2d(m)is_transform2d(diag(3L))

Test if 3D affine transformation matrix

Description

is_transform3d() tests if object is atransform3d() affine transformation matrix

Usage

is_transform3d(x)

Arguments

Value

A logical value

Examples

m <- transform3d(diag(4L))is_transform3d(m)is_transform3d(diag(4L))

Isometric cube grob

Description

isometricCube() is a grid grob function to renderisometric cube faces by automatically wrapping aroundaffineGrob().

Usage

isocubeGrob(  top,  right,  left,  gp_border = grid::gpar(col = "black", lwd = 12),  name = NULL,  gp = grid::gpar(),  vp = NULL)grid.isocube(...)

Arguments

Details

Anyggplot2 objects are coerced to grobs byggplot2::ggplotGrob(). Depending on what you'd liketo do you may want to instead manually convert a ggplot2 objectgg to a grob withgtable::gtable_filter(ggplot2::ggplotGrob(gg), "panel").

Not all graphics devices provided bygrDevices or other R packages support theaffine transformation feature introduced in R 4.2.IfisTRUE(getRversion() >= '4.2.0') then the active graphics device should support this feature ifisTRUE(grDevices::dev.capabilities()$transformations).In particular the following graphics devices should support the affine transformation feature:

• R'sgrDevices::pdf() device

• R's 'cairo' devices e.g.grDevices::cairo_pdf(),grDevices::png(type = 'cairo'),grDevices::svg(),grDevices::x11(type = 'cairo'), etc. IfisTRUE(capabilities('cairo')) then R was compiled with support for the 'cairo' devices .

• R's 'quartz' devices (since R 4.3.0) e.g.grDevices::quartz(),grDevices::png(type = 'quartz'), etc. IfisTRUE(capabilities('aqua')) then R was compiled with support for the 'quartz' devices (generally onlyTRUE on macOS systems).

• ragg's devices (since v1.3.0) e.g.ragg::agg_png(),ragg::agg_capture(), etc.

Value

Agrid::gTree() (grob) object of class "isocube".As a side effectgrid.isocube() draws to the active graphics device.

Examples

if (require("grid") &&    getRversion() >= "4.2.0" &&    isTRUE(dev.capabilities()$transformations)) {  # Only works if active graphics device supports affine transformations  # such as `png(type="cairo")` on R 4.2+  grid.newpage()  gp_text <- gpar(fontsize = 72)  grid.isocube(top = textGrob("top", gp = gp_text),                right = textGrob("right", gp = gp_text),               left = textGrob("left", gp = gp_text))}if (require("grid") &&    getRversion() >= "4.2.0" &&    isTRUE(dev.capabilities()$transformations)) {    colors <- c("#D55E00", "#009E73", "#56B4E9")    spacings <- c(0.25, 0.2, 0.25)    texts <- c("pkgname", "left\nface", "right\nface")    rots <- c(45, 0, 0)    fontsizes <- c(52, 80, 80)    sides <- c("top", "left", "right")    types <- gridpattern::names_polygon_tiling[c(5, 7, 9)]    l_grobs <- list()    grid.newpage()    for (i in 1:3) {        if (requireNamespace("gridpattern", quietly = TRUE)) {            bg <- gridpattern::grid.pattern_polygon_tiling(                       colour = "grey80",                       fill = c(colors[i], "white"),                       type = types[i],                       spacing = spacings[i],                       draw = FALSE)        } else {            bg <- rectGrob(gp = gpar(col = NA, fill = colors[i]))        }        text <- textGrob(texts[i], rot = rots[i],                         gp = gpar(fontsize = fontsizes[i]))        l_grobs[[sides[i]]] <- grobTree(bg, text)    }  grid.newpage()  grid.isocube(top = l_grobs$top,                right = l_grobs$right,               left = l_grobs$left)}# May take more than 5 seconds on CRAN machinesif (require("aRtsy") &&    require("grid") &&    require("ggplot2") &&    requireNamespace("gtable", quietly = TRUE) &&    getRversion() >= "4.2.0" &&    isTRUE(dev.capabilities()$transformations)    ) {  gg <- canvas_planet(colorPalette("lava"), threshold = 3) +    scale_x_continuous(expand=c(0, 0)) +    scale_y_continuous(expand=c(0, 0))grob <- ggplotGrob(gg)grob <- gtable::gtable_filter(grob, "panel") # grab just the panelgrid.newpage()grid.isocube(top = grob, left = grob, right = grob,             gp_border = grid::gpar(col = "darkorange", lwd = 12))}

2D normal vectors

Description

normal2d() is an S3 generic that computes a 2D normal vector.

Usage

normal2d(x, ...)## S3 method for class 'Coord2D'normal2d(x, ..., normalize = TRUE)## S3 method for class 'Line2D'normal2d(x, ..., normalize = TRUE)

Arguments

Value

ACoord2D (normal) vector

Examples

  p <- as_coord2d(x = 2, y = 3)  normal2d(p)  normal2d(p, normalize = FALSE)

3D normal vectors

Description

normal3d() is an S3 generic that computes a 3D normal vector.

Usage

normal3d(x, ...)## S3 method for class 'Coord3D'normal3d(x, cross, ..., normalize = TRUE)## S3 method for class 'character'normal3d(x, ..., normalize = TRUE)## S3 method for class 'Plane3D'normal3d(x, ..., normalize = TRUE)

Arguments

Value

ACoord3D (normal) vector

Examples

normal3d("xy-plane")normal3d(as_coord3d(2, 0, 0), cross = as_coord3d(0, 2, 0))

Convert from 3D rotation matrix to axis-angle representation.

Description

rotate3d_to_AA() converts from (post-multiplied) rotation matrixto an axis-angle representation of 3D rotations.

Usage

rotate3d_to_AA(  mat = diag(4),  unit = getOption("affiner_angular_unit", "degrees"))

Arguments

See Also

https://en.wikipedia.org/wiki/Axis-angle_representation for more detailsabout the Axis-angle representation of 3D rotations.rotate3d() can be used to convert from an axis-angle representation to a rotation matrix.

Examples

 # axis-angle representation of 90 degree rotation about the x-axis rotate3d_to_AA(rotate3d("x-axis", 90, unit = "degrees")) # find Axis-Angle representation of first rotating about x-axis 180 degrees # and then rotating about z-axis 45 degrees R <- rotate3d("x-axis", 180, unit = "degrees") %*%        rotate3d("z-axis", 45, unit = "degrees") AA <- rotate3d_to_AA(R) # Can use `rotate3d()` to convert back to rotation matrix representation all.equal(R, do.call(rotate3d, AA))

1D affine transformation matrices

Description

transform1d(),reflect1d(),scale2d(),andtranslate1d() create 1D affine transformation matrix objects.

Usage

transform1d(mat = diag(2L))project1d(point = as_point1d("origin"), ...)reflect1d(point = as_point1d("origin"), ...)scale1d(x_scale = 1)translate1d(x = as_coord1d(0), ...)

Arguments

Details

transform1d()

User supplied (post-multiplied) affine transformation matrix

.

reflect1d()

Reflections across a point.

scale1d()

Scale the x-coordinates by multiplicative scale factors.

translate1d()

Translate the coordinates by aCoord1D class object parameter.

transform1d() 1D affine transformation matrix objects are meant to bepost-multiplied and therefore shouldnot be multiplied in reverse order.Note theCoord1D class object methods auto-pre-multiply affine transformationswhen "method chaining" so pre-multiplying affine transformation matricesto do a single cumulative transformation instead of a method chain of multiple transformationswill not improve performance as much as as it does in other R packages.

To convert a pre-multiplied 1D affine transformation matrix to a post-multiplied onesimply compute its transpose usingt(). To get an inverse transformation matrixfrom an existing transformation matrix that does the opposite transformationssimply compute its inverse usingsolve().

Value

A 2x2 post-multiplied affine transformation matrix with classes "transform1d" and "at_matrix"

Examples

p <- as_coord1d(x = sample(1:10, 3))# {affiner} affine transformation matrices are post-multiplied# and therefore should **not** go in reverse ordermat <- transform1d(diag(2)) %*%         scale1d(2) %*%         translate1d(x = -1)p1 <- p$  clone()$  transform(mat)# The equivalent result appyling affine transformations via method chainingp2 <- p$  clone()$  transform(diag(2))$  scale(2)$  translate(x = -1)all.equal(p1, p2)

2D affine transformation matrices

Description

transform2d(),project2d(),reflect2d(),rotate2d(),scale2d(),shear2d(),andtranslate2d() create 2D affine transformation matrix objects.

Usage

transform2d(mat = diag(3L))permute2d(permutation = c("xy", "yx"))project2d(line = as_line2d("x-axis"), ..., scale = 0)reflect2d(line = as_line2d("x-axis"), ...)rotate2d(theta = angle(0), ...)scale2d(x_scale = 1, y_scale = x_scale)shear2d(xy_shear = 0, yx_shear = 0)translate2d(x = as_coord2d(0, 0), ...)

Arguments

Details

transform2d()

User supplied (post-multiplied) affine transformation matrix

.

project2d()

Oblique vector projections onto a line parameterized byan oblique projection scale factor.A (degenerate) scale factor of zero results in an orthogonal projection.

reflect2d()

Reflections across a line.To "flip" across both the x-axis and the y-axis usescale2d(-1).

rotate2d()

Rotations around the origin parameterized by anangle().

scale2d()

Scale the x-coordinates and/or the y-coordinates by multiplicative scale factors.

shear2d()

Shear the x-coordinates and/or the y-coordinates using shear factors.

translate2d()

Translate the coordinates by aCoord2D class object parameter.

transform2d() 2D affine transformation matrix objects are meant to bepost-multiplied and therefore shouldnot be multiplied in reverse order.Note theCoord2D class object methods auto-pre-multiply affine transformationswhen "method chaining" so pre-multiplying affine transformation matricesto do a single cumulative transformation instead of a method chain of multiple transformationswill not improve performance as much as as it does in other R packages.

To convert a pre-multiplied 2D affine transformation matrix to a post-multiplied onesimply compute its transpose usingt(). To get an inverse transformation matrixfrom an existing transformation matrix that does the opposite transformationssimply compute its inverse usingsolve().

Value

A 3x3 post-multiplied affine transformation matrix with classes "transform2d" and "at_matrix"

Examples

p <- as_coord2d(x = sample(1:10, 3), y = sample(1:10, 3))# {affiner} affine transformation matrices are post-multiplied# and therefore should **not** go in reverse ordermat <- transform2d(diag(3)) %*%         reflect2d(as_coord2d(-1, 1)) %*%         rotate2d(90, "degrees") %*%         scale2d(1, 2) %*%         shear2d(0.5, 0.5) %*%         translate2d(x = -1, y = -1)p1 <- p$  clone()$  transform(mat)# The equivalent result appyling affine transformations via method chainingp2 <- p$  clone()$  transform(diag(3L))$  reflect(as_coord2d(-1, 1))$  rotate(90, "degrees")$  scale(1, 2)$  shear(0.5, 0.5)$  translate(x = -1, y = -1)all.equal(p1, p2)

3D affine transformation matrices

Description

transform3d(),project3d(),reflect3d(),rotate3d(),scale3d(),shear3d(),andtranslate3d() create 3D affine transformation matrix objects.

Usage

transform3d(mat = diag(4L))permute3d(permutation = c("xyz", "xzy", "yxz", "yzx", "zyx", "zxy"))project3d(  plane = as_plane3d("xy-plane"),  ...,  scale = 0,  alpha = angle(45, "degrees"))reflect3d(plane = as_plane3d("xy-plane"), ...)rotate3d(axis = as_coord3d("z-axis"), theta = angle(0), ...)scale3d(x_scale = 1, y_scale = x_scale, z_scale = x_scale)shear3d(  xy_shear = 0,  xz_shear = 0,  yx_shear = 0,  yz_shear = 0,  zx_shear = 0,  zy_shear = 0)translate3d(x = as_coord3d(0, 0, 0), ...)

Arguments

Details

transform3d()

User supplied (post-multiplied) affine transformation matrix

.

scale3d()

Scale the x-coordinates and/or the y-coordinates and/or the z-coordinatesby multiplicative scale factors.

shear3d()

Shear the x-coordinates and/or the y-coordinatesand/or the z-coordinates using shear factors.

translate3d()

Translate the coordinates by aCoord3D class object parameter.

transform3d() 3D affine transformation matrix objects are meant to bepost-multiplied and therefore shouldnot be multiplied in reverse order.Note theCoord3D class object methods auto-pre-multiply affine transformationswhen "method chaining" so pre-multiplying affine transformation matricesto do a single cumulative transformation instead of a method chain of multiple transformationswill not improve performance as much as as it does in other R packages.

To convert a pre-multiplied 3D affine transformation matrix to a post-multiplied onesimply compute its transpose usingt(). To get an inverse transformation matrixfrom an existing transformation matrix that does the opposite transformationssimply compute its inverse usingsolve().

Value

A 4x4 post-multiplied affine transformation matrix with classes "transform3d" and "at_matrix"

Examples

p <- as_coord3d(x = sample(1:10, 3), y = sample(1:10, 3), z = sample(1:10, 3))# {affiner} affine transformation matrices are post-multiplied# and therefore should **not** go in reverse ordermat <- transform3d(diag(4L)) %*%         rotate3d("z-axis", degrees(90)) %*%         scale3d(1, 2, 1) %*%         translate3d(x = -1, y = -1, z = -1)p1 <- p$  clone()$  transform(mat)# The equivalent result appyling affine transformations via method chainingp2 <- p$  clone()$  transform(diag(4L))$  rotate("z-axis", degrees(90))$  scale(1, 2, 1)$  translate(x = -1, y = -1, z = -1)all.equal(p1, p2)

Angle vector aware trigonometric functions

Description

sine(),cosine(),tangent(),secant(),cosecant(), andcotangent() areangle() aware trigonometric functions that allow for a user chosen angular unit.

Usage

sine(x, unit = getOption("affiner_angular_unit", "degrees"))cosine(x, unit = getOption("affiner_angular_unit", "degrees"))tangent(x, unit = getOption("affiner_angular_unit", "degrees"))secant(x, unit = getOption("affiner_angular_unit", "degrees"))cosecant(x, unit = getOption("affiner_angular_unit", "degrees"))cotangent(x, unit = getOption("affiner_angular_unit", "degrees"))

Arguments

Value

A numeric vector

Examples

sine(pi, "radians")cosine(180, "degrees")tangent(0.5, "turns")a <- angle(0.5, "turns")secant(a)cosecant(a)cotangent(a)