grey/BOSL2
1
0
Fork 0
mirror of https://github.com/BelfrySCAD/BOSL2.git synced 2025-01-04 03:09:45 +00:00
Code Issues Projects Releases Packages Wiki Activity Actions

Merge pull request #747 from revarbat/revarbat_dev

Browse source 
Added [xyz]move().  Removed affine2d planar returns from transform fu…
This commit is contained in:
Revar Desmera 2021-12-31 15:43:08 -08:00 committed by GitHub
commit 1d5c34eeb6
No known key found for this signature in database
GPG key ID: 4AEE18F83AFDEB23
4 changed files with 121 additions and 136 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

22
gears.scad
View file

@ -476,20 +476,18 @@ function spur_gear2d(
) = let(
pitch = is_undef(mod) ? pitch : pitch_value(mod),
pr = pitch_radius(pitch=pitch, teeth=teeth),
tooth_profile = gear_tooth_profile(
pitch = pitch,
teeth = teeth,
pressure_angle = pressure_angle,
clearance = clearance,
backlash = backlash,
interior = interior,
valleys = false
),
pts = concat(
[for (tooth = [0:1:teeth-hide-1])
each rot(tooth*360/teeth,
planar=true,
p=gear_tooth_profile(
pitch = pitch,
teeth = teeth,
pressure_angle = pressure_angle,
clearance = clearance,
backlash = backlash,
interior = interior,
valleys = false
)
)
each rot(tooth*360/teeth, p=tooth_profile)
],
hide>0? [[0,0]] : []
)

4
tests/test_quaternions.scad
View file

@ -250,8 +250,8 @@ test_q_slerp();
module test_q_matrix3() {
assert_approx(q_matrix3(quat_z(37)),rot(37,planar=true));
assert_approx(q_matrix3(quat_z(-49)),rot(-49,planar=true));
assert_approx(q_matrix3(quat_z(37)),affine2d_zrot(37));
assert_approx(q_matrix3(quat_z(-49)),affine2d_zrot(-49));
}
test_q_matrix3();

3
tests/test_transforms.scad
View file

@ -289,12 +289,11 @@ module test_rot() {
for (vec1 = vecs2d) {
for (vec2 = vecs2d) {
assert_approx(
rot(from=vec1, to=vec2, p=pts2d, planar=true),
rot(from=vec1, to=vec2, p=pts2d),
apply(affine2d_zrot(v_theta(vec2)-v_theta(vec1)), pts2d),
info=str(
"from = ", vec1, ", ",
"to = ", vec2, ", ",
"planar = ", true, ", ",
"p=..., 2D"
)
);

194
transforms.scad
View file

@ -190,11 +190,13 @@ module left(x=0, p) {
translate([-x,0,0]) children();
}
function left(x=0, p=_NO_ARG) = assert(is_finite(x), "Invalid number")
move([-x,0,0],p=p);
function left(x=0, p=_NO_ARG) =
assert(is_finite(x), "Invalid number")
move([-x,0,0],p=p);
// Function&Module: right()
// Aliases: xmove()
//
// Usage: As Module
// right(x) ...
@ -230,8 +232,19 @@ module right(x=0, p) {
translate([x,0,0]) children();
}
function right(x=0, p=_NO_ARG) = assert(is_finite(x), "Invalid number")
move([x,0,0],p=p);
function right(x=0, p=_NO_ARG) =
assert(is_finite(x), "Invalid number")
move([x,0,0],p=p);
module xmove(x=0, p) {
assert(is_undef(p), "Module form `xmove()` does not accept p= argument.");
assert(is_finite(x), "Invalid number")
translate([x,0,0]) children();
}
function xmove(x=0, p=_NO_ARG) =
assert(is_finite(x), "Invalid number")
move([x,0,0],p=p);
// Function&Module: fwd()
@ -270,11 +283,13 @@ module fwd(y=0, p) {
translate([0,-y,0]) children();
}
function fwd(y=0, p=_NO_ARG) = assert(is_finite(y), "Invalid number")
move([0,-y,0],p=p);
function fwd(y=0, p=_NO_ARG) =
assert(is_finite(y), "Invalid number")
move([0,-y,0],p=p);
// Function&Module: back()
// Aliases: ymove()
//
// Usage: As Module
// back(y) ...
@ -310,8 +325,19 @@ module back(y=0, p) {
translate([0,y,0]) children();
}
function back(y=0,p=_NO_ARG) = assert(is_finite(y), "Invalid number")
move([0,y,0],p=p);
function back(y=0,p=_NO_ARG) =
assert(is_finite(y), "Invalid number")
move([0,y,0],p=p);
module ymove(y=0, p) {
assert(is_undef(p), "Module form `ymove()` does not accept p= argument.");
assert(is_finite(y), "Invalid number")
translate([0,y,0]) children();
}
function ymove(y=0,p=_NO_ARG) =
assert(is_finite(y), "Invalid number")
move([0,y,0],p=p);
// Function&Module: down()
@ -348,10 +374,13 @@ module down(z=0, p) {
translate([0,0,-z]) children();
}
function down(z=0, p=_NO_ARG) = move([0,0,-z],p=p);
function down(z=0, p=_NO_ARG) =
assert(is_finite(z), "Invalid number")
move([0,0,-z],p=p);
// Function&Module: up()
// Aliases: zmove()
//
// Usage: As Module
// up(z) ...
@ -386,8 +415,19 @@ module up(z=0, p) {
translate([0,0,z]) children();
}
function up(z=0, p=_NO_ARG) = assert(is_finite(z), "Invalid number")
move([0,0,z],p=p);
function up(z=0, p=_NO_ARG) =
assert(is_finite(z), "Invalid number")
move([0,0,z],p=p);
module zmove(z=0, p) {
assert(is_undef(p), "Module form `zmove()` does not accept p= argument.");
assert(is_finite(z), "Invalid number");
translate([0,0,z]) children();
}
function zmove(z=0, p=_NO_ARG) =
assert(is_finite(z), "Invalid number")
move([0,0,z],p=p);
@ -409,10 +449,10 @@ function up(z=0, p=_NO_ARG) = assert(is_finite(z), "Invalid number")
// pts = rot(a, v, p=, [cp=], [reverse=]);
// pts = rot([a], from=, to=, p=, [reverse=]);
// Usage: As a Function to return a transform matrix
// M = rot(a, [cp=], [reverse=], [planar=]);
// M = rot([X,Y,Z], [cp=], [reverse=], [planar=]);
// M = rot(a, v, [cp=], [reverse=], [planar=]);
// M = rot(from=, to=, [a=], [reverse=], [planar=]);
// M = rot(a, [cp=], [reverse=]);
// M = rot([X,Y,Z], [cp=], [reverse=]);
// M = rot(a, v, [cp=], [reverse=]);
// M = rot(from=, to=, [a=], [reverse=]);
//
// Topics: Affine, Matrices, Transforms, Rotation
// See Also: xrot(), yrot(), zrot()
@ -434,19 +474,17 @@ function up(z=0, p=_NO_ARG) = assert(is_finite(z), "Invalid number")
// * Called as a function with a `p` argument containing a list of points, returns the list of rotated points.
// * Called as a function with a [bezier patch](beziers.scad) in the `p` argument, returns the rotated patch.
// * Called as a function with a [VNF structure](vnf.scad) in the `p` argument, returns the rotated VNF.
// * Called as a function without a `p` argument, and `planar` is true, returns the affine2d rotational matrix. The angle `a` must be a scalar.
// * Called as a function without a `p` argument, and `planar` is false, returns the affine3d rotational matrix.
// * Called as a function without a `p` argument, returns the affine3d rotational matrix.
// Note that unlike almost all the other transformations, the `p` argument must be given as a named argument.
//
// Arguments:
// a = Scalar angle or vector of XYZ rotation angles to rotate by, in degrees. If `planar` is true or if `p` holds 2d data, or if you use the `from` and `to` arguments then `a` must be a scalar. Default: `0`
// a = Scalar angle or vector of XYZ rotation angles to rotate by, in degrees. If you use the `from` and `to` arguments then `a` must be a scalar. Default: `0`
// v = vector for the axis of rotation. Default: [0,0,1] or UP
// ---
// cp = centerpoint to rotate around. Default: [0,0,0]
// from = Starting vector for vector-based rotations.
// to = Target vector for vector-based rotations.
// reverse = If true, exactly reverses the rotation, including axis rotation ordering. Default: false
// planar = If called as a function, this specifies if you want to work with 2D points.
// p = If called as a function, this contains data to rotate: a point, list of points, bezier patch or VNF.
//
// Example:
@ -467,11 +505,11 @@ function up(z=0, p=_NO_ARG) = assert(is_finite(z), "Invalid number")
// stroke(rot(30,p=path), closed=true);
module rot(a=0, v, cp, from, to, reverse=false)
{
m = rot(a=a, v=v, cp=cp, from=from, to=to, reverse=reverse, planar=false);
m = rot(a=a, v=v, cp=cp, from=from, to=to, reverse=reverse);
multmatrix(m) children();
}
function rot(a=0, v, cp, from, to, reverse=false, planar=false, p=_NO_ARG, _m) =
function rot(a=0, v, cp, from, to, reverse=false, p=_NO_ARG, _m) =
assert(is_undef(from)==is_undef(to), "from and to must be specified together.")
assert(is_undef(from) || is_vector(from, zero=false), "'from' must be a non-zero vector.")
assert(is_undef(to) || is_vector(to, zero=false), "'to' must be a non-zero vector.")
@ -479,22 +517,8 @@ function rot(a=0, v, cp, from, to, reverse=false, planar=false, p=_NO_ARG, _m) =
assert(is_undef(cp) || is_vector(cp), "'cp' must be a vector.")
assert(is_finite(a) || is_vector(a), "'a' must be a finite scalar or a vector.")
assert(is_bool(reverse))
assert(is_bool(planar))
let(
m = planar? let(
check = assert(is_num(a)),
cp = is_undef(cp)? cp : point2d(cp),
m1 = is_undef(from)? affine2d_zrot(a) :
assert(a==0, "'from' and 'to' cannot be used with 'a' when 'planar' is true.")
assert(approx(point3d(from).z, 0), "'from' must be a 2D vector when 'planar' is true.")
assert(approx(point3d(to).z, 0), "'to' must be a 2D vector when 'planar' is true.")
affine2d_zrot(
v_theta(to) -
v_theta(from)
),
m2 = is_undef(cp)? m1 : (move(cp) * m1 * move(-cp)),
m3 = reverse? rot_inverse(m2) : m2
) m3 : let(
m = let(
from = is_undef(from)? undef : point3d(from),
to = is_undef(to)? undef : point3d(to),
cp = is_undef(cp)? undef : point3d(cp),
@ -534,8 +558,7 @@ function rot(a=0, v, cp, from, to, reverse=false, planar=false, p=_NO_ARG, _m) =
// * Called as a function with a `p` argument containing a list of points, returns the list of rotated points.
// * Called as a function with a [bezier patch](beziers.scad) in the `p` argument, returns the rotated patch.
// * Called as a function with a [VNF structure](vnf.scad) in the `p` argument, returns the rotated VNF.
// * Called as a function without a `p` argument, and `planar` is true, returns the affine2d rotational matrix.
// * Called as a function without a `p` argument, and `planar` is false, returns the affine3d rotational matrix.
// * Called as a function without a `p` argument, returns the affine3d rotational matrix.
//
// Arguments:
// a = angle to rotate by in degrees.
@ -580,8 +603,7 @@ function xrot(a=0, p=_NO_ARG, cp) = rot([a,0,0], cp=cp, p=p);
// * Called as a function with a `p` argument containing a list of points, returns the list of rotated points.
// * Called as a function with a [bezier patch](beziers.scad) in the `p` argument, returns the rotated patch.
// * Called as a function with a [VNF structure](vnf.scad) in the `p` argument, returns the rotated VNF.
// * Called as a function without a `p` argument, and `planar` is true, returns the affine2d rotational matrix.
// * Called as a function without a `p` argument, and `planar` is false, returns the affine3d rotational matrix.
// * Called as a function without a `p` argument, returns the affine3d rotational matrix.
//
// Arguments:
// a = angle to rotate by in degrees.
@ -626,8 +648,7 @@ function yrot(a=0, p=_NO_ARG, cp) = rot([0,a,0], cp=cp, p=p);
// * Called as a function with a `p` argument containing a list of points, returns the list of rotated points.
// * Called as a function with a [bezier patch](beziers.scad) in the `p` argument, returns the rotated patch.
// * Called as a function with a [VNF structure](vnf.scad) in the `p` argument, returns the rotated VNF.
// * Called as a function without a `p` argument, and `planar` is true, returns the affine2d rotational matrix.
// * Called as a function without a `p` argument, and `planar` is false, returns the affine3d rotational matrix.
// * Called as a function without a `p` argument, returns the affine3d rotational matrix.
//
// Arguments:
// a = angle to rotate by in degrees.
@ -716,7 +737,7 @@ function scale(v=1, p=_NO_ARG, cp=[0,0,0]) =
// Usage: Scale Points
// scaled = xscale(x, p, [cp=]);
// Usage: Get Affine Matrix
// mat = xscale(x, [cp=], [planar=]);
// mat = xscale(x, [cp=]);
//
// Topics: Affine, Matrices, Transforms, Scaling
// See Also: scale(), yscale(), zscale()
@ -736,7 +757,6 @@ function scale(v=1, p=_NO_ARG, cp=[0,0,0]) =
// p = A point, path, bezier patch, or VNF to scale, when called as a function.
// ---
// cp = If given as a point, centers the scaling on the point `cp`. If given as a scalar, centers scaling on the point `[cp,0,0]`
// planar = If true, and `p` is not given, then the matrix returned is an affine2d matrix instead of an affine3d matrix.
//
// Example: As Module
// xscale(3) sphere(r=10);
@ -745,9 +765,8 @@ function scale(v=1, p=_NO_ARG, cp=[0,0,0]) =
// path = circle(d=50,$fn=12);
// #stroke(path,closed=true);
// stroke(xscale(2,p=path),closed=true);
module xscale(x=1, p, cp=0, planar) {
module xscale(x=1, p, cp=0) {
assert(is_undef(p), "Module form `xscale()` does not accept p= argument.");
assert(is_undef(planar), "Module form `xscale()` does not accept planar= argument.");
cp = is_num(cp)? [cp,0,0] : cp;
if (cp == [0,0,0]) {
scale([x,1,1]) children();
@ -756,15 +775,12 @@ module xscale(x=1, p, cp=0, planar) {
}
}
function xscale(x=1, p=_NO_ARG, cp=0, planar=false) =
function xscale(x=1, p=_NO_ARG, cp=0) =
assert(is_finite(x))
assert(p==_NO_ARG || is_list(p))
assert(is_finite(cp) || is_vector(cp))
assert(is_bool(planar))
let( cp = is_num(cp)? [cp,0,0] : cp )
(planar || (!is_undef(p) && len(p)==2))
? scale([x,1], cp=cp, p=p)
: scale([x,1,1], cp=cp, p=p);
scale([x,1,1], cp=cp, p=p);
// Function&Module: yscale()
@ -774,7 +790,7 @@ function xscale(x=1, p=_NO_ARG, cp=0, planar=false) =
// Usage: Scale Points
// scaled = yscale(y, p, [cp=]);
// Usage: Get Affine Matrix
// mat = yscale(y, [cp=], [planar=]);
// mat = yscale(y, [cp=]);
//
// Topics: Affine, Matrices, Transforms, Scaling
// See Also: scale(), xscale(), zscale()
@ -794,7 +810,6 @@ function xscale(x=1, p=_NO_ARG, cp=0, planar=false) =
// p = A point, path, bezier patch, or VNF to scale, when called as a function.
// ---
// cp = If given as a point, centers the scaling on the point `cp`. If given as a scalar, centers scaling on the point `[0,cp,0]`
// planar = If true, and `p` is not given, then the matrix returned is an affine2d matrix instead of an affine3d matrix.
//
// Example: As Module
// yscale(3) sphere(r=10);
@ -803,9 +818,8 @@ function xscale(x=1, p=_NO_ARG, cp=0, planar=false) =
// path = circle(d=50,$fn=12);
// #stroke(path,closed=true);
// stroke(yscale(2,p=path),closed=true);
module yscale(y=1, p, cp=0, planar) {
module yscale(y=1, p, cp=0) {
assert(is_undef(p), "Module form `yscale()` does not accept p= argument.");
assert(is_undef(planar), "Module form `yscale()` does not accept planar= argument.");
cp = is_num(cp)? [0,cp,0] : cp;
if (cp == [0,0,0]) {
scale([1,y,1]) children();
@ -814,15 +828,12 @@ module yscale(y=1, p, cp=0, planar) {
}
}
function yscale(y=1, p=_NO_ARG, cp=0, planar=false) =
function yscale(y=1, p=_NO_ARG, cp=0) =
assert(is_finite(y))
assert(p==_NO_ARG || is_list(p))
assert(is_finite(cp) || is_vector(cp))
assert(is_bool(planar))
let( cp = is_num(cp)? [0,cp,0] : cp )
(planar || (!is_undef(p) && len(p)==2))
? scale([1,y], cp=cp, p=p)
: scale([1,y,1], cp=cp, p=p);
scale([1,y,1], cp=cp, p=p);
// Function&Module: zscale()
@ -958,7 +969,7 @@ function mirror(v, p=_NO_ARG) =
// Usage: As Function
// pt = xflip(p, [x]);
// Usage: Get Affine Matrix
// pt = xflip([x], [planar=]);
// pt = xflip([x]);
//
// Topics: Affine, Matrices, Transforms, Reflection, Mirroring
// See Also: mirror(), yflip(), zflip()
@ -970,14 +981,11 @@ function mirror(v, p=_NO_ARG) =
// * Called as a function with a list of points in the `p` argument, returns the list of points, with each one mirrored across the line/plane.
// * Called as a function with a [bezier patch](beziers.scad) in the `p` argument, returns the mirrored patch.
// * Called as a function with a [VNF structure](vnf.scad) in the `p` argument, returns the mirrored VNF.
// * Called as a function without a `p` argument, and `planar=true`, returns the affine2d 3x3 mirror matrix.
// * Called as a function without a `p` argument, and `planar=false`, returns the affine3d 4x4 mirror matrix.
// * Called as a function without a `p` argument, returns the affine3d 4x4 mirror matrix.
//
// Arguments:
// x = The X coordinate of the plane of reflection. Default: 0
// p = If given, the point, path, patch, or VNF to mirror. Function use only.
// ---
// planar = If true, and p is not given, returns a 2D affine transformation matrix. Function use only. Default: False
//
// Example:
// xflip() yrot(90) cylinder(d1=10, d2=0, h=20);
@ -988,26 +996,21 @@ function mirror(v, p=_NO_ARG) =
// xflip(x=-5) yrot(90) cylinder(d1=10, d2=0, h=20);
// color("blue", 0.25) left(5) cube([0.01,15,15], center=true);
// color("red", 0.333) yrot(90) cylinder(d1=10, d2=0, h=20);
module xflip(p, x=0, planar) {
module xflip(p, x=0) {
assert(is_undef(p), "Module form `zflip()` does not accept p= argument.");
assert(is_undef(planar), "Module form `zflip()` does not accept planar= argument.");
translate([x,0,0])
mirror([1,0,0])
translate([-x,0,0]) children();
}
function xflip(p=_NO_ARG, x=0, planar=false) =
function xflip(p=_NO_ARG, x=0) =
assert(is_finite(x))
assert(is_bool(planar))
assert(p==_NO_ARG || is_list(p),"Invalid point list")
let( v = RIGHT )
x == 0 ? mirror(v,p=p) :
let(
v = RIGHT,
n = planar? point2d(v) : v
)
x == 0 ? mirror(n,p=p) :
let(
cp = x * n,
m = move(cp) * mirror(n) * move(-cp)
cp = x * v,
m = move(cp) * mirror(v) * move(-cp)
)
p==_NO_ARG? m : apply(m, p);
@ -1019,7 +1022,7 @@ function xflip(p=_NO_ARG, x=0, planar=false) =
// Usage: As Function
// pt = yflip(p, [y]);
// Usage: Get Affine Matrix
// pt = yflip([y], [planar=]);
// pt = yflip([y]);
//
// Topics: Affine, Matrices, Transforms, Reflection, Mirroring
// See Also: mirror(), xflip(), zflip()
@ -1031,14 +1034,11 @@ function xflip(p=_NO_ARG, x=0, planar=false) =
// * Called as a function with a list of points in the `p` argument, returns the list of points, with each one mirrored across the line/plane.
// * Called as a function with a [bezier patch](beziers.scad) in the `p` argument, returns the mirrored patch.
// * Called as a function with a [VNF structure](vnf.scad) in the `p` argument, returns the mirrored VNF.
// * Called as a function without a `p` argument, and `planar=true`, returns the affine2d 3x3 mirror matrix.
// * Called as a function without a `p` argument, and `planar=false`, returns the affine3d 4x4 mirror matrix.
// * Called as a function without a `p` argument, returns the affine3d 4x4 mirror matrix.
//
// Arguments:
// p = If given, the point, path, patch, or VNF to mirror. Function use only.
// y = The Y coordinate of the plane of reflection. Default: 0
// ---
// planar = If true, and p is not given, returns a 2D affine transformation matrix. Function use only. Default: False
//
// Example:
// yflip() xrot(90) cylinder(d1=10, d2=0, h=20);
@ -1049,26 +1049,21 @@ function xflip(p=_NO_ARG, x=0, planar=false) =
// yflip(y=5) xrot(90) cylinder(d1=10, d2=0, h=20);
// color("blue", 0.25) back(5) cube([15,0.01,15], center=true);
// color("red", 0.333) xrot(90) cylinder(d1=10, d2=0, h=20);
module yflip(p, y=0, planar) {
module yflip(p, y=0) {
assert(is_undef(p), "Module form `yflip()` does not accept p= argument.");
assert(is_undef(planar), "Module form `yflip()` does not accept planar= argument.");
translate([0,y,0])
mirror([0,1,0])
translate([0,-y,0]) children();
}
function yflip(p=_NO_ARG, y=0, planar=false) =
function yflip(p=_NO_ARG, y=0) =
assert(is_finite(y))
assert(is_bool(planar))
assert(p==_NO_ARG || is_list(p),"Invalid point list")
let( v = BACK )
y == 0 ? mirror(v,p=p) :
let(
v = BACK,
n = planar? point2d(v) : v
)
y == 0 ? mirror(n,p=p) :
let(
cp = y * n,
m = move(cp) * mirror(n) * move(-cp)
cp = y * v,
m = move(cp) * mirror(v) * move(-cp)
)
p==_NO_ARG? m : apply(m, p);
@ -1219,7 +1214,7 @@ module frame_map(x,y,z,p,reverse=false)
// Usage: As Function
// pts = skew(p, [sxy=], [sxz=], [syx=], [syz=], [szx=], [szy=]);
// Usage: Get Affine Matrix
// mat = skew([sxy=], [sxz=], [syx=], [syz=], [szx=], [szy=], [planar=]);
// mat = skew([sxy=], [sxz=], [syx=], [syz=], [szx=], [szy=]);
// Topics: Affine, Matrices, Transforms, Skewing
//
// Description:
@ -1229,8 +1224,7 @@ module frame_map(x,y,z,p,reverse=false)
// * Called as a function with a list of points in the `p` argument, returns the list of skewed points.
// * Called as a function with a [bezier patch](beziers.scad) in the `p` argument, returns the skewed patch.
// * Called as a function with a [VNF structure](vnf.scad) in the `p` argument, returns the skewed VNF.
// * Called as a function without a `p` argument, and with `planar` true, returns the affine2d 3x3 skew matrix.
// * Called as a function without a `p` argument, and with `planar` false, returns the affine3d 4x4 skew matrix.
// * Called as a function without a `p` argument, returns the affine3d 4x4 skew matrix.
// Each skew factor is a multiplier. For example, if `sxy=2`, then it will skew along the X axis by 2x the value of the Y axis.
// Arguments:
// p = If given, the point, path, patch, or VNF to skew. Function use only.
@ -1274,21 +1268,15 @@ module skew(p, sxy=0, sxz=0, syx=0, syz=0, szx=0, szy=0)
) children();
}
function skew(p=_NO_ARG, sxy=0, sxz=0, syx=0, syz=0, szx=0, szy=0, planar=false) =
function skew(p=_NO_ARG, sxy=0, sxz=0, syx=0, syz=0, szx=0, szy=0) =
assert(is_finite(sxy))
assert(is_finite(sxz))
assert(is_finite(syx))
assert(is_finite(syz))
assert(is_finite(szx))
assert(is_finite(szy))
assert(is_bool(planar))
let(
planar = planar || (is_list(p) && is_num(p.x) && len(p)==2),
m = planar? [
[ 1, sxy, 0],
[syx, 1, 0],
[ 0, 0, 1]
] : affine3d_skew(sxy=sxy, sxz=sxz, syx=syx, syz=syz, szx=szx, szy=szy)
m = affine3d_skew(sxy=sxy, sxz=sxz, syx=syx, syz=syz, szx=szx, szy=szy)
)
p==_NO_ARG? m : apply(m, p);