diff --git a/gears.scad b/gears.scad index 607986c..eff47cd 100644 --- a/gears.scad +++ b/gears.scad @@ -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]] : [] ) diff --git a/tests/test_quaternions.scad b/tests/test_quaternions.scad index fe95ebc..f0f0fe8 100644 --- a/tests/test_quaternions.scad +++ b/tests/test_quaternions.scad @@ -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(); diff --git a/tests/test_transforms.scad b/tests/test_transforms.scad index 89d5b51..2314594 100644 --- a/tests/test_transforms.scad +++ b/tests/test_transforms.scad @@ -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" ) ); diff --git a/transforms.scad b/transforms.scad index 9210a8d..c48287b 100644 --- a/transforms.scad +++ b/transforms.scad @@ -12,7 +12,7 @@ // . // Almost all of the transformation functions take a point, a point // list, bezier patch, or VNF as a second positional argument to -// operate on. The exceptions are rot(), frame_map() and skew(). +// operate on. The exceptions are rot(), frame_map() and skew(). // Includes: // include // FileGroup: Basic Modeling @@ -23,21 +23,21 @@ // Section: Affine Transformations // OpenSCAD provides various built-in modules to transform geometry by // translation, scaling, rotation, and mirroring. All of these operations -// are affine transformations. A three-dimensional affine transformation +// are affine transformations. A three-dimensional affine transformation // can be represented by a 4x4 matrix. The transformation shortcuts in this // file generally have three modes of operation. They can operate // directly on geometry like their OpenSCAD built-in equivalents. For example, // `left(10) cube()`. They can operate on a list of points (or various other -// types of geometric data). For example, operating on a list of points: `points = left(10, [[1,2,3],[4,5,6]])`. +// types of geometric data). For example, operating on a list of points: `points = left(10, [[1,2,3],[4,5,6]])`. // The third option is that the shortcut can return the transformation matrix -// corresponding to its action. For example, `M=left(10)`. +// corresponding to its action. For example, `M=left(10)`. // . // This capability allows you to store and manipulate transformations, and can // be useful in more advanced modeling. You can multiply these matrices // together, analogously to applying a sequence of operations with the // built-in transformations. So you can write `zrot(37)left(5)cube()` // to perform two operations on a cube. You can also store -// that same transformation by multiplying the matrices together: `M = zrot(37) * left(5)`. +// that same transformation by multiplying the matrices together: `M = zrot(37) * left(5)`. // Note that the order is exactly the same as the order used to apply the transformation. // . // Suppose you have constructed `M` as above. What now? You can use @@ -60,7 +60,7 @@ // the affine transformed point as `tran_point = M * point`. However, this syntax hides a complication that // arises if you have a list of points. A list of points like `[[1,2,3,1],[4,5,6,1],[7,8,9,1]]` has the augmented points // as row vectors on the list. In order to transform such a list, it needs to be muliplied on the right -// side, not the left side. +// side, not the left side. @@ -85,7 +85,7 @@ _NO_ARG = [true,[123232345],false]; // mat = move([x=], [y=], [z=]); // // Topics: Affine, Matrices, Transforms, Translation -// See Also: left(), right(), fwd(), back(), down(), up(), spherical_to_xyz(), altaz_to_xyz(), cylindrical_to_xyz(), polar_to_xy() +// See Also: left(), right(), fwd(), back(), down(), up(), spherical_to_xyz(), altaz_to_xyz(), cylindrical_to_xyz(), polar_to_xy() // // Description: // Translates position by the given amount. @@ -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() @@ -266,15 +279,17 @@ function right(x=0, p=_NO_ARG) = assert(is_finite(x), "Invalid number") // mat3d = fwd(4); // Returns: [[1,0,0,0],[0,1,0,-4],[0,0,1,0],[0,0,0,1]] module fwd(y=0, p) { assert(is_undef(p), "Module form `fwd()` does not accept p= argument."); - assert(is_finite(y), "Invalid number") + assert(is_finite(y), "Invalid number") 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) ... @@ -306,12 +321,23 @@ function fwd(y=0, p=_NO_ARG) = assert(is_finite(y), "Invalid number") // mat3d = back(4); // Returns: [[1,0,0,0],[0,1,0,4],[0,0,1,0],[0,0,0,1]] module back(y=0, p) { assert(is_undef(p), "Module form `back()` does not accept p= argument."); - assert(is_finite(y), "Invalid number") + assert(is_finite(y), "Invalid number") 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() @@ -424,7 +464,7 @@ function up(z=0, p=_NO_ARG) = assert(is_finite(z), "Invalid number") // * `rot([20,30,40])` or `rot(a=[20,30,40])` rotates 20 degrees around the X axis, then 30 degrees around the Y axis, then 40 degrees around the Z axis. // * `rot(30, [1,1,0])` or `rot(a=30, v=[1,1,0])` rotates 30 degrees around the axis vector `[1,1,0]`. // * `rot(from=[0,0,1], to=[1,0,0])` rotates the `from` vector to line up with the `to` vector, in this case the top to the right and hence equivalent to `rot(a=90,v=[0,1,0]`. -// * `rot(from=[0,1,1], to=[1,1,0], a=45)` rotates 45 degrees around the `from` vector ([0,1,1]) and then rotates the `from` vector to align with the `to` vector. Equivalent to `rot(from=[0,1,1],to=[1,1,0]) rot(a=45,v=[0,1,1])`. You can also regard `a` as as post-rotation around the `to` vector. For this form, `a` must be a scalar. +// * `rot(from=[0,1,1], to=[1,1,0], a=45)` rotates 45 degrees around the `from` vector ([0,1,1]) and then rotates the `from` vector to align with the `to` vector. Equivalent to `rot(from=[0,1,1],to=[1,1,0]) rot(a=45,v=[0,1,1])`. You can also regard `a` as as post-rotation around the `to` vector. For this form, `a` must be a scalar. // * If the `cp` centerpoint argument is given, then rotations are performed around that centerpoint. So `rot(args...,cp=[1,2,3])` is equivalent to `move(-[1,2,3])rot(args...)move([1,2,3])`. // * If the `reverse` argument is true, then the rotations performed will be exactly reversed. // . @@ -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. -// Note that unlike almost all the other transformations, the `p` argument must be given as a named argument. +// * 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); @@ -1148,7 +1143,7 @@ function zflip(p=_NO_ARG, z=0) = // coordinate systems to each other by using the canonical coordinate system as an intermediary. // You cannot use the `reverse` option with non-orthogonal inputs. Note that only the direction // of the specified vectors matters: the transformation will not apply scaling, though it can -// skew if your provide non-orthogonal axes. +// skew if your provide non-orthogonal axes. // Arguments: // x = Destination 3D vector for x axis. // y = Destination 3D vector for y axis. @@ -1169,7 +1164,7 @@ function zflip(p=_NO_ARG, z=0) = // multmatrix(mat) { // color("purple") stroke([[0,0,0],10*[1,1,0]]); // color("green") stroke([[0,0,0],10*[-1,1,0]]); -// } +// } function frame_map(x,y,z, p=_NO_ARG, reverse=false) = p != _NO_ARG ? apply(frame_map(x,y,z,reverse=reverse), 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. @@ -1274,26 +1268,20 @@ 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); -// Section: Applying transformation matrices to +// Section: Applying transformation matrices to /// Internal Function: is_2d_transform() @@ -1325,13 +1313,13 @@ function is_2d_transform(t) = // z-parameters are zero, except we allow t[2][ // Topics: Affine, Matrices, Transforms // Description: // Applies the specified transformation matrix `transform` to a point, point list, bezier patch or VNF. -// When `points` contains 2D or 3D points the transform matrix may be a 4x4 affine matrix or a 3x4 matrix--- +// When `points` contains 2D or 3D points the transform matrix may be a 4x4 affine matrix or a 3x4 matrix--- // the 4x4 matrix with its final row removed. When the data is 2D the matrix must not operate on the Z axis, // except possibly by scaling it. When points contains 2D data you can also supply the transform as // a 3x3 affine transformation matrix or the corresponding 2x3 matrix with the last row deleted. // . // Any other combination of matrices will produce an error, including acting with a 2D matrix (3x3) on 3D data. -// The output of apply is always the same dimension as the input---projections are not supported. +// The output of apply is always the same dimension as the input---projections are not supported. // Arguments: // transform = The 2D (3x3 or 2x3) or 3D (4x4 or 3x4) transformation matrix to apply. // points = The point, point list, bezier patch, or VNF to apply the transformation to. @@ -1383,7 +1371,7 @@ function _apply(transform,points) = matrix = [for(i=[0:1:tdim]) [for(j=[0:1:datadim-1]) transform[j][i]]] / scale ) tdim==datadim ? [for(p=points) concat(p,1)] * matrix - : tdim == 3 && datadim == 2 ? + : tdim == 3 && datadim == 2 ? assert(is_2d_transform(transform), str("Transforms is 3D and acts on Z, but points are 2D")) [for(p=points) concat(p,[0,1])]*matrix : assert(false, str("Unsupported combination: ",len(transform),"x",len(transform[0])," transform (dimension ",tdim,