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@boredzo
Created January 5, 2016 06:02
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Skew operator for OpenSCAD
/*skew takes an array of six angles:
*x along y
*x along z
*y along x
*y along z
*z along x
*z along y
*/
module skew(dims) {
matrix = [
[ 1, dims[0]/45, dims[1]/45, 0 ],
[ dims[2]/45, 1, dims[4]/45, 0 ],
[ dims[5]/45, dims[3]/45, 1, 0 ],
[ 0, 0, 0, 1 ]
];
multmatrix(matrix)
children();
}
skew([45, 0, 0, 0, 0, 0])
cube([10,10,10]);
@dguerizec
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It should be tan(dims[0]) instead of dims[0]/45, and so on for all the others.

@ziggy90127
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/*skew takes an array of six angles:
 *x along y
 *x along z
 *y along x
 *y along z
 *z along x
 *z along y
 */
module skew(dims) {
matrix = [
	[ 1, tan(dims[0]), tan(dims[1]), 0 ],
	[ tan(dims[2]), 1, tan(dims[3]), 0 ],
	[ tan(dims[4]), tan(dims[5]), 1, 0 ],
	[ 0, 0, 0, 1 ]
];
multmatrix(matrix)
children();
}

@nash8114
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Thanks for this module. Saved me the hassle of figuring out the correct Matrix.
Thanks to dguerizec and ziggy90127 for correcting the matrix formula and posting the complete solution.

@ygoe
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ygoe commented Aug 7, 2022

Thank you, works wonderfully (only tried the corrected version from the comment). I've changed the interface a bit to make it easier to use:

// Skews the child geometry.
// xy: Angle towards X along Y axis.
// xz: Angle towards X along Z axis.
// yx: Angle towards Y along X axis.
// yz: Angle towards Y along Z axis.
// zx: Angle towards Z along X axis.
// zy: Angle towards Z along Y axis.
module skew(xy = 0, xz = 0, yx = 0, yz = 0, zx = 0, zy = 0) {
	matrix = [
		[ 1, tan(xy), tan(xz), 0 ],
		[ tan(yx), 1, tan(yz), 0 ],
		[ tan(zx), tan(zy), 1, 0 ],
		[ 0, 0, 0, 1 ]
	];
	multmatrix(matrix)
	children();
}

Example:

skew(xz = 20, yx = 40)
cube([5, 5, 10]);

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