86 lines
4.7 KiB
OpenSCAD
86 lines
4.7 KiB
OpenSCAD
//
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// NopSCADlib Copyright Chris Palmer 2018
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// nop.head@gmail.com
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// hydraraptor.blogspot.com
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//
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// This file is part of NopSCADlib.
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//
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// NopSCADlib is free software: you can redistribute it and/or modify it under the terms of the
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// GNU General Public License as published by the Free Software Foundation, either version 3 of
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// the License, or (at your option) any later version.
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//
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// NopSCADlib is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY;
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// without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
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// See the GNU General Public License for more details.
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//
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// You should have received a copy of the GNU General Public License along with NopSCADlib.
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// If not, see <https://www.gnu.org/licenses/>.
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//
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//
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//! Maths utilities for manipulating vectors and matrices.
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//
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function sqr(x) = x * x;
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function translate(v) = let(u = is_list(v) ? len(v) == 2 ? [v.x, v.y, 0] //! Generate a 4x4 translation matrix, ```v``` can be ```[x, y]```, ```[x, y, z]``` or ```z```
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: v
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: [0, 0, v])
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[ [1, 0, 0, u.x],
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[0, 1, 0, u.y],
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[0, 0, 1, u.z],
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[0, 0, 0, 1] ];
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function rotate(a, v) = //! Generate a 4x4 rotation matrix, ```a``` can be a vector of three angles or a single angle around ```z```, or around axis ```v```
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is_undef(v) ? let(av = is_list(a) ? a : [0, 0, a],
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cx = cos(av[0]),
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cy = cos(av[1]),
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cz = cos(av[2]),
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sx = sin(av[0]),
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sy = sin(av[1]),
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sz = sin(av[2]))
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[
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[ cy * cz, sx * sy * cz - cx * sz, cx * sy * cz + sx * sz, 0],
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[ cy * sz, sx * sy * sz + cx * cz, cx * sy * sz - sx * cz, 0],
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[-sy, sx * cy, cx * cy, 0],
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[ 0, 0, 0, 1]
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]
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: let(s = sin(a),
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c = cos(a),
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C = 1 - c,
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m = sqr(v.x) + sqr(v.y) + sqr(v.z), // m used instead of norm to avoid irrational roots as much as possible
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u = v / sqrt(m))
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[
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[ C * v.x * v.x / m + c, C * v.x * v.y / m - u.z * s, C * v.x * v.z / m + u.y * s, 0],
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[ C * v.y * v.x / m + u.z * s, C * v.y * v.y / m + c, C * v.y * v.z / m - u.x * s, 0],
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[ C * v.z * v.x / m - u.y * s, C * v.z * v.y / m + u.x * s, C * v.z * v.z / m + c, 0],
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[ 0, 0, 0, 1]
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];
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function scale(v) = let(s = is_list(v) ? v : [v, v, v]) //! Generate a 4x4 matrix that scales by ```v```, which can be a vector of xyz factors or a scalar to scale all axes equally
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[
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[s.x, 0, 0, 0],
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[0, s.y, 0, 0],
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[0, 0, s.z, 0],
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[0, 0, 0, 1]
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];
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function vec3(v) = [v.x, v.y, v.z]; //! Return a 3 vector with the first three elements of ```v```
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function vec4(v) = [v.x, v.y, v.z, 1]; //! Return a 4 vector with the first three elements of ```v```
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function transform(v, m) = vec3(m * [v.x, v.y, v.z, 1]); //! Apply 4x4 transform to a 3 vector by extending it and cropping it again
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function transform_points(path, m) = [for(p = path) transform(p, m)]; //! Apply transform to a path
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function unit(v) = let(n = norm(v)) n ? v / n : v; //! Convert ```v``` to a unit vector
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function transpose(m) = [ for(j = [0 : len(m[0]) - 1]) [ for(i = [0 : len(m) - 1]) m[i][j] ] ]; //! Transpose an arbitrary size matrix
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function identity(n, x = 1) = [for(i = [0 : n - 1]) [for(j = [0 : n - 1]) i == j ? x : 0] ]; //! Construct an arbitrary size identity matrix
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function reverse(v) = let(n = len(v) - 1) n < 0 ? [] : [for(i = [0 : n]) v[n - i]]; //! Reverse a vector
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function angle_between(v1, v2) = acos(v1 * v2 / (norm(v1) * norm(v2))); //! Return the angle between two vectors
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// https://www.gregslabaugh.net/publications/euler.pdf
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function euler(R) = let(ay = asin(-R[2][0]), cy = cos(ay)) //! Convert a rotation matrix to a Euler rotation vector.
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cy ? [ atan2(R[2][1] / cy, R[2][2] / cy), ay, atan2(R[1][0] / cy, R[0][0] / cy) ]
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: R[2][0] < 0 ? [atan2( R[0][1], R[0][2]), 180, 0]
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: [atan2(-R[0][1], -R[0][2]), -180, 0];
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