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rotate around an arbitrary axis
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@@ -14,6 +14,36 @@
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include <__private__/__to2d.scad>;
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include <__private__/__to3d.scad>;
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function _q_rotate_p_3d(p, a, v) =
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let(
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axis = v / norm(v),
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s = sin(a / 2),
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x = s * axis[0],
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y = s * axis[1],
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z = s * axis[2],
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w = cos(a / 2),
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x2 = x + x,
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y2 = y + y,
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z2 = z + z,
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xx = x * x2,
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yx = y * x2,
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yy = y * y2,
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zx = z * x2,
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zy = z * y2,
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zz = z * z2,
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wx = w * x2,
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wy = w * y2,
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wz = w * z2
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)
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[
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(1 - yy - zz) * p[0] + (yx - wz) * p[1] + (zx + wy) * p[2],
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(yx + wz) * p[0] + (1 - xx - zz) * p[1] + (zy - wx) * p[2],
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(zx - wy) * p[0] + (zy + wx) * p[1] + (1 - xx - yy) * p[2]
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];
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function _rotx(pt, a) =
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let(cosa = cos(a), sina = sin(a))
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[
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@@ -48,10 +78,21 @@ function to_avect(a) =
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)
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);
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function rotate_p(point, a) =
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function _rotate_p(p, a) =
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let(angle = to_avect(a))
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len(point) == 3 ?
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_rotate_p_3d(point, angle) :
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len(p) == 3 ?
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_rotate_p_3d(p, angle) :
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__to2d(
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_rotate_p_3d(__to3d(point), angle)
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_rotate_p_3d(__to3d(p), angle)
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);
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function _q_rotate_p(p, a, v) =
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len(p) == 3 ?
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_q_rotate_p_3d(p, a, v) :
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__to2d(
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_q_rotate_p_3d(__to3d(p), a, v)
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);
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function rotate_p(point, a, v) =
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v == undef ? _rotate_p(point, a) : _q_rotate_p(p, a, v);
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