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Justin Lin 2017-04-25 15:47:08 +08:00
parent 07b4a648dd
commit ebed0b5292
2 changed files with 4 additions and 39 deletions
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src/archimedean_spiral.scad
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@ -1,7 +1,7 @@
/**
* archimedean_spiral.scad
*
* Gets all points and angles on the path of an archimedean_spiral. The distance between two points is almost constant.
* Gets all points and angles on the path of an archimedean spiral. The distance between two points is almost constant.
*
* It returns a vector of [[x, y], angle].
*

41
src/golden_spiral.scad
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@ -1,52 +1,17 @@
/**
* archimedean_spiral.scad
* golden_spiral.scad
*
* Gets all points and angles on the path of an archimedean_spiral. The distance between two points is almost constant.
* Gets all points and angles on the path of a golden spiral. The distance between two points is almost constant.
*
* It returns a vector of [[x, y], angle].
*
* In polar coordinates (r, <EFBFBD>c) Archimedean spiral can be described by the equation r = b<EFBFBD>c where
* <EFBFBD>c is measured in radians. For being consistent with OpenSCAD, the function here use degrees.
*
* An init_angle less than 180 degrees is not recommended because the function uses an approximate
* approach. If you really want an init_angle less than 180 degrees, a larger arm_distance
* is required. To avoid a small error value at the calculated distance between two points, you
* may try a smaller point_distance.
*
* @copyright Justin Lin, 2017
* @license https://opensource.org/licenses/lgpl-3.0.html
*
* @see https://openhome.cc/eGossip/OpenSCAD/lib-archimedean_spiral.html
* @see https://openhome.cc/eGossip/OpenSCAD/lib-golden_spiral.html
*
**/
function _radian_step(b, theta, l) =
let(r_square = pow(b * theta, 2))
acos((2 * r_square - pow(l, 2)) / (2 * r_square)) / 180 * 3.14159;
function _find_radians(b, point_distance, radians, n, count = 1) =
let(pre_radians = radians[count - 1])
count == n ? radians : (
_find_radians(
b,
point_distance,
concat(
radians,
[pre_radians + _radian_step(b, pre_radians, point_distance)]
),
n,
count + 1)
);
/*
In polar coordinates (r, <EFBFBD>c) Archimedean spiral can be described by the equation r = b<EFBFBD>c where
<EFBFBD>c is measured in radians. For being consistent with OpenSCAD, the function here use degrees.
An init_angle angle less than 180 degrees is not recommended because the function uses an
approximate approach. If you really want an angle less than 180 degrees, a larger arm_distance
is required. To avoid a small error value at the calculated distance between two points, you
may try a smaller point_distance.
*/
function _fast_fibonacci_sub(nth) =
let(
_f = _fast_fibonacci_2_elems(floor(nth / 2)),