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71 lines
2.3 KiB
Markdown
71 lines
2.3 KiB
Markdown
# archimedean_spiral
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Gets all points and angles on the path of an archimedean spiral. The distance between two points is almost constant.
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It returns a vector of `[[x, y], angle]`.
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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 reduce the error value at the calculated distance between two points, you may try a smaller `point_distance`.
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## Parameters
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- `arm_distance` : If any ray from the origin intersects two successive turnings of the spiral, we'll have two points. The `arm_distance` is the distance between these two points.
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- `init_angle` : In polar coordinates `(r, θ)` Archimedean spiral can be described by the equation `r = bθ ` where `θ` is measured in radians. For being consistent with OpenSCAD, the function here use degrees. The `init_angle` is which angle the first point want to start.
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- `point_distance` : Distance between two points on the path.
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- `num_of_points` : How many points do you want?
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- `rt_dir` : `"CT_CLK"` for counterclockwise. `"CLK"` for clockwise. The default value is `"CT_CLK"`.
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## Examples
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use <polyline2d.scad>;
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use <archimedean_spiral.scad>;
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points_angles = archimedean_spiral(
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arm_distance = 10,
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init_angle = 180,
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point_distance = 5,
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num_of_points = 100
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);
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points = [for(pa = points_angles) pa[0]];
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polyline2d(points, width = 1);
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use <archimedean_spiral.scad>;
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points_angles = archimedean_spiral(
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arm_distance = 10,
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init_angle = 180,
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point_distance = 5,
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num_of_points = 100
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);
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for(pa = points_angles) {
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translate(pa[0])
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circle(2);
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}
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use <archimedean_spiral.scad>;
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t = "3.141592653589793238462643383279502884197169399375105820974944592307816406286";
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points_angles = archimedean_spiral(
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arm_distance = 15,
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init_angle = 450,
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point_distance = 12,
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num_of_points = len(t)
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);
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for(i = [0: len(points_angles) - 1]) {
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translate(points_angles[i][0])
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rotate(points_angles[i][1] + 90)
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text(t[i], valign = "center", halign = "center");
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}
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