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added archimedean_spiral

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Justin Lin
2017-03-27 15:32:36 +08:00
parent 077ee6dd74
commit 4edecfe0c6
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# archimedean_spiral
Get 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]`.
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`.
## Parameters
- `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.
- `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.
- `point_distance` : Distance between two points on the path.
- `num_of_points` : How many points do you want?
## Examples
include <polyline2d.scad>;
points_angles = archimedean_spiral(
arm_distance = 10,
init_angle = 180,
point_distance = 5,
num_of_points = 100
);
points = [for(pa = points_angles) pa[0]];
polyline2d(points, width = 1);
![archimedean_spiral](images/lib-archimedean_spiral-1.JPG)
points_angles = archimedean_spiral(
arm_distance = 10,
init_angle = 180,
point_distance = 5,
num_of_points = 100
);
for(pa = points_angles) {
translate(pa[0])
circle(2);
}
![archimedean_spiral](images/lib-archimedean_spiral-2.JPG)
t = "3.141592653589793238462643383279502884197169399375105820974944592307816406286";
points = archimedean_spiral(
arm_distance = 15,
init_angle = 450,
point_distance = 12,
num_of_points = len(t)
);
for(i = [0: len(points) - 1]) {
translate(points[i][0])
rotate(points[i][1] + 90)
text(t[i], valign = "center", halign = "center");
}
![archimedean_spiral](images/lib-archimedean_spiral-3.JPG)