# archimedean_spiral

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]`.

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?
• `rt_dir` : `"CT_CLK"` for counterclockwise. `"CLK"` for clockwise. The default value is `"CT_CLK"`.

## Examples

``````use <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];

polyline2d(points, width = 1);
`````` ``````use <archimedean_spiral.scad>;

points_angles = archimedean_spiral(
arm_distance = 10,
init_angle = 180,
point_distance = 5,
num_of_points = 100
);

for(pa = points_angles) {
translate(pa)
circle(2);
}
`````` ``````use <archimedean_spiral.scad>;

t = "3.141592653589793238462643383279502884197169399375105820974944592307816406286";

points_angles = archimedean_spiral(
arm_distance = 15,
init_angle = 450,
point_distance = 12,
num_of_points = len(t)
);

for(i = [0: len(points_angles) - 1]) {
translate(points_angles[i])
rotate(points_angles[i] + 90)
text(t[i], valign = "center", halign = "center");
}
`````` 