It extrudes a 2D shape along a path. This module is suitable for a path created by a continuous function.

When using this module, you should use points to represent the 2D shape. If your 2D shape is not solid, indexes of triangles are required. See sweep for details.

## Parameters

`shape_pts`

: A list of points represent a shape. See the example below.`path_pts`

: A list of points represent the path.`triangles`

:`"SOLID"`

(default),`"HOLLOW"`

or user-defined indexes. See example below.`twist`

: The number of degrees of through which the shape is extruded.`scale`

: Scales the 2D shape by this value over the length of the extrusion. Scale can be a scalar or a vector.`closed`

: If the first point and the last point of`path_pts`

has the same coordinate, setting`closed`

to`true`

will connect them automatically.`method`

: Which method does`path_extrude`

take to**guess**how to generate sections? It accepts two value,`"AXIS_ANGLE"`

(default) and`"EULER_ANGLE"`

.**Since:**1.3.

## Examples

```
use <path_extrude.scad>;
use <bezier_curve.scad>;
t_step = 0.05;
width = 2;
p0 = [0, 0, 0];
p1 = [40, 60, 35];
p2 = [-50, 70, 0];
p3 = [20, 150, -35];
p4 = [30, 50, -3];
shape_pts = [
[5, -5],
[3, 4],
[0, 5],
[-5, -5]
];
path_pts = bezier_curve(t_step,
[p0, p1, p2, p3, p4]
);
path_extrude(shape_pts, path_pts);
```

```
use <path_extrude.scad>;
use <bezier_curve.scad>;
t_step = 0.05;
p0 = [0, 0, 0];
p1 = [40, 60, 35];
p2 = [-50, 70, 0];
p3 = [20, 150, -35];
p4 = [30, 50, -3];
shape_pts = [
// outer
[5, 0],
[3, 9],
[0, 10],
[-5, 0],
// inner
[3, 2],
[2, 7],
[0, 7],
[-3, 2]
];
path_pts = bezier_curve(t_step,
[p0, p1, p2, p3, p4]
);
path_extrude(shape_pts, path_pts, triangles = "HOLLOW");
```

```
use <path_extrude.scad>;
use <bezier_curve.scad>;
t_step = 0.05;
p0 = [0, 0, 0];
p1 = [40, 60, 35];
p2 = [-50, 70, 0];
p3 = [20, 150, -5];
p4 = [50, 50, -3];
shape_pts = [
// outer
[10, 0],
[-5, 10],
[-10, 0],
// inner
[7, 1],
[-4, 8],
[-7, 1]
];
path_pts = bezier_curve(t_step,
[p0, p1, p2, p3, p4]
);
path_extrude(
shape_pts,
path_pts,
triangles = [
[0, 4, 3],
[0, 1, 4],
[1, 5, 4],
[1, 2, 5],
[2, 3, 5],
[2, 0, 3]
]
);
```

## About `path_extrude`

(Important!!)

`path_extrude`

is actually a workaround when you have/provide only path points.

If you want to extrude a shape along a path precisely, providing enough information about how to rotate sections is necessary. If you want to extrude a shape along a helix, `helix_extrude`

is more suitable because it knows how to dig out necessary data for rotating sections precisely.

```
use <helix_extrude.scad>;
shape_pts = [
[0,0],
[3, 1],
[0, 2]
];
helix_extrude(shape_pts,
radius = 5,
levels = 5,
level_dist = 3,
vt_dir = "SPI_UP"
);
```

If you have only points, what `path_extrude`

can do is to **guess** data about rotations. The different algorithm will dig out different data. For example:

```
use <helix.scad>;
use <path_extrude.scad>;
shape_pts = [
[0,0],
[3, 1],
[0, 2]
];
points = helix(
radius = 5,
levels = 5,
level_dist = 3,
vt_dir = "SPI_UP"
);
path_extrude(shape_pts, points);
```

You might think this is wrong. Actually, it's not. It's the correct/default behavior of `path_extrude`

. Because **you don't provide other information**, what `path_extrude`

can do is to **guess** how to generate sections from points. You think it's a bug in `path_extrude`

because your brain has information that path points do not provide.

The `method`

parameter is default to `"AXIS_ANGLE"`

, a way to guess information from points. It accepts `"EULER_ANGLE"`

, too.

```
use <helix.scad>;
use <path_extrude.scad>;
shape_pts = [
[0,0],
[3, 1],
[0, 2]
];
points = helix(
radius = 5,
levels = 5,
level_dist = 3,
vt_dir = "SPI_UP"
);
path_extrude(shape_pts, points, method = "EULER_ANGLE");
```

`"EULER_ANGLE"`

generates the same section at the same point. You might think the model is correct. But, that's because what it guesses from points just match your expectation.

`"EULER_ANGLE"`

will generate an abrupt when the path is exactly vertical. The problem happened in (older) Blender, too.

```
use <path_extrude.scad>;
shape_pts = [[5, -5], [5, 5], [-5, 5], [-5, -5]];
path_pts = [
[20, 20, 0],
[18.2, 18.2, 2],
[16.8, 16.8, 4],
[15.8, 15.8, 6],
[15.2, 15.2, 8],
[15, 15, 10],
[15.2, 15.2, 12],
[15.8, 15.8, 14],
[16.8, 16.8, 16],
[18.2, 18.2, 18],
[20, 20, 20]
];
path_extrude(shape_pts, path_pts, method = "EULER_ANGLE");
```

The problem doesn't happen when `method`

is `"AXIS_ANGLE"`

.

```
use <path_extrude.scad>;
shape_pts = [[5, -5], [5, 5], [-5, 5], [-5, -5]];
path_pts = [
[20, 20, 0],
[18.2, 18.2, 2],
[16.8, 16.8, 4],
[15.8, 15.8, 6],
[15.2, 15.2, 8],
[15, 15, 10],
[15.2, 15.2, 12],
[15.8, 15.8, 14],
[16.8, 16.8, 16],
[18.2, 18.2, 18],
[20, 20, 20]
];
path_extrude(shape_pts, path_pts, method = "AXIS_ANGLE");
```

So, which is the correct method? Both methods are correct when you provide only points. `method`

is just a way you tell `path_extrude`

how to guess more information when extruding.

`"EULER_ANGLE"`

will generate an abrupt when the path is exactly vertical. Some users might think it's a bug so `"AXIS_ANGLE"`

is the default value.

`"EULER_ANGLE"`

, however, generates the same section at the same point. This means that you don't have to adjust sections if you want to extrude along a closed path. It's an advantage when extruding. For example:

```
use <shape_pentagram.scad>;
use <path_extrude.scad>;
use <torus_knot.scad>;
p = 2;
q = 3;
phi_step = 0.05;
star_radius = 0.5;
pts = torus_knot(p, q, phi_step);
shape_pentagram_pts = shape_pentagram(star_radius);
// not closed perfectly
translate([-8, 0, 0])
path_extrude(
shape_pentagram_pts,
[each pts, pts[0]],
closed = true,
method = "AXIS_ANGLE"
);
// adjust it
path_extrude(
shape_pentagram_pts,
[each pts, pts[0]],
closed = true,
twist = 188,
method = "AXIS_ANGLE"
);
// "EULER_ANGLE" is easy in this situation
translate([0, 8, 0])
path_extrude(
shape_pentagram_pts,
[each pts, pts[0]],
closed = true,
method = "EULER_ANGLE"
);
```

Both methods are useful. If `"AXIS_ANGLE"`

doesn't guess out what you want, choose `"EULER_ANGLE"`

, and vice versa.

For more information, see #issue 3 and #issue 5.