/ BOSL2 Public

# 2D Shapes Tutorial

## Primitives

There are two built-in 2D primitive shapes that OpenSCAD provides: `square()`, and `circle()`. You can still use them in the familiar ways that OpenSCAD provides:

```include <BOSL2/std.scad>
square([60,40], center=true);```

```include <BOSL2/std.scad>
circle(r=50);```

```include <BOSL2/std.scad>
circle(d=100, \$fn=8);```

These modules have also been enhanced in the BOSL2 library in three ways: Anchoring, spin, and attachability.

#### Anchoring:

When you create a `square()`, you can specify what corner or side will be anchored at the origin. This is used in place of the `center=` argument, and is more flexible. The `anchor=` argument takes a vector as a value, pointing roughly towards the side or corner you want to align to the origin. For example, to align the center of the back edge to the origin, set the anchor to `[0,1]`:

```include <BOSL2/std.scad>
square([60,40], anchor=[0,1]);```

To align the front right corner to the origin:

```include <BOSL2/std.scad>
square([60,40], anchor=[1,-1]);```

To center:

```include <BOSL2/std.scad>
square([60,40], anchor=[0,0]);```

To make it clearer when giving vectors, there are several standard vector constants defined:

Constant Direction Value
`LEFT` X- `[-1, 0, 0]`
`RIGHT` X+ `[ 1, 0, 0]`
`FRONT`/`FORWARD`/`FWD` Y- `[ 0,-1, 0]`
`BACK` Y+ `[ 0, 1, 0]`
`BOTTOM`/`BOT`/`BTM`/`DOWN` Z- `[ 0, 0,-1]` (3D only.)
`TOP`/`UP` Z+ `[ 0, 0, 1]` (3D only.)
`CENTER`/`CTR` Centered `[ 0, 0, 0]`

Note that even though these are 3D vectors, you can use most of them, (except `UP`/`DOWN`, of course) for anchors in 2D shapes:

```include <BOSL2/std.scad>
square([60,40], anchor=BACK);```

```include <BOSL2/std.scad>
square([60,40], anchor=CENTER);```

You can add vectors together to point to corners:

```include <BOSL2/std.scad>
square([60,40], anchor=FRONT+RIGHT);```

For `circle()`, the anchor vector can point at any part of the circle perimeter:

```include <BOSL2/std.scad>
circle(d=50, anchor=polar_to_xy(1,150));```

Note that the radius does not matter for the anchor because only the anchor's direction affects the result. You can see the typical anchor points by giving `show_anchors()` as a child of the shape:

```include <BOSL2/std.scad>
square([60,40], center=true)
show_anchors();```

```include <BOSL2/std.scad>
circle(d=50)
show_anchors();```

#### Spin:

The second way that `square()` and `circle()` have been enhanced is with spin. When you create the shape, you can spin it in place with the `spin=` argument. You just pass it a number of degrees to rotate clockwise:

```include <BOSL2/std.scad>
square([60,40], anchor=CENTER, spin=30);```

Anchoring or centering is performed before the spin:

```include <BOSL2/std.scad>
square([60,40], anchor=BACK, spin=30);```

For circles, spin can be useful when `\$fn=` is also given:

```include <BOSL2/std.scad>
circle(d=50, \$fn=6, spin=15);```

Since anchoring is performed before spin, you can use them together to spin around the anchor:

```include <BOSL2/std.scad>
circle(d=50, \$fn=6, anchor=LEFT, spin=15);```

#### Attachability:

The third way `square()` and `circle()` have been enhanced is that you can attach them together at anchoring points in various ways. This is done by making one shape a child of the shape you want to attach to. By default, just making one shape a child of the other will position the child shape at the center of the parent shape.

```include <BOSL2/std.scad>
square(50, center=true)
#square(50, spin=45, center=true);```

```include <BOSL2/std.scad>
square(50, center=true)
#square([20,40], anchor=FWD);```

By adding the `position()` module, you can position the child at any anchorpoint on the parent:

```include <BOSL2/std.scad>
square(50, center=true)
position(BACK)
#square(25, spin=45, center=true);```

```include <BOSL2/std.scad>
square(50, center=true)
position(FWD+RIGHT)
#square(25, spin=45, center=true);```

```include <BOSL2/std.scad>
circle(d=50)
position(polar_to_xy(1,60))
#circle(d=10);```

Anchorpoints aren't just positions on the parent, though. They also have an orientation. In most cases, the orientation of an anchorpoint is outward away from the face of the wall, generally away from the center of the shape. You can see this with the `show_anchors()` module:

```include <BOSL2/std.scad>
square(50, center=true)
show_anchors();```

```include <BOSL2/std.scad>
circle(d=50)
show_anchors();```

If you want to orient the child to match the orientation of an anchorpoint, you can use the `orient()` module. It does not position the child. It only rotates it:

```include <BOSL2/std.scad>
square(50, center=true)
orient(anchor=LEFT)
#square([10,40], anchor=FWD);```

```include <BOSL2/std.scad>
square(50, center=true)
orient(anchor=FWD)
#square([10,40], anchor=FWD);```

```include <BOSL2/std.scad>
square(50, center=true)
orient(anchor=RIGHT)
#square([10,40], anchor=FWD);```

```include <BOSL2/std.scad>
circle(d=50)
orient(polar_to_xy(1,30))
#square([10,40], anchor=FWD);```

You can use `position()` and `orient()` together to both position and orient to an anchorpoint:

```include <BOSL2/std.scad>
square(50, center=true)
position(RIGHT+BACK)
orient(anchor=RIGHT+BACK)
#square([10,40], anchor=FWD);```

```include <BOSL2/std.scad>
circle(d=50)
position(polar_to_xy(1,30))
orient(polar_to_xy(1,30))
#square([10,40], anchor=FWD);```

But it's simpler to just use the `attach()` module to do both at once:

```include <BOSL2/std.scad>
square(50, center=true)
attach(LEFT+BACK)
#square([10,40], anchor=FWD);```

```include <BOSL2/std.scad>
circle(d=50)
attach(polar_to_xy(1,30))
#square([10,40], center=true);```

Instead of specifying the `anchor=` in the child, you can pass a second argument to `attach()` that tells it which side of the child to attach to the parent:

```include <BOSL2/std.scad>
square([10,50], center=true)
attach(BACK, LEFT)
#square([10,40], center=true);```

```include <BOSL2/std.scad>
circle(d=50)
attach(polar_to_xy(1,30), LEFT)
#square([10,40], center=true);```

#### Rectangles

The BOSL2 library provides an alternative to `square()`, that support more features. It is called `rect()`. You can use it in the same way you use `square()`, but it also provides extended functionality. For example, it allows you to round the corners:

```include <BOSL2/std.scad>
rect([60,40], rounding=10);```

Or chamfer them:

```include <BOSL2/std.scad>
rect([60,40], chamfer=10);```

You can even specify which corners get rounded or chamfered. If you pass a list of four size numbers to the `rounding=` or `chamfer=` arguments, it will give each corner its own size. In order, it goes from the back-right (quadrant I) corner, counter-clockwise around to the back-left (quadrant II) corner, to the forward-left (quadrant III) corner, to the forward-right (quadrant IV) corner:

If a size is given as `0`, then there is no rounding and/or chamfering for that quadrant's corner:

```include <BOSL2/std.scad>
rect([60,40], rounding=[0,5,10,15]);```

```include <BOSL2/std.scad>
rect([60,40], chamfer=[0,5,10,15]);```

You can give both `rounding=` and `chamfer=` arguments to mix rounding and chamfering, but only if you specify per corner. If you want a rounding in a corner, specify a 0 chamfer for that corner, and vice versa:

```include <BOSL2/std.scad>
rect([60,40], rounding=[5,0,10,0], chamfer=[0,5,0,15]);```

#### Ellipses

The BOSL2 library also provides an enhanced equivalent of `circle()` called `ellipse()`. You can use it in the same way you use `circle()`, but it also provides extended functionality. For example, it allows more control over its size.

Since a circle in OpenSCAD can only be approximated by a regular polygon with a number of straight sides, this can lead to size and shape inaccuracies. To counter this, the `realign=` and `circum=` arguments are also provided.

The `realign=` argument, if set `true`, rotates the `ellipse()` by half the angle between the polygon sides:

```include <BOSL2/std.scad>
ellipse(d=100, \$fn=8);
#ellipse(d=100, \$fn=8, realign=true);```

The `circum=` argument, if true, makes it so that the polygon forming the `ellipse()` circumscribes the ideal circle instead of inscribing it.

Inscribing the ideal circle:

```include <BOSL2/std.scad>
color("green") ellipse(d=100, \$fn=360);
ellipse(d=100, \$fn=6);```

Circumscribing the ideal circle:

```include <BOSL2/std.scad>
ellipse(d=100, \$fn=6, circum=true);
color("green") ellipse(d=100, \$fn=360);```

The `ellipse()` module, as its name suggests, can be given separate X and Y radii or diameters. To do this, just give `r=` or `d=` with a list of two radii or diameters:

```include <BOSL2/std.scad>
ellipse(r=[30,20]);```

```include <BOSL2/std.scad>
ellipse(d=[60,40]);```

Like `circle()`, you can anchor, spin and attach `ellipse()` shapes:

```include <BOSL2/std.scad>
ellipse(d=50, anchor=BACK);```

```include <BOSL2/std.scad>
ellipse(d=50, anchor=FRONT+RIGHT);```

```include <BOSL2/std.scad>
ellipse(d=50)
attach(BACK+RIGHT, FRONT+LEFT)
ellipse(d=30);```

#### Right Triangles

The BOSL2 library provides a simple way to make a 2D right triangle by using the `right_triangle()` module:

```include <BOSL2/std.scad>
right_triangle([40,30]);```

You can use `xflip()` and `yflip()` to change which quadrant the triangle is formed in:

```include <BOSL2/std.scad>
xflip() right_triangle([40,30]);```

```include <BOSL2/std.scad>
yflip() right_triangle([40,30]);```

```include <BOSL2/std.scad>
xflip() yflip() right_triangle([40,30]);```

Or, alternatively, just rotate it into the correct quadrant with `spin=`:

```include <BOSL2/std.scad>
right_triangle([40,30], spin=90);```

```include <BOSL2/std.scad>
right_triangle([40,30], spin=-90);```

You can also use anchoring with right triangles:

```include <BOSL2/std.scad>
right_triangle([40,30], anchor=FWD+RIGHT);```

#### Trapezoids

OpenSCAD doesn't provide a simple way to make general 2D triangles, trapezoids, or parallelograms. The BOSL2 library can provide all of these shapes with the `trapezoid()` module.

To make a simple triangle, just make one of the widths zero:

```include <BOSL2/std.scad>
trapezoid(w1=50, w2=0, h=40);```

To make a right triangle, you need to use the `shift=` argument, to shift the back of the trapezoid along the X axis:

```include <BOSL2/std.scad>
trapezoid(w1=50, w2=0, h=50, shift=-25);```

```include <BOSL2/std.scad>
trapezoid(w1=50, w2=0, h=50, shift=25);```

```include <BOSL2/std.scad>
trapezoid(w1=0, w2=50, h=50, shift=-25);```

```include <BOSL2/std.scad>
trapezoid(w1=0, w2=50, h=50, shift=25);```

You can make a trapezoid by specifying non-zero widths for both the front (`w1=`) and back (`w2=`):

```include <BOSL2/std.scad>
trapezoid(w1=30, w2=50, h=50);```

A parallelogram is just a matter of using the same width for front and back, with a shift along the X axis:

```include <BOSL2/std.scad>
trapezoid(w1=50, w2=50, shift=20, h=50);```

A quadrilateral can be made by having unequal, non-zero front (`w1=`) and back (`w2=`) widths, with the back shifted along the X axis:

```include <BOSL2/std.scad>
trapezoid(w1=50, w2=30, shift=20, h=50);```

You can use `anchor=` and `spin=`, just like with other attachable shapes. However, the anchor point orientations are based on the side angles of the faces, and may not be what you expect:

```include <BOSL2/std.scad>
trapezoid(w1=30, w2=50, h=50)
show_anchors();```

#### Regular N-Gons

OpenSCAD lets you make regular N-gons (pentagon, hexagon, etc) by using `circle()` with `\$fn`. While this is concise, it may be less than obvious at first glance:

```include <BOSL2/std.scad>
circle(d=50, \$fn=5);```

The BOSL2 library has modules that are named more clearly, for common N-gons:

```include <BOSL2/std.scad>
pentagon(d=50);```

```include <BOSL2/std.scad>
hexagon(d=50);```

```include <BOSL2/std.scad>
octagon(d=50);```

```include <BOSL2/std.scad>
regular_ngon(n=7, d=50);```

These modules also provide you with extra functionality. They can be sized by side length:

```include <BOSL2/std.scad>
pentagon(side=20);```

They can be sized by circumscribed circle radius/diameter:

```include <BOSL2/std.scad>
pentagon(ir=25);
pentagon(id=50);```

They can be rotated by half a side:

```include <BOSL2/std.scad>
left(30)  pentagon(d=50, realign=true);
right(30) pentagon(d=50, realign=false);```

They can be rounded:

```include <BOSL2/std.scad>
pentagon(d=50, rounding=10);```

```include <BOSL2/std.scad>
hexagon(d=50, rounding=10);```

They also have somewhat different attachment behavior. A circle with a small `\$fn=` will attach things at the ideal circle, not along the created polygon:

```include <BOSL2/std.scad>
color("green") stroke(circle(d=50), closed=true);
circle(d=50,\$fn=6)
show_anchors();```

While an N-gon will attach along the polygon itself:

```include <BOSL2/std.scad>
hexagon(d=50)
show_anchors(custom=false);```

You can use `anchor=` and `spin=`, just like with other attachable shapes. However, the anchor points are based on where the anchor vector would intersect the side of the N-gon, and may not be where you expect them:

```include <BOSL2/std.scad>
pentagon(d=50)
show_anchors(custom=false);```

N-gons also have named anchor points for their sides and tips:

```include <BOSL2/std.scad>
pentagon(d=30)
show_anchors(std=false);```

#### Stars

The BOSL2 library has stars as a basic supported shape. They can have any number of points. You can specify a star's shape by point count, inner and outer vertex radius/diameters:

```include <BOSL2/std.scad>
star(n=3, id=10, d=50);```

```include <BOSL2/std.scad>
star(n=5, id=15, r=25);```

```include <BOSL2/std.scad>
star(n=10, id=30, d=50);```

Or you can specify the star shape by point count and number of points to step:

```include <BOSL2/std.scad>
star(n=7, step=2, d=50);```

```include <BOSL2/std.scad>
star(n=7, step=3, d=50);```

If the `realign=` argument is given a true value, then the star will be rotated by half a point angle:

```include <BOSL2/std.scad>
left(30) star(n=5, step=2, d=50);
right(30) star(n=5, step=2, d=50, realign=true);```

The `align_tip=` argument can be given a vector so that you can align the first point in a specific direction:

```include <BOSL2/std.scad>
star(n=5, ir=15, or=30, align_tip=BACK)
attach("tip0") color("blue") anchor_arrow2d();```

```include <BOSL2/std.scad>
star(n=5, ir=15, or=30, align_tip=BACK+RIGHT)
attach("tip0") color("blue") anchor_arrow2d();```

Similarly, the first indentation or pit can be oriented towards a specific vector with `align_pit=`:

```include <BOSL2/std.scad>
star(n=5, ir=15, or=30, align_pit=BACK)
attach("pit0") color("blue") anchor_arrow2d();```

```include <BOSL2/std.scad>
star(n=5, ir=15, or=30, align_pit=BACK+RIGHT)
attach("pit0") color("blue") anchor_arrow2d();```

You can use `anchor=` and `spin=`, just like with other attachable shapes. However, the anchor points are based on the furthest extents of the shape, and may not be where you expect them:

```include <BOSL2/std.scad>
star(n=5, step=2, d=50)
show_anchors(custom=false);```

Stars also have named anchor points for their pits, tips, and midpoints between tips:

```include <BOSL2/std.scad>
star(n=5, step=2, d=40)
show_anchors(std=false);```

#### Teardrop2D

Often when 3D printing, you may want to make a circular hole in a vertical wall. If the hole is too big, however, the overhang at the top of the hole can cause problems with printing on an FDM/FFF printer. If you don't want to use support material, you can just use the teardrop shape. The `teardrop2d()` module will let you make a 2D version of the teardrop shape, so that you can extrude it later:

```include <BOSL2/std.scad>
teardrop2d(r=20);```

```include <BOSL2/std.scad>
teardrop2d(d=50);```

The default overhang angle is 45 degrees, but you can adjust that with the `ang=` argument:

```include <BOSL2/std.scad>
teardrop2d(d=50, ang=30);```

If you prefer to flatten the top of the teardrop, to encourage bridging, you can use the `cap_h=` argument:

```include <BOSL2/std.scad>
teardrop2d(d=50, cap_h=25);```

```include <BOSL2/std.scad>
teardrop2d(d=50, ang=30, cap_h=30);```

You can use `anchor=` and `spin=`, just like with other attachable shapes. However, the anchor points are based on the furthest extents of the shape, and may not be where you expect them:

```include <BOSL2/std.scad>
teardrop2d(d=50, ang=30, cap_h=30)
show_anchors();```

#### Glued Circles

A more unusal shape that BOSL2 provides is Glued Circles. It's basically a pair of circles, connected by what looks like a gloopy glued miniscus:

```include <BOSL2/std.scad>

The `r=`/`d=` arguments can specify the radius or diameter of the two circles:

```include <BOSL2/std.scad>

```include <BOSL2/std.scad>

The `spread=` argument specifies the distance between the centers of the two circles:

```include <BOSL2/std.scad>

```include <BOSL2/std.scad>

The `tangent=` argument gives the angle of the tangent of the meniscus on the two circles:

```include <BOSL2/std.scad>

```include <BOSL2/std.scad>

```include <BOSL2/std.scad>

One useful thing you can do is to string a few `glued_circle()`s in a line then extrude them to make a ribbed wall:

```include <BOSL2/std.scad>
\$fn=36;  s=10;
linear_extrude(height=50,convexity=16,center=true)
xcopies(s*sqrt(2),n=3)

You can use `anchor=` and `spin=`, just like with other attachable shapes. However, the anchor points are based on the furthest extents of the shape, and may not be where you expect them:

```include <BOSL2/std.scad>
show_anchors();```

Basic Modeling:

Math:

Data Management: