Stdlib: functions for various quadrilaterals

Right now ZMA has a very limited constraint solver. This makes it hard to express relationships between points. For example, it's difficult to express a parallelogram. Here's my best attempt in KCL:

// Creates a parallelogram with the given side lengths.
fn pgram = (side1, side2) => {
  d1 = side1/2
  d2 = side2/2
  l = sqrt(d1 ^ 2 + d2 ^ 2)
  theta = toDegrees(atan(d2 / d1))
  angle1 = 2 * theta
  angle2 = 2 * (90 - angle1)
  return startSketchAt([0, 0])
  |> angledLine({ angle: angle1, length: l }, %)
  |> angledLine({ angle: angle2, length: l }, %)
  |> angledLine({ angle: 180 + angle1, length: l }, %)
  |> angledLine({ angle: 180 + angle2, length: l }, %)
  |> close(%)
}

I had to break out some pen and paper to do geometry in order to figure out the correct relationships and get this code correct. It took some debugging, I got it wrong at first. We shouldn't make KCL users do this themselves.

One option is to offer a powerful constraint solver, so they can say "this parallelogram has diagonal distances of 6 and 15" using the Dimension tool. That tool lets users constrain points to be a certain distance away. That'll be a significant change from ZMA.

Another option is to offer a range of different stdlib functions to define a parallelogram, for example parallelogram.withSides(number, number) or parallelogram.withAngles(number, number) to define them based on the minor/acute and major/obtuse angles.

We can definitely do the former option, but we should also offer the latter option. The latter will be quicker to implement and will help users get through more and more tasks without needing a constraint solver. Of course, we can't possibly offer a function for every shape users will ever imagine. But we can offer a range of functions for common problems, to let users get further and further in their work before they need a constraint solver.

Suggestions:

Std.Parallelogram
Std.Rhombus
Std.Square
Std.Rectangle
Std.Triangle.Equilateral
Std.Triangle.Isosceles
Std.Triangle.RightAngle
Std.Polygon.WithSideLength
Std.Polygon.WithInternalAngle
Std.Circle.Fraction (produces semicircles, quarter-circles, or whatever percentage of a circle you want)
Std.Gear (ask Nick Boone for what varieties)

These should be namespaced, both for readability and organization.

KittyCAD / modeling-app

Stdlib: functions for various quadrilaterals #4375