Equation curves

An equation curve is a curve you describe with a rule instead of drawing it with clicks. You type the rule, and SolidCraft draws the curve that follows it, exactly, every time.

It is the way to get shapes that are hard to draw by hand: a smooth wave, a parabola, a spiral, or the curved side of a gear tooth.

Your first curve: a straight ramp

1. Start a sketch: SOLID › CREATE › Create Sketch, then click a plane.
2. Click SKETCH › CREATE › Equation Curve. A window opens with a wave already filled in.
3. Set Form to Explicit. Now there is one rule to fill in, y(x): how high is the curve at each x?
4. Type x / 2 in y(x), 0 in Start and 40 in End.
5. Click OK.

The rule says: the height is half of how far along you are. At x = 10 the curve is 5 high, at x = 40 it is 20 high. Start and End say where along x the curve begins and stops.

Explicit: one rule for the height

With Explicit, you write the height y using x. Try these (same steps, other rules):

In the wave, 8 is how tall each bump is and 5 stretches it sideways: try x / 10 and the waves get twice as long.

Parametric: a rule for x and a rule for y

Some curves go back on themselves, like a circle: for one x there are two heights. For those, set Form to Parametric and give two rules, x(t) and y(t).

Think of t as a clock. It starts at Start and ticks up to End. At every moment the two rules say where the pen is: across (x) and up (y). The curve is the path the pen draws while the clock runs.

For the circle, cos and sin walk the pen around, and 20 is how far from the middle it stays. 2 * pi is one full turn, so the circle closes. In the spiral, the distance from the middle (2 * t) grows while the clock runs, so the pen moves outwards as it goes round.

Angles are in radians

sin, cos and tan count angles in radians, not degrees: a full turn is 2 * pi (about 6.28), half a turn is pi. You can also write an angle with its unit for Start and End, such as 360 deg.

A number without a unit is in your design’s unit (millimetres unless you changed it).

Using parameters: a gear tooth

Rules can use the design’s parameters. Here a parameter r (20 mm) is the size of a base circle, and the curve is the involute of that circle: the path the end of a string makes as you unwind it from the circle. The sides of most gear teeth have this shape.

Change r in the Parameters dialog and the curve redraws itself to match: the rule is kept, not just the shape.

From curve to part

An equation curve is an ordinary sketch curve, so you can build with it:

• A curve that ends where it starts closes by itself, smoothly. Extrude it and you get a solid. This flower uses a radius that goes in and out six times as the clock goes round once:

  Rule in x(t)	Rule in y(t)	Start	End
  (20 + 4 * cos(6 * t)) * cos(t)	(20 + 4 * cos(6 * t)) * sin(t)	0	2 * pi

  

• An open curve can be closed with lines: draw lines from its two ends, then extrude the shape. For example, close a wave with three lines down to the x axis to get a wavy strip.

• It can be the path of a sweep.

Changing a curve

Right-click the curve and choose Edit Equation Curve. The same window opens with the rules in it; change them and click OK.

When something goes wrong

• The curve is tiny or huge. Check the numbers in the rule and the Start/End range: sin never goes past 1, so sin(x) alone is at most 1 mm high. Multiply it (8 * sin(x)).
• The wave has too few bumps, or far too many. Remember radians: sin(x) repeats every 2 * pi (6.28) along x, not every 360.
• The circle has a gap. End must be a whole turn: 2 * pi, or 360 deg.
• A rule is rejected. Use * for multiply (2 * t, not 2t), and close every bracket.

For scripts and agents

The commands are sketch.equation_curve and sketch.equation_curve.edit (see the command reference). The curve is a fit point spline through points worked out from the rules, as many as keep it within the Tolerance (0.01 mm unless you set another), up to 500. Its points are fixed, so other curves can start at its ends. When a parameter a rule uses changes, the points follow. The pictures on this page come from the scripts in docs/book/scripts/equation-*.json.