Bezier Curve

A free-form curve shaped by control points — for organic outlines, cams and anything a circular arc cannot follow.

In the viewport

1. Click Bezier on the sketch toolbar.
2. Click the poles in order: the start, the control points, then the end. Each click adds one point to the statement, and the curve preview updates as you go.
3. Esc ends the curve.

A pole that snaps onto an existing vertex gets a coincident written for it.

The code behind it

plate.part.js

import { sketch, bezier, line } from 'fluidcad/core';
import { coincident, fix, horizontal, vertical, distance } from 'fluidcad/constraints';

sketch("xz", () => {
    // Half a vase silhouette, ready to be revolved about its centreline.
    const base = line([0, 0], [30, 0]);
    // A cubic bezier: start, two control points, end. Every literal pole is
    // a solver point — .point(1) and .point(2) are the control points, and
    // .start() / .end() are .point(0) / .point(3).
    const side = bezier([30, 0], [60, 40], [5, 70], [20, 110]);
    const rim = line([20, 110], [0, 110]);
    const centerline = line([0, 110], [0, 0]);
    // Join the curve to the lines so the profile closes; the curve itself is
    // not a solver entity, only its poles are.
    coincident(base.end(), side.start());
    coincident(side.end(), rim.start());
    coincident(rim.end(), centerline.start());
    coincident(centerline.end(), base.start());
    horizontal(base);
    horizontal(rim);
    vertical(centerline);
    fix(base.start(), [0, 0]);
    distance(centerline.start(), centerline.end(), 110);
})

By hand

bezier(p0, p1, ..., pn)

The first point is the start and the last the end; the points between are control points. The number of points sets the degree:

Points	Curve
2	A straight line
3	Quadratic (one control point)
4	Cubic (two control points)

A control point can also be another entity's accessor (l.end()), in which case the curve rides that point.

Accessors

Accessor	Meaning
b.point(i)	The i-th pole, 0-based — point(0) is the start
b.start()	Same as point(0)
b.end()	The last pole

note

The curve itself is not a solver entity. Its poles are: constrain b.point(i), b.start() and b.end() and the solve reshapes the curve. tangent, distance and the other entity-level constraints do not accept a bezier.