flexy

A library that bends three.js box geometries along Bezier Curves

Demo

Play along with different curves and double bends!

How to install

As an es6 module

``
npm install flexy
`

How to use it

`js
import * as flexy from 'flexy';
import * as THREE from 'three';

const R = 3;
const startPoint = new Vector3(R, 0, 0);
const controlPoint1 = new Vector3(R, R * 0.55, 0);
const controlPoint2 = new Vector3(R * 0.45, R, 0);
const endPoint = new Vector3(0, R, 0);

// This is a cubic bezier curve. The direction that we're "drawing" the curve, affects the final outcome.
// In this case we're drawing from x = R -> x = 0
// So the point of our geometry with the smallest x coordinate will end up on the x = R position.
// That will make the modified geometry appear as it was also rotated.
const curve = new CubicBezierCurve3(startPoint, controlPoint1, controlPoint2, endPoint);

// Indicates the orientation of the hypothetical plane that the curve could "rest" upon. For example, a curve in the x-y plane, could be rest flat upon the (0, 0, 1) or (0, 0, -1) plane.
// This is usefull to the modifier because it can consistently calculate the tangent lines for each point in the curve, therefore bend every point of the geometry to the correct position.
const orientation = new new THREE.Vector3(0, 0, 1);

flexy.bend({
THREE,
curve,
orientation,
bufferGeometry: mesh.geometry,
axis: 'x'
});
``

Behind the scenes

First, we generate a mesh using the THREE.BoxGeometry constructor.
!plot

Then we need a curve that our geometry will be placed & streched/bent upon (in our case the X axis).
!plot

First we have to normalize each x coordinate of the box, to a point at our curve. For example, the far left x coordinates, will be normalize to the point at the start of the curve.

Next, we calculate the tangent for of these normalized coordinates.
!plot

And we procceed by calculating vectors that are orthogonal/perpendicular to the tangent vectors (the purple lines).
!plot

Now all we have to do, is to rotated them (counter)clockwise in order to match the (0, y, z) angle that the current x coordintate has.
!plot

Here are the resulting normals.
!plot

Finally we need to set the length of each normal, equal to the (0, y, z) length.
!plot

in order to get something like this:
!plot

Here's another screenshot that emphasizes the relationship between the curve and the box after the box.
!plot