Class Curve

Main features

• LIFO of vectors push, pop
• linear interpolation of position, speed, length
• manipulate origin of the curve origin
• geometrical transforms translate, affine, ...

Getting started

A curve is a discrete set of Vector objects that describes a polygonal curve in ND-space. It has an origin that is common to all points. The curve can be parametrized with different speeds along it.

Create a curve

First create a set of vectors that represents the polygonal curve and a choose a time step.

let positions = [Vector3.ex, Vector3.ey, Vector3.exn, Vector3.eyn];
let dt = 0.1;

If you want to set a variable time step along the curve you can specify dt as an array

let dt = [0.1, 0.01, 1];

Note If positions is of size N then dt is of size N-1.

Then choose your origin and construct the curve :

const origin = Vector3.zeros
let curve = new Curve(positions, origin, dt); // origin is (0, 0, 0)

Note It's preferable that the origin does not reference an object contained in the positions array and that references in positions points to different instances.

Positions

The positions array stores position of curve samples relative to this.origin, when affecting a new origin, the new relative positions are recomputed. It's the same process as what was done for Point3 class.

LIFO Structure

You can push/pop elements of the curve. When pushing you have to specify the position vector to insert. You can also specify a time step dt which correspond to the duration to perform a displacement from the last stored to the position to insert.

Example

curve.push(Vector3.ez) // push with default value of time step
curve.push(Vector3.ez, 0.1) // push with given value of time step

However when popping a value a couple with duration and position is always returned.

Example

arr = curve.pop() // [u, dt]

Interpolation

As polygonal curves, we can perform linear interpolation between two points of the curve. This allows to get the speed, position and many other values along the curve as if it was a polygonal continuous curve.

All the interpolation functions uses x parameter, a real value between 0 and 1 :

• x = 0 denotes the starting of the curve
• x = 1 denotes the ending of the curve
• x = 0.5 denotes the middle of the curve

Note γ denotes the position vector on the curve according to the parametrization with x.

Example

let u = curve.position(0.5); // middle point of the curve
let v = curve.length(1); // total length of the curve
let w = curve.speed(0); // initial speed of the curve

Translation and Transformation

Apply matrix transform, translations and affine transforms the same way as for Point3 class..

curve.translate(u);
curve.transform(m);
curve.affine(m, u);

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