# Drawing Curves

## How To Draw Curves

If you want to draw a circular path then it is easy enough to generate the points, in the XY plane, for this using

`var path = [];for(var theta = 0; theta < 2 * Math.PI; theta +=deltaTheta ) { path.push(new BABYLON.Vector3(radius * Math.cos(theta), radius * Math.sin(theta), 0));`

When you are of a mind to do it you can work out some quite complex paths by hand.

What follows is how to draw some mathematical curves by using the Babylon.js *Curve3* object, from which you can extract the array of points you need to draw lines, ribbons, tubes and extruded shapes.

The general form is

`var curve = BABYLON.Curve3.Create.CURVETYPE(parameters);`

## Arc Through Three Points

Available from version 5.0.0. Given three points in space, not in a straight line, it is always possible to draw join the points up using a circular arc or to draw a circle through the three points.

`var arc = BABYLON.Curve3.ArcThru3Points(first, second, third, steps, closed, fullCircle)`

**first***Vector3*the first point the arc must pass through.**second***Vector3*the second point the arc must pass through.**third***Vector3*the third point the arc must pass through.**steps***number*the larger the number of steps the more detailed the arc.**closed***boolean*optional with default false, when true forms the chord from the first and third point**fullCircle***boolean*optional with default false, when true forms the complete circle through the three points

This static method returns an instance of *Curve3*.

Just use the Curve3 *getPoints()* method to fill your array : *getPoints()* returns an array of successive *Vector3*.

The *length()* method returns the curve length.

`var path = arc.getPoints();var l = arc.length();`

## Quadratic Bezier Curve

http://en.wikipedia.org/wiki/B%C3%A9zier_curve#Quadratic_curves

`var bezier2 = BABYLON.Curve3.CreateQuadraticBezier(origin, control, destination, nb_of_points);`

**origin**:*Vector3*the origin point,**control**:*Vector3*the control point,**destination**:*Vector3*the destination point,**nb_of_points**:*number*number of points wanted in the path array.

This static method returns an instance of *Curve3*.

Just use the Curve3 *getPoints()* method to fill your array : *getPoints()* returns an array of successive *Vector3*.

The *length()* method returns the curve length.

`var path = bezier2.getPoints();var l = bezier2.length();`

## Cubic Bezier curve

http://en.wikipedia.org/wiki/B%C3%A9zier_curve# Higher-order_curves

`var bezier3 = BABYLON.Curve3.CreateCubicBezier(origin, control1, control2, destination, nb_of_points)`

**origin**:*Vector3*the origin point,**control1**:*Vector3*the first control point,**control2**:*Vector3*the second control point,**destination**:*Vector3*the destination point,**nb_of_points**:*number*the wanted final curve number of points in the array.

This static method returns an instance of *Curve3*.

Just use the Curve3 *getPoints()* method to fill your array : *getPoints()* returns an array of successive *Vector3*.

The *length()* method returns the curve length.

`var path = bezier3.getPoints();var l = bezier3.length();`

## Hermite Spline

http://en.wikipedia.org/wiki/Cubic_Hermite_spline

`var hermite = BABYLON.Curve3.CreateHermiteSpline(p1, t1, p2, t2, nbPoints);`

**p1**:*Vector3*the origin point,**t1**:*Vector3*the origin tangent vector,**p2**:*Vector3*the destination point,**t2**:*Vector3*the destination tangent vector,**nbPoints**:*number*the wanted final curve number of points in the array.

*Curve3*.

Just use the Curve3 *getPoints()* method to fill your array : *getPoints()* returns an array of successive *Vector3*.

The *length()* method returns the curve length.

`var path = hermite.getPoints();var l = hermite.length();`

## Catmull-Rom Spline

https://en.wikipedia.org/wiki/Cubic_Hermite_spline#Catmull.E2.80.93Rom_spline

`var nbPoints = 20; // the number of points between each Vector3 control pointsvar points = [vec1, vec2, ..., vecN]; // an array of Vector3 the curve must pass through : the control pointsvar closed = true; // closes the curve when truevar catmullRom = BABYLON.Curve3.CreateCatmullRomSpline(points, nbPoints, closed);`

**points**:*Vector3*an array of Vector3 (the control points) the curve will pass through,**nbPoints**:*number*the wanted curve number of points between each control point,**closed**:*boolean*optional with default*false*; available from BJS V3.3; when true forms a closed curve.

*Curve3*.

Just use the Curve3 *getPoints()* method to fill your array : *getPoints()* returns an array of successive *Vector3*.

The *length()* method returns the curve length.

`var path = catmullRom.getPoints();var l = catmullRom.length();`

## Custom Curve3 Object

You can also make your own Curve3 object from a simple array of successive Vector3.

Why would you do this and not just use the points to draw a line?

Because the *Curve3* object has a useful method, the *continue()* method, that allows you place the start of one *Curve3* onto the end of another *Curve3* without any calculations to match the start and end points of the curves.

### Example 1

Create an array of Vector3 along a simple sinus curve.

`var mySinus = [];for (var i = 0; i < 30; i++) { mySinus.push( new BABYLON.Vector3(i, Math.sin(i / 10), 0) );}var mySinusCurve = new BABYLON.Curve3(mySinus);`

You would like to continue your *mySinus* curve with a *bezier3* curve and then join on a *bezier2*.

`var myFullCurve = mySinusCurve.continue(bezier3).continue(bezier2);`

The *continue()* method returns a new *Curve3* object and leaves *mySinusCurve3*, *bezier3* and *bezier2* unchanged.

If you then need to draw the curve or use it for whatever you want you just get the array of points with the *getPoints()* method. This method simply returns an array of successive *Vector3*.

`var path = myFullCurve.getPoints();var extruded = BABYLON.Mesh.ExtrudeShape("extrudedShape", shape, path, 1, 0, scene);`

If you need then to know the curve length, just use the * length()* method.

`var l = myFullCurve.length();`

### Example 2

Here is an example where a Hermite Spline is used to close smoothly a concatenation of two Bezier curves. As the spline is closing the curves the first and last points of the open continued curve need to be read from the array.

- The first and last points of the concatenation are used as last and first point of the Hermite spline.
- The first and last segments of the concatenation are used as last and first tangent vectors of the Hermite. Since these segments are quite small, they are scaled according to the concatenation
*length*so the longer the concatenation, the more curved the spline.

```
// two concatened cubic Beziervar cubicA = BABYLON.Curve3.CreateCubicBezier(vA0, vA1, vA2, vA3, 50);var cubicB = BABYLON.Curve3.CreateCubicBezier(vB0, vB1, vB2, vB3, 50);var continued = cubicA.continue(cubicB);
// initial Hermite values from continued first and last segmentsvar t = continued.length() / 2; // tangent scale factorvar points = continued.getPoints();var p1 = points[points.length - 1]; // last continued point = first hermite pointvar t1 = (p1.subtract(points[points.length - 2])).scale(t); // last segment scaled = hermite tangent t1var p2 = points[0]; // first continued point = last hermite pointvar t2 = (points[1].subtract(p2)).scale(t); // first segment scaled = hermite tangent t2
var hermite = BABYLON.Curve3.CreateHermiteSpline(p1, t1, p2, t2, 50);continued = continued.continue(hermite);
// finally drawing a smooth closed curvevar closedCurve = BABYLON.Mesh.CreateLines("closed", continued.getPoints(), scene);
```

The orange and yellow curves are the original Bezier curves.

In light blue, these two curves are continued by each other and a hermite curve is also added in continuation to close the path.