How To

Draw Curves


How To Draw Curves

If you want to draw a circular path then it 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);

Quadratic Bezier Curve

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

Wikipedia Quadratic Bezier Curve

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();

Playground Example - Bezier Quadratic Curve -


Cubic Bezier curve

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

Wikipedia Cubic Bezier Curve

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();

Playground Example - Bezier Cubic Curve -


;

Hermite Spline

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

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.

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

Playground Example - Hermite Spline -


Catmull-Rom Spline

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

Wikibooks Cubic Hermite spline

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

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

Playground example - Catmull-Rom Spline -


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();

Playgound Example - Joined Curves -


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 segment are quite small, they are scaled according to the concatenation length so the longer the concatenation, the more curved the spline.
// two concatened cubic Bezier
var 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 segments
var t = continued.length() / 2;                             // tangent scale factor
var points = continued.getPoints();
var p1 = points[points.length - 1];                         // last continued point = first hermite point
var t1 = (p1.subtract(points[points.length - 2])).scale(t); // last segment scaled = hermite tangent t1
var p2 = points[0];                                         // first continued point = last hermite point
var 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 curve
var closedCurve = BABYLON.Mesh.CreateLines("closed", continued.getPoints(), scene);

Playground Example - Closed Joined Curves -


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

Further Reading

Basic - Level 1

How To Create Parametric Shapes

More Advanced - Level 3

How To Use Path3D