BabylonJS - Curve3
BabylonJS has built in api to create some of the complex mathematics curve. We have earlier seen ribbon, lines created using complex equation to draw the pattern and calculate the co-ordinates for the paths given to the mesh. We have a built-in API here to avoid doing complex calculation, just like in Curves API.
The curves which are explained are as follows −
- Quadratic Bezier curve
- Cubic Bezier curve
- Hermite spline
- Catmull-Rom spline
Quadratic Bezier Curve
In this section, we will learn about the Quadratic Bezier Curve.
Syntax
var bezier = BABYLON.Curve3.CreateQuadraticBezier(origin, control, destination, nb_of_points);
Parameters
Consider the following parameters related to the Quadratic Bezier Curve.
Origin − Origin point for the curve.
Control − Control points for the curve.
Destination − Destination point.
Noofpoints − Points in array.
Cubic Bezeir Curve
In this section, we will learn about the Cubic Bezier Curve.
Syntax
var bezier3 = BABYLON.Curve3.CreateCubicBezier(origin, control1, control2, destination, nb_of_points)
Parameters
Consider the following parameters related to the Cubic Bezier Curve.
Origin − Origin point.
control1 − First control point in vector form.
control2 − Second control point in vector form.
Destination − Destination point in vector form.
no_of_points − Numberof points in array form.
HermiteSpline Curve
In this section, we will learn about the Hermite Spline Curve.
Syntax
var hermite = BABYLON.Curve3.CreateHermiteSpline(p1, t1, p2, t2, nbPoints);
Parameters
Consider the following parameters related to the Hermite Spline Curve −
p1 − Origin point for the curve.
t1 − Origin tangent vector point.
p2 − Destination point.
t2 − Destination tangent vector.
NbPoints − Array of points for the final curve.
Catmull-Rom Spline Curve
In this section, we will learn about the Catmull-Rom Spline Curve.
Syntax
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);
Parameters
Consider the following parameters related to the Catmull-Rom Spline Curve −
Points − An array of Vector3, the curve must pass through the control points.
NbPoints − The number of points between each Vector3 control points.
var path = catmullRom.getPoints(); // getPoints() returns an array of successive Vector3.
var l = catmullRom.length(); // method returns the curve length.
Demo
<!doctype html>
<html>
<head>
<meta charset = "utf-8">
<title>BabylonJs - Basic Element-Creating Scene</title>
<script src = "babylon.js"></script>
<style>
canvas {width: 100%; height: 100%;}
</style>
</head>
<body>
<canvas id = "renderCanvas"></canvas>
<script type = "text/javascript">
var canvas = document.getElementById("renderCanvas");
var engine = new BABYLON.Engine(canvas, true);
var createScene = function() {
var scene = new BABYLON.Scene(engine);
scene.clearColor = new BABYLON.Color3( .5, .5, .5);
// camera
var camera = new BABYLON.ArcRotateCamera("camera1", 0, 0, 0, new BABYLON.Vector3(5, 3, 0), scene);
camera.setPosition(new BABYLON.Vector3(0, 0, -100));
camera.attachControl(canvas, true);
// lights
var light = new BABYLON.HemisphericLight("light1", new BABYLON.Vector3(1, 0.5, 0), scene);
light.intensity = 0.8;
var spot = new BABYLON.SpotLight(
"spot",
new BABYLON.Vector3(25, 15, -10),
new BABYLON.Vector3(-1, -0.8, 1), 15, 1, scene);
spot.diffuse = new BABYLON.Color3(1, 1, 1);
spot.specular = new BABYLON.Color3(0, 0, 0);
spot.intensity = 0.2;
// material
var mat = new BABYLON.StandardMaterial("mat1", scene);
mat.alpha = 1.0;
mat.diffuseColor = new BABYLON.Color3(0.5, 0.5, 1.0);
mat.backFaceCulling = false;
//mat.wireframe = true;
var makeTextPlane = function(text, color, size) {
var dynamicTexture = new BABYLON.DynamicTexture("DynamicTexture", 50, scene, true);
dynamicTexture.hasAlpha = true;
dynamicTexture.drawText(text, 5, 40, "bold 36px Arial", color , "transparent", true);
var plane = new BABYLON.Mesh.CreatePlane("TextPlane", size, scene, true);
plane.material = new BABYLON.StandardMaterial("TextPlaneMaterial", scene);
plane.material.backFaceCulling = false;
plane.material.specularColor = new BABYLON.Color3(0, 0, 0);
plane.material.diffuseTexture = dynamicTexture;
return plane;
};
// show axis
var showAxis = function(size) {
var axisX = BABYLON.Mesh.CreateLines("axisX", [
new BABYLON.Vector3(-size * 0.95, 0.05 * size, 0),
new BABYLON.Vector3(-size, 0, 0),
new BABYLON.Vector3(-size * 0.95, -0.05 * size, 0),
new BABYLON.Vector3(-size, 0, 0),
new BABYLON.Vector3.Zero(),
new BABYLON.Vector3(size, 0, 0),
new BABYLON.Vector3(size * 0.95, 0.05 * size, 0),
new BABYLON.Vector3(size, 0, 0),
new BABYLON.Vector3(size * 0.95, -0.05 * size, 0)
], scene);
axisX.color = new BABYLON.Color3(1, 0, 0);
var xChar = makeTextPlane("X", "red", size / 10);
xChar.position = new BABYLON.Vector3(0.9 * size, -0.05 * size, 0);
var xChar1 = makeTextPlane("-X", "red", size / 10);
xChar1.position = new BABYLON.Vector3(-0.9 * size, 0.05 * size, 0);
var xcor = [];
for (i =- 20; i <= 20; i++) {
xcor[i] = makeTextPlane(i, "red", size / 10);
xcor[i].position = new BABYLON.Vector3(i, 0, 0);
}
var axisY = BABYLON.Mesh.CreateLines("axisY", [
new BABYLON.Vector3( -0.05 * size, -size * 0.95, 0),
new BABYLON.Vector3(0, -size, 0),
new BABYLON.Vector3(0.05 * size, -size * 0.95, 0),
new BABYLON.Vector3(0, -size, 0),
new BABYLON.Vector3.Zero(),
new BABYLON.Vector3(0, size, 0),
new BABYLON.Vector3( -0.05 * size, size * 0.95, 0),
new BABYLON.Vector3(0, size, 0),
new BABYLON.Vector3( 0.05 * size, size * 0.95, 0)
], scene);
axisY.color = new BABYLON.Color3(0, 1, 0);
var yChar = makeTextPlane("Y", "green", size / 10);
yChar.position = new BABYLON.Vector3(0, 0.9 * size, -0.05 * size);
var yChar1 = makeTextPlane("-Y", "green", size / 10);
yChar1.position = new BABYLON.Vector3(0, -0.9 * size, 0.05 * size);
var ycor = [];
for (y =- 20; y <= 20; y++) {
xcor[y] = makeTextPlane(y, "green", size / 10);
xcor[y].position = new BABYLON.Vector3(0, y, 0);
}
var axisZ = BABYLON.Mesh.CreateLines("axisZ", [
new BABYLON.Vector3( 0 , -0.05 * size, -size * 0.95),
new BABYLON.Vector3(0, 0, -size),
new BABYLON.Vector3( 0 , 0.05 * size, -size * 0.95),
new BABYLON.Vector3(0, 0, -size),
new BABYLON.Vector3.Zero(),
new BABYLON.Vector3(0, 0, size),
new BABYLON.Vector3( 0 , -0.05 * size, size * 0.95),
new BABYLON.Vector3(0, 0, size),
new BABYLON.Vector3( 0, 0.05 * size, size * 0.95)
], scene);
axisZ.color = new BABYLON.Color3(0, 0, 1);
var zChar = makeTextPlane("Z", "blue", size / 10);
zChar.position = new BABYLON.Vector3(0, 0.05 * size, 0.9 * size);
var zChar1 = makeTextPlane("-Z", "blue", size / 10);
zChar1.position = new BABYLON.Vector3(0, 0.05 * size, -0.9 * size);
var zcor = [];
for (z =- 20; z <= 20; z++) {
xcor[z] = makeTextPlane(z, "green", size / 10);
xcor[z].position = new BABYLON.Vector3(0, 0, z);
}
};
var quadraticBezierVectors = BABYLON.Curve3.CreateQuadraticBezier(
BABYLON.Vector3.Zero(),
new BABYLON.Vector3(10, 5, 5),
new BABYLON.Vector3(5, 10, 0), 15);
var quadraticBezierCurve = BABYLON.Mesh.CreateLines("qbezier", quadraticBezierVectors.getPoints(), scene);
quadraticBezierCurve.color = new BABYLON.Color3(1, 1, 0.5);
var cubicBezierVectors = BABYLON.Curve3.CreateCubicBezier(
BABYLON.Vector3.Zero(),
new BABYLON.Vector3(10, 5, 20),
new BABYLON.Vector3(-50, 5, -20),
new BABYLON.Vector3( -10, 20, 10), 60);
var cubicBezierCurve = BABYLON.Mesh.CreateLines("cbezier", cubicBezierVectors.getPoints(), scene);
cubicBezierCurve.color = new BABYLON.Color3(1, 0, 0);
var continued = cubicBezierVectors.continue(cubicBezierVectors).continue(quadraticBezierVectors);
var points = continued.getPoints();
var nbPoints = 60;
var l = continued.length() / 2;
var p1 = points[points.length - 1];
var t1 = (p1.subtract(points[points.length - 2])).scale(l);
var p2 = points[0];
var t2 = (points[1].subtract(p2)).scale(l);
var hermite = BABYLON.Curve3.CreateHermiteSpline(p1, t1, p2, t2, nbPoints);
continued = continued.continue(hermite);
var points = continued.getPoints();
var continuedCurve = BABYLON.Mesh.CreateLines("continued", points, scene);
continuedCurve.position = new BABYLON.Vector3(20, -20, 20);
continuedCurve.color = new BABYLON.Color3(0, 0, 0);
var nbPoints = 20; // the number of points between each Vector3 control points
var points = [new BABYLON.Vector3(10, 5, 20),
new BABYLON.Vector3(-20, 5, -20),
new BABYLON.Vector3(-25, 5, -20),
new BABYLON.Vector3( -30, 20, 10),]; // an array of Vector3 the curve must pass through : the control points
var catmullRom = BABYLON.Curve3.CreateCatmullRomSpline(points, nbPoints);
var path = catmullRom.getPoints();
var l = catmullRom.length();
var finalcatmullCurve = BABYLON.Mesh.CreateLines("continued", path, scene);
var mySinus = [];
for (var i = 0; i < 30; i++) {
mySinus.push( new BABYLON.Vector3(i, Math.sin(i / 10), 0) );
}
var mySinusCurve3 = new BABYLON.Curve3(mySinus);
var myFullCurve = mySinusCurve3.continue(cubicBezierVectors).continue(quadraticBezierVectors);
var points1 = myFullCurve.getPoints();
var curve3d = BABYLON.Mesh.CreateLines("continued", points1, scene);
curve3d.color = new BABYLON.Color3(0.9, 1, 0.2);
showAxis(20);
return scene;
};
var scene = createScene();
engine.runRenderLoop(function() {
scene.render();
});
</script>
</body>
</html>
Output
The above line of code will generate the following output −
