BabylonJS内置了api来创建一些复杂的数学曲线.我们之前已经看过使用复杂方程创建的带状线,用于绘制图案并计算给予网格的路径的坐标.我们这里有一个内置的API,以避免进行复杂的计算,就像在Curves API中一样.
解释的曲线如下 :
二次贝塞尔曲线
Cubic Bezier曲线
Hermite spline
Catmull-Rom spline
在本节中,我们将了解二次贝塞尔曲线.
var bezier = BABYLON.Curve3.CreateQuadraticBezier(origin, control, destination, nb_of_points);
考虑以下与二次贝塞尔曲线相关的参数.
Origin : 曲线的原点.
控制 : 曲线的控制点.
目的地 : 目的地点.
Noofpoints : 数组中的点.
在本节中,我们将了解Cubic Bezier曲线.
var bezier3 = BABYLON.Curve3.CreateCubicBezier(origin, control1, control2, destination, nb_of_points)
考虑以下与Cubic Bezier曲线相关的参数.
Origin : 原点.
control1 : 矢量形式的第一个控制点.
control2 : 矢量形式的第二个控制点.
目的地 : 矢量形式的目标点.
no_of_points : 数组形式的点数.
在本节中,我们将了解Hermite样条曲线.
var hermite = BABYLON.Curve3.CreateHermiteSpline(p1, t1, p2, t2, nbPoints);
考虑以下与Hermite样条曲线相关的参数 :
p1 : 曲线的原点.
t1 : 原点切线向量点.
p2 : 目的地点.
t2 : 目标切线向量.
NbPoints : 最终曲线的点数组.
本节内容,我们将了解Catmull-Rom样条曲线.
var nbPoints = 20;//每个Vector3控制点之间的点数 var points = [vec1,vec2,...,vecN];//曲线必须通过的Vector3数组:控制点 var catmullRom = BABYLON.Curve3.CreateCatmullRomSpline(points,nbPoints);
考虑以下与Catmull-Rom样条曲线相关的参数 :
积分 : 一个Vector3数组,曲线必须通过控制点.
NbPoints : 每个Vector3控制点之间的点数.
var path = catmullRom.getPoints( );//getPoints()返回连续Vector3的数组. var l = catmullRom.length();//方法返回曲线长度.
<!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>
以上代码行将生成以下输出 :