BabylonJS - Curve3
BabylonJS 内置了 api 来创建一些复杂的数学曲线。我们之前已经看到过丝带，使用复杂方程创建的线条来绘制图案并计算给定网格的路径的坐标。我们这里有一个内置的API，可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
- 三次贝塞尔曲线
- Hermite 样条线
- Catmull-Rom 样条线
二次贝塞尔曲线
在本节中，我们将了解二次贝塞尔曲线。
语法
var bezier = BABYLON.Curve3.CreateQuadraticBezier(origin, control, destination, nb_of_points);
参数
考虑以下与二次贝塞尔曲线相关的参数。
原点 − 曲线的原点。
控制 − 曲线的控制点。
目的地 − 目的地点。
无点 −数组中的点。
三次贝塞尔曲线
在本节中，我们将了解三次贝塞尔曲线。
语法
var bezier3 = BABYLON.Curve3.CreateCubicBezier(origin, control1, control2, destination, nb_of_points)
参数
考虑以下与三次贝塞尔曲线相关的参数。
Origin − 原点。
control1 − 矢量形式的第一个控制点。
control2 −向量形式的第二个控制点。
目的地 − 向量形式的目的地点。
no_of_points − 数组形式的点数。
HermiteSpline 曲线
在本节中，我们将了解 Hermite 样条曲线。
语法
var hermite = BABYLON.Curve3.CreateHermiteSpline(p1, t1, p2, t2, nbPoints);
参数
考虑与 Hermite 样条曲线相关的以下参数 −
p1 − 曲线的原点。
t1 − 原点切向量点。
p2 − 目标点。
t2 − 目标切向量。
NbPoints −最终曲线的点数组。
Catmull-Rom 样条曲线
在本节中，我们将了解 Catmull-Rom 样条曲线。
语法
var nbPoints = 20; // 每个 Vector3 控制点之间的点数 var points = [vec1, vec2, ..., vecN]; // 曲线必须经过的 Vector3 数组:控制点 var catmullRom = BABYLON.Curve3.CreateCatmullRomSpline(points, nbPoints);
参数
考虑以下与 Catmull-Rom 样条曲线相关的参数 −
Points − Vector3 数组，曲线必须经过控制点。
NbPoints − 每个 Vector3 控制点之间的点数。
var path = catmullRom.getPoints(); // getPoints() 返回连续 Vector3 数组。 var l = catmullRom.length(); // 方法返回曲线长度。
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);
// 相机
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);
// 灯光
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;
// 材料
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;
};
// 显示轴
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>
输出
上述代码行将生成以下输出 −
