BabylonJS - 曲線3

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BabylonJS 內建了 API 來建立一些複雜的數學曲線。我們之前已經看到了使用複雜方程建立的帶狀物和線條，用於繪製圖案並計算網格給定路徑的座標。我們這裡有一個內建的 API 來避免進行復雜的計算，就像在曲線 API 中一樣。

解釋的曲線如下：

  • 二次貝塞爾曲線
  • 三次貝塞爾曲線
  • 埃爾米特樣條曲線
  • Catmull-Rom 樣條曲線

二次貝塞爾曲線

在本節中，我們將學習二次貝塞爾曲線。

語法

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

引數

考慮以下與二次貝塞爾曲線相關的引數。

  • 起點 - 曲線的起點。

  • 控制點 - 曲線的控制點。

  • 終點 - 終點。

  • 點數 - 陣列中的點數。

三次貝塞爾曲線

在本節中，我們將學習三次貝塞爾曲線。

語法

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

引數

考慮以下與三次貝塞爾曲線相關的引數。

  • 起點 - 起點。

  • 控制點1 - 第一個控制點，以向量形式表示。

  • 控制點2 - 第二個控制點，以向量形式表示。

  • 終點 - 終點，以向量形式表示。

  • 點數 - 陣列形式的點數。

埃爾米特樣條曲線

在本節中，我們將學習埃爾米特樣條曲線。

語法

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

引數

考慮以下與埃爾米特樣條曲線相關的引數：

  • p1 - 曲線的起點。

  • t1 - 起點切線向量點。

  • p2 - 終點。

  • t2 - 終點切線向量。

  • 點數 - 最終曲線的點陣列。

Catmull-Rom 樣條曲線

在本節中，我們將學習 Catmull-Rom 樣條曲線。

語法

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);

引數

考慮以下與 Catmull-Rom 樣條曲線相關的引數：

  • 點 - Vector3 陣列，曲線必須穿過控制點。

  • 點數 - 每個 Vector3 控制點之間的點數。

var path = catmullRom.getPoints(); // getPoints() returns an array of successive Vector3.
var l = catmullRom.length(); // method returns the curve length.

演示

<!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>

輸出

以上程式碼行將生成以下輸出：

Catmull-Rom Spline Curve
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