如何为旋转的陀螺制作动画？

Question

今天是光明节，我正在尝试制作陀螺 (dreidel) 的动画：

我可以让它绕自己的轴旋转。这是我的代码：

import static javafx.scene.paint.Color.*;

import javafx.animation.KeyFrame;
import javafx.animation.KeyValue;
import javafx.animation.Timeline;
import javafx.application.Application;
import javafx.beans.property.DoubleProperty;
import javafx.beans.property.SimpleDoubleProperty;
import javafx.geometry.Point3D;
import javafx.scene.Camera;
import javafx.scene.Group;
import javafx.scene.PerspectiveCamera;
import javafx.scene.Scene;
import javafx.scene.SceneAntialiasing;
import javafx.scene.paint.PhongMaterial;
import javafx.scene.shape.Box;
import javafx.scene.shape.Cylinder;
import javafx.scene.shape.Sphere;
import javafx.scene.transform.Rotate;
import javafx.scene.transform.Translate;
import javafx.stage.Stage;
import javafx.util.Duration;

public class DreidelAnim extends Application {

    private double bodyBase = 30;
    private double bodyHeight = bodyBase * 3 / 2;
    private double baseRadius = bodyBase / 2;

    @Override
    public void start(Stage stage) throws Exception {
        DoubleProperty spinAngle = new SimpleDoubleProperty();
        Rotate spin = new Rotate(0, Rotate.Z_AXIS);
        spin.angleProperty().bind(spinAngle);

        Timeline spinAnim = new Timeline(new KeyFrame(Duration.seconds(2), new KeyValue(spinAngle, 360)));
        spinAnim.setCycleCount(Timeline.INDEFINITE);
        spinAnim.play();

        Group dreidel = createDreidel();
        Translate zTrans = new Translate(0, 0, -(bodyHeight/2 + baseRadius));
        dreidel.getTransforms().addAll(spin, zTrans);

        Scene scene = new Scene(dreidel, 200, 200, true, SceneAntialiasing.BALANCED);
        scene.setFill(SKYBLUE);
        scene.setCamera(createCamera());

        stage.setScene(scene);
        stage.show();
    }

    private Group createDreidel() {
        double handleHeight = bodyBase * 3/4;
        Cylinder handle = new Cylinder(bodyBase / 6, handleHeight);
        handle.setTranslateZ(-(bodyHeight + handleHeight) / 2);
        handle.setRotationAxis(Rotate.X_AXIS);
        handle.setRotate(90);
        handle.setMaterial(new PhongMaterial(RED));

        Box body = new Box(bodyBase, bodyBase, bodyHeight);
        body.setMaterial(new PhongMaterial(BLUE));

        Sphere base = new Sphere(baseRadius);
        base.setTranslateZ(bodyHeight / 2);
        base.setMaterial(new PhongMaterial(GREEN));

        return new Group(handle, body, base);
    }

    private Camera createCamera() {
        PerspectiveCamera camera = new PerspectiveCamera(true);
        camera.setFarClip(1000);

        int xy = 150;
        Translate trans = new Translate(-xy, xy, -120);
        Rotate rotXY = new Rotate(70, new Point3D(1, 1, 0));
        Rotate rotZ = new Rotate(45, new Point3D(0, 0, 1));
        camera.getTransforms().addAll(trans, rotXY, rotZ);

        return camera;
    }

    public static void main(String[] args) {
        launch();
    }
}

我创建了一个简单的模型，将它绕轴旋转，然后平移它，使其尖端位于 (0, 0, 0) 上。这是结果：

我怎样才能实现类似于顶部图片的东西，它也绕旋转轴旋转？

Answer 1

物体围绕其旋转的轴的旋转称为Precession。陀螺运动需要旋转 2 圈：

对象绕其内轴（平行于红色手柄）的旋转。
围绕静态轴旋转内部轴之一（在本例中为 z）。

从表面上看，您需要 2 个 Animation 个实例。然而，这两个旋转实际上是相同的。两者的枢轴点都是 (0, 0, 0)（在 zTrans 之后）并且它们都围绕 z 轴，只有其中一个倾斜了一个角度。

修改后的代码如下：

import static javafx.scene.paint.Color.*;

import javafx.animation.KeyFrame;
import javafx.animation.KeyValue;
import javafx.animation.Timeline;
import javafx.application.Application;
import javafx.beans.property.DoubleProperty;
import javafx.beans.property.SimpleDoubleProperty;
import javafx.geometry.Point3D;
import javafx.scene.Camera;
import javafx.scene.Group;
import javafx.scene.PerspectiveCamera;
import javafx.scene.Scene;
import javafx.scene.SceneAntialiasing;
import javafx.scene.paint.PhongMaterial;
import javafx.scene.shape.Box;
import javafx.scene.shape.Cylinder;
import javafx.scene.shape.Sphere;
import javafx.scene.transform.Rotate;
import javafx.scene.transform.Translate;
import javafx.stage.Stage;
import javafx.util.Duration;

public class FinalDreidelSpin extends Application {

    private double bodyBase = 30;
    private double bodyHeight = bodyBase * 3 / 2;
    private double baseRadius = bodyBase / 2;

    @Override
    public void start(Stage stage) throws Exception {
        double tiltAngle = 40;
        DoubleProperty spinAngle = new SimpleDoubleProperty();

        Rotate spin = new Rotate(0, Rotate.Z_AXIS);
        Rotate tilt = new Rotate(tiltAngle, Rotate.X_AXIS);

        spin.angleProperty().bind(spinAngle);

        Timeline spinAnim = new Timeline();
        spinAnim.getKeyFrames().add(new KeyFrame(Duration.seconds(2), new KeyValue(spinAngle, 360)));
        spinAnim.setCycleCount(Timeline.INDEFINITE);
        spinAnim.play();

        Group dreidel = createDreidel();
        Translate zTrans = new Translate(0, 0, -(bodyHeight/2 + baseRadius));
        dreidel.getTransforms().addAll(spin, tilt, spin, zTrans);

        Scene scene = new Scene(new Group(dreidel, createAxes()), 200, 200, true, SceneAntialiasing.BALANCED);
        scene.setFill(SKYBLUE);
        scene.setCamera(createCamera());

        stage.setScene(scene);
        stage.show();
    }

    private Group createDreidel() {
        double handleHeight = bodyBase * 3/4;
        Cylinder handle = new Cylinder(bodyBase / 6, handleHeight);
        handle.setTranslateZ(-(bodyHeight + handleHeight) / 2);
        handle.setRotationAxis(Rotate.X_AXIS);
        handle.setRotate(90);
        handle.setMaterial(new PhongMaterial(RED));

        Box body = new Box(bodyBase, bodyBase, bodyHeight);
        body.setMaterial(new PhongMaterial(BLUE));

        Sphere base = new Sphere(baseRadius);
        base.setTranslateZ(bodyHeight / 2);
        base.setMaterial(new PhongMaterial(GREEN));

        return new Group(handle, body, base);
    }

    private Camera createCamera() {
        PerspectiveCamera camera = new PerspectiveCamera(true);
        camera.setFarClip(1000);

        int xy = 150;
        Translate trans = new Translate(-xy, xy, -100);
        Rotate rotXY = new Rotate(70, new Point3D(1, 1, 0));
        Rotate rotZ = new Rotate(45, new Point3D(0, 0, 1));
        camera.getTransforms().addAll(trans, rotXY, rotZ);

        return camera;
    }

    private Group createAxes() {
        int axisWidth = 1;
        int axisLength = 400;

        Cylinder xAxis = new Cylinder(axisWidth, axisLength);
        xAxis.setMaterial(new PhongMaterial(CYAN));

        Cylinder yAxis = new Cylinder(axisWidth, axisLength);
        yAxis.setRotationAxis(Rotate.Z_AXIS);
        yAxis.setRotate(90);
        yAxis.setMaterial(new PhongMaterial(MAGENTA));

        Cylinder zAxis = new Cylinder(axisWidth, axisLength);
        zAxis.setRotationAxis(Rotate.X_AXIS);
        zAxis.setRotate(90);
        zAxis.setMaterial(new PhongMaterial(YELLOW));

        return new Group(xAxis, yAxis, zAxis);
    }

    public static void main(String[] args) {
        launch();
    }
}

为了方便查看，我在其中添加了坐标轴表示。请注意 getTransforms() 列表不要求其对象是唯一的（与 getChildren() 不同），这允许我们重复使用相同的动画。动画的顺序也很重要，如下所述。

倾斜是围绕 x 或 y 轴的简单旋转。
如果我们tilt然后spin，getTransforms().addAll(tilt, spin, zTrans)，我们会得到内部旋转（上面列出的1），只有倾斜：

如果我们 spin 然后 tilt，getTransforms().addAll(spin, tilt, zTrans)，我们会得到岁差（上面列出的 2）：

在完整代码中组合 2 将给出所需的结果：

Answer 2

这是另一个可能的答案，非常基于@user1803551 方法，但使用可以使用纹理图像和不同进动周期的 3D 网格。

这是它的样子：

为了应用纹理，我将使用 net 陀螺 body 的概念，以及此图像：

即基于此image。

最后我会为手柄添加一个普通的圆柱体。

我不会详细介绍如何为body创建TriangleMesh，但我们定义了9个顶点（3D坐标），16个纹理坐标（2D）和14个三角形包括顶点索引和纹理索引的面。立方体由其边 width 定义，金字塔由其 height 定义。净尺寸为 L = 4 * width, H = 2 * width + height.

例如，面 0 的顶点为 0 - 2 - 1，纹理索引为 8 - 3 - 7，其中顶点 0 的坐标为 {width / 2, width / 2, width / 2}，纹理索引 8 的坐标为 {width, 2 * width}，在 [0, 1] 之间归一化：{width / L, 2 * width / H}。

在这种情况下，为了示例，这些值是硬编码的：

float width = 375f;
float height = 351f;

这是 3D 形状 class:

class DreidelMesh extends Group {

    float width = 375f;
    float height = 351f; 

    public DreidelMesh(){
        MeshView bodyMesh = new MeshView(createBodyMesh());
        PhongMaterial material = new PhongMaterial();
        material.setDiffuseMap(new Image(getClass().getResourceAsStream("3dreidel3d.png")));
        bodyMesh.setMaterial(material);

        Cylinder handle = new Cylinder(45, 260);
        handle.setTranslateY(-(handle.getHeight() + width) / 2);
        material = new PhongMaterial(Color.web("#daaf6d"));
        handle.setMaterial(material);

        getTransforms().add(new Rotate(90, Rotate.X_AXIS));
        getChildren().addAll(bodyMesh, handle);
    }

    private TriangleMesh createBodyMesh() {
        TriangleMesh m = new TriangleMesh();

        float L = 4f * width;
        float H = 2f * width + height;
        float w2 = width / 2f;

        // POINTS
        m.getPoints().addAll(
             w2,  w2,  w2, 
             w2,  w2, -w2, 
             w2, -w2,  w2, 
             w2, -w2, -w2, 
            -w2,  w2,  w2, 
            -w2,  w2, -w2, 
            -w2, -w2,  w2, 
            -w2, -w2, -w2, 
             0f,  w2 + height,  0f
        );

        // TEXTURES
        m.getTexCoords().addAll(
            width / L, 0f, 
            2f * width/ L, 0f, 
            0f, width / H,
            width / L, width / H, 
            2f * width/ L, width / H, 
            3f * width/ L, width / H, 
            1f, width / H, 
            0f, 2f * width / H,
            width / L, 2f * width / H, 
            2f * width/ L, 2f * width / H, 
            3f * width/ L, 2f * width / H, 
            1f, 2f * width / H, 
            width / 2f / L, 1f,
            3f * width / 2f / L, 1f,
            5f * width / 2f / L, 1f,
            7f * width / 2f / L, 1f
        );

        // FACES
        m.getFaces().addAll(
            0,  8, 2,  3, 1,  7,           
            2,  3, 3,  2, 1,  7,           
            4,  9, 5, 10, 6,  4,           
            6,  4, 5, 10, 7,  5,           
            0,  8, 1,  7, 8, 12,        
            4,  9, 0,  8, 8, 13,           
            5, 10, 4,  9, 8, 14,           
            1, 11, 5, 10, 8, 15,            
            2,  3, 6,  4, 3,  0,            
            3,  0, 6,  4, 7,  1,            
            0,  8, 4,  9, 2,  3,          
            2,  3, 4,  9, 6,  4,           
            1, 11, 3,  6, 5, 10,           
            5, 10, 3,  6, 7,  5
        );
        return m;
    }
}

最后，这个形状被添加到场景中，我将提供两个动画（而不是一个），一个用于旋转，一个用于进动较慢：

@Override
public void start(Stage stage) {
    double tiltAngle = 15;
    DoubleProperty spinAngle = new SimpleDoubleProperty();
    DoubleProperty precessionAngle = new SimpleDoubleProperty();

    Rotate spin = new Rotate(0, Rotate.Z_AXIS);
    Rotate precession = new Rotate(0, Rotate.Z_AXIS);
    Rotate tilt = new Rotate(tiltAngle, Rotate.X_AXIS);

    spin.angleProperty().bind(spinAngle);
    precession.angleProperty().bind(precessionAngle);

    Timeline spinAnim = new Timeline();
    spinAnim.getKeyFrames().add(new KeyFrame(Duration.seconds(1.5), new KeyValue(spinAngle, 360)));
    spinAnim.setCycleCount(Timeline.INDEFINITE);
    spinAnim.play();

    Timeline precessionAnim = new Timeline();
    precessionAnim.getKeyFrames().add(new KeyFrame(Duration.seconds(4), new KeyValue(precessionAngle, 360)));
    precessionAnim.setCycleCount(Timeline.INDEFINITE);
    precessionAnim.play();

    Group dreidel = new Group(new DreidelMesh());
    Translate zTrans = new Translate(0, 0, - dreidel.getBoundsInLocal().getMaxZ());
    dreidel.getTransforms().addAll(precession, tilt, spin, zTrans);

    Scene scene = new Scene(new Group(dreidel), 300, 300, true, SceneAntialiasing.BALANCED);
    scene.setFill(SKYBLUE);
    scene.setCamera(createCamera());

    stage.setScene(scene);
    stage.setTitle("JavaFX 3D - Dreidel");
    stage.show();
}

运行应用程序将显示上面显示的动画。

如何为旋转的陀螺制作动画？

How to animate a spinning top?

java

animation

javafx

javafx-8

javafx-3d