45. Scale

A vector multiplied by a positive number results in vector in the same direction.

---

We use this example vector, with origin located at 0,0,0.

        // *** 1. Start (vec=x+1.5y+2z) (Blue)
        Vector3f vec = new Vector3f(1.0f,1.5f,2.0f);
        Arrow arrow = new Arrow(vec);
        arrow.setLineWidth(3);
        Geometry geoArrow = new Geometry("arrow",arrow);
        geoArrow.setMaterial(mat);
        rootNode.attachChild(geoArrow);
        // *** 1. End

---

We can use math functions to write the magnitude, and we can multiply the vector by the inverse of this number.

        // *** 2. Start (normalizing vector using math)
        float magnitude = FastMath.sqrt(
                vec.x*vec.x+vec.y*vec.y+vec.z*vec.z);
        Vector3f normMath = vec.mult(1f/magnitude);
        System.out.println("normMath = " + normMath);
        // *** 2. End

---

We could also normalize with Vector3f methods.

        // *** 3. Start (normalized vecotor) (Red)
        Vector3f vecNorm = vec.normalize();
        vec.normalizeLocal(); // In-place normalization
        System.out.print("vec = " + vec + ", vecNorm = " + vecNorm);
        Arrow arrow1 = new Arrow(vec);
        arrow1.setLineWidth(3);
        Geometry geoArrow1 = new Geometry("arrowNorm",arrow1);
        geoArrow1.setMaterial(mat1);
        rootNode.attachChild(geoArrow1);
        // *** 3. End

---

We create an opposite direction vector from the normalized vector.

        // *** 4. Start (Opposite) (Green)
        vec.negateLocal(); // In place negation
        Arrow arrow2 = new Arrow(vec);
        arrow2.setLineWidth(3);
        Geometry geoArrow2 = new Geometry("arrowNormNeg",arrow2);
        geoArrow2.setMaterial(mat2);
        rootNode.attachChild(geoArrow2);
        // *** 4. End

---

The three components (x,y,z) are shown. For the y and z arrows, we translate in either x or both x and y.

        // *** 5. Start (Components) (Yellow)
        Vector3f vecCopy = new Vector3f(1.0f,1.5f,2.0f);
        Vector3f vecX = new Vector3f(vecCopy.x,0,0); // only x
        Arrow arrowX = new Arrow(vecX); 
        arrowX.setLineWidth(2);
        Geometry geoArrowX = new Geometry("arrowX",arrowX);
        geoArrowX.setMaterial(mat3);
        rootNode.attachChild(geoArrowX);
        Vector3f vecY = new Vector3f(0,vecCopy.y,0); // only y
        Arrow arrowY = new Arrow(vecY);
        arrowY.setLineWidth(3);
        Geometry geoArrowY = new Geometry("arrowY",arrowY);
        geoArrowY.setLocalTranslation(vecX); // displaced in x
        geoArrowY.setMaterial(mat3);
        rootNode.attachChild(geoArrowY);
        Arrow arrowZ = new Arrow(new Vector3f(0,0,vecCopy.z));
        arrowZ.setLineWidth(4);
        Geometry geoArrowZ = new Geometry("arrowZ",arrowZ);
        geoArrowZ.setLocalTranslation(
                new Vector3f(
                vecCopy.x,vecCopy.y,0)); // displaced in x,y
        geoArrowZ.setMaterial(mat3);
        rootNode.attachChild(geoArrowZ);
        // *** 5. End

---

// JMonkey45.java

package mygame;

import com.jme3.app.SimpleApplication;
import com.jme3.material.Material;
import com.jme3.math.ColorRGBA;
import com.jme3.math.FastMath;
import com.jme3.math.Vector3f;
import com.jme3.renderer.RenderManager;
import com.jme3.scene.Geometry;
import com.jme3.scene.debug.Arrow;

public class JMonkey45 extends SimpleApplication {

    public static void main(String[] args) {
        JMonkey45 app = new JMonkey45();
        app.start();
    }
    
    @Override
    public void simpleInitApp() {
        viewPort.setBackgroundColor(ColorRGBA.LightGray);
        flyCam.setEnabled(false);
        Material mat = new Material(assetManager, 
                "Common/MatDefs/Misc/Unshaded.j3md");
        mat.setColor("Color", ColorRGBA.Blue);
        Material mat1 = new Material(assetManager, 
                "Common/MatDefs/Misc/Unshaded.j3md");
        mat1.setColor("Color", ColorRGBA.Red);
        Material mat2 = new Material(assetManager, 
                "Common/MatDefs/Misc/Unshaded.j3md");
        mat2.setColor("Color", ColorRGBA.Green);
        Material mat3 = new Material(assetManager, 
                "Common/MatDefs/Misc/Unshaded.j3md");
        mat3.setColor("Color", ColorRGBA.Yellow);
        
        // *** 1. Start (vec=x+1.5y+2z) (Blue)
        Vector3f vec = new Vector3f(1.0f,1.5f,2.0f);
        Arrow arrow = new Arrow(vec);
        arrow.setLineWidth(3);
        Geometry geoArrow = new Geometry("arrow",arrow);
        geoArrow.setMaterial(mat);
        rootNode.attachChild(geoArrow);
        // *** 1. End
        
        // *** 2. Start (normalizing vector using math)
        float magnitude = FastMath.sqrt(
                vec.x*vec.x+vec.y*vec.y+vec.z*vec.z);
        Vector3f normMath = vec.mult(1f/magnitude);
        System.out.println("normMath = " + normMath);
        // *** 2. End
        
        // *** 3. Start (normalized vecotor) (Red)
        Vector3f vecNorm = vec.normalize();
        vec.normalizeLocal(); // In-place normalization
        System.out.print("vec = " + vec + ", vecNorm = " + vecNorm);
        Arrow arrow1 = new Arrow(vec);
        arrow1.setLineWidth(3);
        Geometry geoArrow1 = new Geometry("arrowNorm",arrow1);
        geoArrow1.setMaterial(mat1);
        rootNode.attachChild(geoArrow1);
        // *** 3. End
        
        // *** 4. Start (Opposite) (Green)
        vec.negateLocal(); // In place negation
        Arrow arrow2 = new Arrow(vec);
        arrow2.setLineWidth(3);
        Geometry geoArrow2 = new Geometry("arrowNormNeg",arrow2);
        geoArrow2.setMaterial(mat2);
        rootNode.attachChild(geoArrow2);
        // *** 4. End
        
        // *** 5. Start (Components) (Yellow)
        Vector3f vecCopy = new Vector3f(1.0f,1.5f,2.0f);
        Vector3f vecX = new Vector3f(vecCopy.x,0,0); // only x
        Arrow arrowX = new Arrow(vecX); 
        arrowX.setLineWidth(2);
        Geometry geoArrowX = new Geometry("arrowX",arrowX);
        geoArrowX.setMaterial(mat3);
        rootNode.attachChild(geoArrowX);
        Vector3f vecY = new Vector3f(0,vecCopy.y,0); // only y
        Arrow arrowY = new Arrow(vecY);
        arrowY.setLineWidth(3);
        Geometry geoArrowY = new Geometry("arrowY",arrowY);
        geoArrowY.setLocalTranslation(vecX); // displaced in x
        geoArrowY.setMaterial(mat3);
        rootNode.attachChild(geoArrowY);
        Arrow arrowZ = new Arrow(new Vector3f(0,0,vecCopy.z));
        arrowZ.setLineWidth(4);
        Geometry geoArrowZ = new Geometry("arrowZ",arrowZ);
        geoArrowZ.setLocalTranslation(
                new Vector3f(
                vecCopy.x,vecCopy.y,0)); // displaced in x,y
        geoArrowZ.setMaterial(mat3);
        rootNode.attachChild(geoArrowZ);
        // *** 5. End
    }

    @Override
    public void simpleUpdate(float tpf) {
        rootNode.rotate(tpf,tpf,tpf);
     }

    @Override
    public void simpleRender(RenderManager rm) {
    }
}

---

Output: