47. Vector Products

Two multiplications between vectors are dot product and cross product.

---

The example vectors are on the x-y plane, with vecA being 45 degrees below the +x axis and vecB 45 degrees above the +x axis.

        // *** 1. Start (vectors x-y, x+y, both in xy plane)
        Vector3f vecA = new Vector3f(1,-1,0); // x-y
        Vector3f vecB = new Vector3f(1,1,0); // x+y
        vecA.normalizeLocal(); // normalize them
        vecB.normalizeLocal(); // |vecA|=|vecB|=1
        // *** 1. End

---

With the dot product, we can find the angle between two vectors.

        // *** 2. Start (dot product to find ang)
        float dot = vecA.dot(vecB);
        // vecA.vecB = |vecA| |vecB| cos(AB) = cos(AB)
        float angRad = FastMath.acos(dot);
        float ang = FastMath.RAD_TO_DEG*angRad; // 90 deg
        System.out.println("vecA = " + vecA);
        System.out.println("vecB = " + vecB);
        System.out.println("dot = " + dot);
        System.out.println("ang = " + ang);
        // *** 2. End

---

With the cross product, we can find the angle between two vectors, as well as the plane normal.

        // *** 3. Start (cross product to find Ang, vecN)
        // vecN in z since vecA,vecB in x,y plane
        // direction of vecN depends on right-hand rule
        Vector3f cross = vecA.cross(vecB);
        // vecA x vecB = |vecA| |vecB| sin(AB) vecN 
        // vecA x vecB = sin(AB) vecN
        float len = cross.length();
        float angRad1 = FastMath.asin(len);
        float ang1 = FastMath.RAD_TO_DEG*angRad1; // 90 deg
        Vector3f vecN = new Vector3f(); // z
        vecN = cross.mult(1/len);
        System.out.println("cross = " + cross);
        System.out.println("ang1 = " + ang1); 
        System.out.println("vecN = " + vecN);
        // *** 3. End

---

Three arrows are drawn. Two for the two example vectors, as well as the normal to the plane, formed by the 2 example vectors.

        // *** 4. Starts (arrows for vecA, vecB, vecN)
        Arrow arrowA = new Arrow(vecA);
        arrowA.setLineWidth(4);
        Geometry geoArrowA = new Geometry("geoArrowA",arrowA);
        Material matArrowA = new Material(assetManager,
                "Common/MatDefs/Misc/Unshaded.j3md");
        matArrowA.setColor("Color", ColorRGBA.Red);
        geoArrowA.setMaterial(matArrowA);
        rootNode.attachChild(geoArrowA);
        Arrow arrowB = new Arrow(vecB);
        arrowB.setLineWidth(4);
        Geometry geoArrowB = new Geometry("geoArrowB",arrowB);
        Material matArrowB = new Material(assetManager,
                "Common/MatDefs/Misc/Unshaded.j3md");
        matArrowB.setColor("Color", ColorRGBA.Green);
        geoArrowB.setMaterial(matArrowB);
        rootNode.attachChild(geoArrowB);
        Arrow arrowN = new Arrow(vecN);
        arrowN.setLineWidth(4);
        Geometry geoArrowN = new Geometry("geoArrowN",arrowN);
        Material matArrowN = new Material(assetManager,
                "Common/MatDefs/Misc/Unshaded.j3md");
        matArrowN.setColor("Color", ColorRGBA.Blue);
        geoArrowN.setMaterial(matArrowN);
        rootNode.attachChild(geoArrowN);
        // *** 4. End

---

// JMonkey47.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;
import com.jme3.system.AppSettings;

public class JMonkey47 extends SimpleApplication {

    public static void main(String[] args) {
        AppSettings settings = new AppSettings(true);
        settings.setFrameRate(60);
        settings.setTitle("Multiplying Vectors !");
        JMonkey47 app = new JMonkey47();
        app.setSettings(settings);
        app.start();
    }

    @Override
    public void simpleInitApp() {
        flyCam.setEnabled(false);
        viewPort.setBackgroundColor(ColorRGBA.White);
        
        // *** 1. Start (vectors x-y, x+y, both in xy plane)
        Vector3f vecA = new Vector3f(1,-1,0); // x-y
        Vector3f vecB = new Vector3f(1,1,0); // x+y
        vecA.normalizeLocal(); // normalize them
        vecB.normalizeLocal(); // |vecA|=|vecB|=1
        // *** 1. End
        
        // *** 2. Start (dot product to find ang)
        float dot = vecA.dot(vecB);
        // vecA.vecB = |vecA| |vecB| cos(AB) = cos(AB)
        float angRad = FastMath.acos(dot);
        float ang = FastMath.RAD_TO_DEG*angRad; // 90 deg
        System.out.println("vecA = " + vecA);
        System.out.println("vecB = " + vecB);
        System.out.println("dot = " + dot);
        System.out.println("ang = " + ang);
        // *** 2. End
        
        // *** 3. Start (cross product to find Ang, vecN)
        // vecN in z since vecA,vecB in x,y plane
        // direction of vecN depends on right-hand rule
        Vector3f cross = vecA.cross(vecB);
        // vecA x vecB = |vecA| |vecB| sin(AB) vecN 
        // vecA x vecB = sin(AB) vecN
        float len = cross.length();
        float angRad1 = FastMath.asin(len);
        float ang1 = FastMath.RAD_TO_DEG*angRad1; // 90 deg
        Vector3f vecN = new Vector3f(); // z
        vecN = cross.mult(1/len);
        System.out.println("cross = " + cross);
        System.out.println("ang1 = " + ang1); 
        System.out.println("vecN = " + vecN);
        // *** 3. End
        
        // *** 4. Starts (arrows for vecA, vecB, vecN)
        Arrow arrowA = new Arrow(vecA);
        arrowA.setLineWidth(4);
        Geometry geoArrowA = new Geometry("geoArrowA",arrowA);
        Material matArrowA = new Material(assetManager,
                "Common/MatDefs/Misc/Unshaded.j3md");
        matArrowA.setColor("Color", ColorRGBA.Red);
        geoArrowA.setMaterial(matArrowA);
        rootNode.attachChild(geoArrowA);
        Arrow arrowB = new Arrow(vecB);
        arrowB.setLineWidth(4);
        Geometry geoArrowB = new Geometry("geoArrowB",arrowB);
        Material matArrowB = new Material(assetManager,
                "Common/MatDefs/Misc/Unshaded.j3md");
        matArrowB.setColor("Color", ColorRGBA.Green);
        geoArrowB.setMaterial(matArrowB);
        rootNode.attachChild(geoArrowB);
        Arrow arrowN = new Arrow(vecN);
        arrowN.setLineWidth(4);
        Geometry geoArrowN = new Geometry("geoArrowN",arrowN);
        Material matArrowN = new Material(assetManager,
                "Common/MatDefs/Misc/Unshaded.j3md");
        matArrowN.setColor("Color", ColorRGBA.Blue);
        geoArrowN.setMaterial(matArrowN);
        rootNode.attachChild(geoArrowN);
        // *** 4. End
    }

    @Override
    public void simpleUpdate(float tpf) {
        rootNode.rotate(0,tpf,0);
    }

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

---

Output: