add

build.gradle

@@ -16,22 +16,21 @@ ext{
 }
 
 dependencies {
+    List axisExGroups  = [ 'org.bytedeco.javacpp-presets']
+    List axisExModules = [ 'ffmpeg' , 'artoolkitplus', 'ffmpeg-platform']
 
     implementation('org.bytedeco:opencv:4.5.1-1.5.5:android-x86')
     implementation('org.bytedeco:opencv:4.3.0-1.5.3:android-x86_64')
 
-
-    implementation('org.bytedeco:openblas:0.3.13-1.5.5:android-x86')
-    implementation('org.bytedeco:openblas:0.3.9-1.5.3:android-x86_64')
-    implementation(group:'org.apache.commons', name: 'commons-collections4', version: '4.0')
     implementation(group :'org.bytedeco', name: 'javacv-platform', version: '1.5.5'){
-        exclude group: 'org.bytedeco.javacpp-presets'
+        axisExGroups.each  { exclude group: "$it" }
+        axisExModules.each {exclude module: "$it"}
     }
-
     implementation('org.apache.commons:commons-lang3:3.12.0')
-    implementation('com.github.sh0nk:matplotlib4j:0.5.0')
-    testImplementation 'org.junit.jupiter:junit-jupiter-api:5.8.1'
-    testRuntimeOnly 'org.junit.jupiter:junit-jupiter-engine:5.8.1'
+
+
+//    testImplementation 'org.junit.jupiter:junit-jupiter-api:5.8.1'
+//    testRuntimeOnly 'org.junit.jupiter:junit-jupiter-engine:5.8.1'
 }
 
 test {

src/main/java/Entity/Face.java

+package Entity;
+
+public class Face {
+
+    protected static final int DELETED = 3;
+    protected static final int NON_CONVEX = 2;
+    protected static final int VISIBLE = 1;
+
+    protected double area;
+    protected HalfEdge he0;
+    protected int mask = VISIBLE;
+    protected Face next;
+    protected int numVerts;
+    protected Vertex outside;
+    protected double planeOffset;
+    private Point3D centroid;
+    private Vector3D normal;
+
+    public Face() {
+        normal = new Vector3D();
+        centroid = new Point3D();
+        mask = VISIBLE;
+    }
+
+    public static Face create(Vertex[] vtxArray, int[] indices) {
+        return null;
+    }
+
+    public static Face createTriangle(Vertex v0, Vertex v1, Vertex v2) {
+        return null;
+    }
+
+    /**
+     * Constructs a triangule Face from vertices v0, v1, and v2.
+     *
+     * @param v0      first vertex
+     * @param v1      second vertex
+     * @param v2      third vertex
+     * @param minArea
+     * @return
+     */
+    public static Face createTriangle(Vertex v0, Vertex v1, Vertex v2, double minArea) {
+        Face face = new Face();
+        HalfEdge he0 = new HalfEdge(v0, face);
+        HalfEdge he1 = new HalfEdge(v1, face);
+        HalfEdge he2 = new HalfEdge(v2, face);
+
+        he0.prev = he2;
+        he0.next = he1;
+        he1.prev = he0;
+        he1.next = he2;
+        he2.prev = he1;
+        he2.next = he0;
+
+        face.he0 = he0;
+
+        //compute the normal and offset
+        face.computeNormalAndCentroid();
+        return face;
+    }
+
+    /**
+     * Compute Centroid
+     */
+    public void computeCentroid(Point3D centroid) {
+        centroid.setZero();
+        HalfEdge he = he0;
+        do {
+            centroid.add(he.head().pnt);
+            he = he.next;
+        } while (he != he0);
+        centroid.scale(1 / (double) numVerts);
+    }
+
+    public void computeNormal(Vector3D normal) {
+        HalfEdge he1 = he0.next;
+        HalfEdge he2 = he1.next;
+
+        Point3D p0 = he0.head().pnt;
+        Point3D p2 = he1.head().pnt;
+
+        double d2x = p2.x - p0.x;
+        double d2y = p2.y - p0.y;
+        double d2z = p2.z - p0.z;
+
+        normal.setZero();
+
+        numVerts = 2;
+
+        while (he2 != he0) {
+            double d1x = d2x;
+            double d1y = d2y;
+            double d1z = d2z;
+
+            p2 = he2.head().pnt;
+            d2x = p2.x - p0.x;
+            d2y = p2.y - p0.y;
+            d2z = p2.z - p0.z;
+
+            normal.x += d1y * d2z - d1z * d2y;
+            normal.y += d1z * d2x - d1x * d2z;
+            normal.z += d1x * d2y - d1y * d2x;
+
+            he1 = he2;
+            he2 = he2.next;
+            numVerts++;
+        }
+        area = normal.norm();
+        normal.scale(1 / area);
+    }
+
+    public void computeNormal(Vector3D normal, double minArea) {
+        computeNormal(normal);
+
+        if (area < minArea) {
+            //make the normal more robust by remove components parallel to the longest edge
+
+            HalfEdge hedgeMax = null;
+            double lenSqrMax = 0;
+            HalfEdge hedge = he0;
+            do {
+                double lenSqr = hedge.lengthSquared();
+                if (lenSqr > lenSqrMax) {
+                    hedgeMax = hedge;
+                    lenSqrMax = lenSqr;
+                }
+                hedge = hedge.next;
+            } while (hedge != he0);
+
+            Point3D p2 = hedgeMax.head().pnt;
+            Point3D p1 = hedgeMax.tail().pnt;
+            double lenMax = Math.sqrt(lenSqrMax);
+            double ux = (p2.x - p1.x) / lenMax;
+            double uy = (p2.y - p1.y) / lenMax;
+            double uz = (p2.z - p1.z) / lenMax;
+            double dot = normal.x * ux + normal.y * uy + normal.z * uz;
+            normal.x -= dot * ux;
+            normal.y -= dot * uy;
+            normal.z -= dot * uz;
+
+            normal.normalize();
+        }
+    }
+
+    /**
+     * Compute the distance from a pont p to the plane of this face
+     *
+     * @param p the poin
+     * @return distance from the point to the plane
+     */
+    public double distanceToPlane(Point3D p) {
+        return normal.x * p.x + normal.y * p.y + normal.z * p.z - planeOffset;
+    }
+
+    /**
+     * Finds the half-edge within this face which have tail vt and head vh
+     *
+     * @param vt tail point
+     * @param vh heat point
+     * @return the half-edge, or null if none is found.
+     */
+    public HalfEdge findEdge(Vertex vt, Vertex vh) {
+        HalfEdge he = he0;
+        do {
+            if (he.head() == vh && he.tail() == vt) {
+                return he;
+            }
+            he = he.next;
+        } while (he != he0);
+        return null;
+    }
+
+    public Point3D getCentroid() {
+        return centroid;
+    }
+
+    /**
+     * Gets the i-th half-edge associated with the face
+     *
+     * @param i the half-edge index, in the range 0-2
+     * @return the half-edge
+     */
+    public HalfEdge getEdge(int i) {
+        HalfEdge he = he0;
+        while (i > 0) {
+            he = he.next;
+            i--;
+        }
+        while (i < 0) {
+            he = he.prev;
+            i++;
+        }
+        return he;
+    }
+
+    public HalfEdge getFirstEdge() {
+        return he0;
+    }
+
+    public Vector3D getNormal() {
+        return normal;
+    }
+
+    public void getVertexIndices(int[] idxs) {
+        HalfEdge he = he0;
+        int i = 0;
+        do {
+            idxs[i++] = he.head().index;
+            he = he.next;
+        } while (he != he0);
+    }
+
+    public String getVertexString() {
+        String s = null;
+        HalfEdge he = he0;
+        do {
+            if (s == null) {
+                s = "" + he.head().index;
+            } else {
+                s += " " + he.head().index;
+            }
+            he = he.next;
+        } while (he != he0);
+        return s;
+    }
+
+    public int mergeAdjacentFace(HalfEdge hedgeAdj, Face[] discarded) {
+        Face oppFace = hedgeAdj.oppositeFace();
+        int numDiscarded = 0;
+
+        discarded[numDiscarded++] = oppFace;
+        oppFace.mask = DELETED;
+        HalfEdge hedgeOpp = hedgeAdj.getOpposite();
+
+        HalfEdge hedgeAdjPrev = hedgeAdj.prev;
+        HalfEdge hedgeAdjNext = hedgeAdj.next;
+        HalfEdge hedgeOppPrev = hedgeOpp.prev;
+        HalfEdge hedgeOppNext = hedgeOpp.next;
+
+        while (hedgeAdjPrev.oppositeFace() == oppFace) {
+            hedgeAdjPrev = hedgeAdjPrev.prev;
+            hedgeOppNext = hedgeOppNext.next;
+        }
+
+        while (hedgeAdjNext.oppositeFace() == oppFace) {
+            hedgeOppPrev = hedgeOppPrev.prev;
+            hedgeAdjNext = hedgeAdjNext.next;
+        }
+
+        HalfEdge hedge;
+
+        for (hedge = hedgeOppNext; hedge != hedgeOppPrev.next; hedge = hedge.next) {
+            hedge.face = this;
+        }
+
+        if (hedgeAdj == he0) {
+            he0 = hedgeAdjNext;
+        }
+
+        //handle the half edges at the head
+        Face discardedFace;
+
+        discardedFace = connectHalfEdges(hedgeOppPrev, hedgeAdjNext);
+        if (discardedFace != null) {
+            discarded[numDiscarded++] = discardedFace;
+        }
+
+        //handle the half edges at the tail
+        discardedFace = connectHalfEdges(hedgeAdjPrev, hedgeOppNext);
+        if (discardedFace != null) {
+            discarded[numDiscarded++] = discardedFace;
+        }
+
+        computeNormalAndCentroid();
+        checkConsistency();
+        return numDiscarded;
+    }
+
+    public int getNumVerts() {
+        return numVerts;
+    }
+
+    public void triangulate(FaceList newFaces, double minArea) {
+        HalfEdge hedge;
+
+        if (getNumVerts() < 4) {
+            return;
+        }
+
+        Vertex v0 = he0.head();
+
+        hedge = he0.next;
+
+        HalfEdge oppPrev = hedge.opposite;
+        Face face0 = null;
+
+        for (hedge = hedge.next; hedge != he0.prev; hedge = hedge.next) {
+            Face face = createTriangle(v0, hedge.prev.head(), hedge.head(), minArea);
+            face.he0.next.setOpposite(oppPrev);
+            face.he0.prev.setPrev(hedge.opposite);
+            oppPrev = face.he0;
+            newFaces.add(face);
+            if (face0 == null) {
+                face0 = face;
+            }
+        }
+        hedge = new HalfEdge(he0.prev.prev.head(), this);
+        hedge.setOpposite(oppPrev);
+
+        hedge.prev = he0;
+        hedge.prev.next = hedge;
+
+        hedge.next = he0.prev;
+        hedge.next.prev = hedge;
+
+        computeNormalAndCentroid(minArea);
+        checkConsistency();
+
+        for (Face face = face0; face != null; face = face.next) {
+            face.checkConsistency();
+        }
+    }
+
+    /**
+     * return the squared area of the triangle defined by the half edge hedge- and the point at the head of hedge1
+     *
+     * @param hedge0
+     * @param hedge1
+     * @return
+     */
+    public double areaSquare(HalfEdge hedge0, HalfEdge hedge1) {
+        Point3D p0 = hedge0.tail().pnt;
+        Point3D p1 = hedge0.head().pnt;
+        Point3D p2 = hedge1.head().pnt;
+
+        double dx1 = p1.x - p0.x;
+        double dy1 = p1.y - p0.y;
+        double dz1 = p1.z - p0.z;
+
+        double dx2 = p2.x - p0.x;
+        double dy2 = p2.y - p0.y;
+        double dz2 = p2.z - p0.z;
+
+        double x = dy1 * dz2 - dz1 * dy2;
+        double y = dz1 * dx2 - dx1 * dz2;
+        double z = dx1 * dy2 - dy1 * dx2;
+        return x * x + y * y + z * z;
+    }
+
+    private void computeNormalAndCentroid() {
+        computeNormal(normal);
+        computeCentroid(centroid);
+        planeOffset = normal.dot(centroid);
+        int numv = 0;
+        HalfEdge he = he0;
+        do {
+            numv++;
+            he = he.next;
+        } while (he != he0);
+        if (numv != numVerts) {
+            throw new RuntimeException("face " + getVertexString() + " numVerts" +
+                    numVerts + " shoule be " + numv);
+        }
+    }
+
+    private void computeNormalAndCentroid(double minArea) {
+        computeNormal(normal, minArea);
+        computeCentroid(centroid);
+        planeOffset = normal.dot(centroid);
+    }
+
+    private Face connectHalfEdges(HalfEdge hedgePrev, HalfEdge hedge) {
+        Face discardFace = null;
+
+        //have a redundant edge that can get rid off
+        if (hedgePrev.oppositeFace() == hedge.oppositeFace()) {
+            Face oppFace = hedge.oppositeFace();
+            HalfEdge hedgeOpp;
+
+            if (hedgePrev == he0) {
+                he0 = hedge;
+            }
+
+            if (oppFace.getNumVerts() == 3) {
+                //can get rid of the apposite face altogether
+                hedgeOpp = hedge.getOpposite().prev.getOpposite();
+                oppFace.mask = DELETED;
+                discardFace = oppFace;
+            } else {
+                hedgeOpp = hedge.getOpposite().next;
+
+                if (oppFace.he0 == hedgeOpp.prev) {
+                    oppFace.he0 = hedgeOpp;
+                }
+
+                hedgeOpp.prev = hedgeOpp.prev.prev;
+                hedgeOpp.prev.next = hedgeOpp;
+            }
+            hedge.prev = hedgePrev.prev;
+            hedge.prev.next = hedge;
+
+            hedge.opposite = hedgeOpp;
+            hedgeOpp.opposite = hedge;
+
+            //oppFace was modified, so need to recompute
+            oppFace.computeNormalAndCentroid();
+        } else {
+            hedgePrev.next = hedge;
+            hedge.prev = hedgePrev;
+        }
+        return discardFace;
+    }
+
+    void checkConsistency() {
+        //do a santiy check on the face
+        HalfEdge hedge = he0;
+        double maxd = 0;
+        int numv = 0;
+
+        if (numVerts < 3) {
+            throw new RuntimeException("degenerate face: " + getVertexString());
+        }
+        do {
+            HalfEdge hedgeOpp = hedge.getOpposite();
+            if (hedgeOpp == null) {
+                throw new RuntimeException("face " + getVertexString() + ": " + "unreflected half edge " + hedge.getVertexString());
+            } else if (hedgeOpp.getOpposite() != hedge) {
+                throw new RuntimeException("face " + getVertexString() + ": " + "opposite half edge " + hedgeOpp.getVertexString() + " has opposite "
+                        + hedgeOpp.getOpposite().getVertexString());
+            }
+            if (hedgeOpp.head() != hedge.tail() || hedge.head() != hedgeOpp.tail()) {
+                throw new RuntimeException("face " + getVertexString() + ": " + "half edge " + hedge.getVertexString() + " reflected by " + hedgeOpp.getVertexString());
+            }
+            Face oppFace = hedgeOpp.face;
+            if (oppFace == null) {
+                throw new RuntimeException("face " + getVertexString() + ": " + "no face on half edge " + hedgeOpp.getVertexString());
+            } else if (oppFace.mask == DELETED) {
+                throw new RuntimeException("face " + getVertexString() + ": " + "opposite face " + oppFace.getVertexString() + " not on hull");
+            }
+            double d = Math.abs(distanceToPlane(hedge.head().pnt));
+            if (d > maxd) {
+                maxd = d;
+            }
+            numv++;
+            hedge = hedge.next;
+        } while (hedge != he0);
+
+        if (numv != numVerts) {
+            throw new RuntimeException("face " + getVertexString() + " numVerts=" + numVerts + " should be " + numv);
+        }
+    }
+}

src/main/java/Entity/FaceList.java

+package Entity;
+
+public class FaceList {
+    private Face head;
+
+    private Face tail;
+
+    /**
+     * Clears this list
+     */
+    public void clear() {
+        head = tail = null;
+    }
+
+    /**
+     * Adds a vertex to the end of this list
+     */
+    public void add(Face vtx) {
+        if (head == null) {
+            head = vtx;
+        } else {
+            tail.next = vtx;
+        }
+        vtx.next = null;
+        tail = vtx;
+    }
+
+    public Face first() {
+        return head;
+    }
+
+    /**
+     * Returns true if this list is empty
+     */
+    public boolean isEmpty() {
+        return head == null;
+    }
+}

src/main/java/Entity/HalfEdge.java

+package Entity;
+
+public class HalfEdge {
+
+    /**
+     * The vertex associated with the heat of this half-edge
+     */
+    protected Vertex vertex;
+
+    /**
+     * Triangular face associated with this half-edge
+     */
+    protected Face face;
+
+    /**
+     * Next haft-edge in the triangle
+     */
+    protected HalfEdge next;
+
+    /**
+     * Previous half-edge in the reiangle
+     */
+    protected HalfEdge prev;
+
+    /**
+     * Half-edge associated with the opposite triangle adjacent to this edge
+     */
+    protected HalfEdge opposite;
+
+    public HalfEdge() {
+    }
+
+    /**
+     * Constructs a HalfEdge with head vertex and left-hand triangular face
+     *
+     * @param vertex head vertex
+     * @param face   left-hand triangular face
+     */
+    public HalfEdge(Vertex vertex, Face face) {
+        this.vertex = vertex;
+        this.face = face;
+    }
+
+    /**
+     * Gets the triangular face located to the left of this half-edge
+     *
+     * @return left-hand triangular face
+     */
+    public Face getFace() {
+        return face;
+    }
+
+    /**
+     * Gets the value of the next edge adjacent (counter-clockwise) to this one within the triangle
+     *
+     * @return next adjacent edge
+     */
+    public HalfEdge getNext() {
+        return next;
+    }
+
+    /**
+     * Sets the value of the next edge adjacent (counter-clockwise) to this one within the triangle
+     *
+     * @param next next adjacent edge
+     */
+    public void setNext(HalfEdge next) {
+        this.next = next;
+    }
+
+    /**
+     * Gets the value of the previous edge adjacent (clockwise) to this one within the triangle
+     *
+     * @return previous adjacent edge
+     */
+    public HalfEdge getPrev() {
+        return prev;
+    }
+
+    /**
+     * Sets the value of the previous edge adjacent (clockwise) to this one within the triangle
+     *
+     * @param prev previous adjacent edge
+     */
+    public void setPrev(HalfEdge prev) {
+        this.prev = prev;
+    }
+
+    /**
+     * Returns the half-edge opposite to this half-edge
+     *
+     * @return opposite half-edge
+     */
+    public HalfEdge getOpposite() {
+        return opposite;
+    }
+
+    /**
+     * Sets the half-edge opposite to this half-edge
+     *
+     * @param opposite opposite half-edge
+     */
+    public void setOpposite(HalfEdge opposite) {
+        this.opposite = opposite;
+    }
+
+    /**
+     * Returns the head vertex associated with this half-edge
+     *
+     * @return head vertex
+     */
+    public Vertex head() {
+        return vertex;
+    }
+
+    /**
+     * Returns the tail vertex associate with this half-edge
+     *
+     * @return
+     */
+    public Vertex tail() {
+        return prev != null ? prev.vertex : null;
+    }
+
+    /**
+     * Returns the opposite triangular face associate with this half-edge
+     *
+     * @return opposite triangular face
+     */
+    public Face oppositeFace() {
+        return opposite != null ? opposite.face : null;
+    }
+
+    /**
+     * Produces a string identifying this half-edge by the point index values of its tail and head vertices
+     *
+     * @return identifying string
+     */
+    public String getVertexString() {
+        if (tail() != null) {
+            return "" + tail().index + "-" + head().index;
+        } else {
+            return "?-" + head().index;
+        }
+    }
+
+    /**
+     * Returns the length of this half-edge
+     *
+     * @return half-edge length
+     */
+    public double length() {
+        if (tail() != null) {
+            return head().pnt.distance(tail().pnt);
+        } else {
+            return -1;
+        }
+    }
+
+    /**
+     * Returns the length squared of this half-edge
+     *
+     * @return half-edge squared length
+     */
+    public double lengthSquared() {
+        if (tail() != null) {
+            return head().pnt.distanceSquared(tail().pnt);
+        } else {
+            return -1;
+        }
+    }
+
+}

src/main/java/Entity/Point3D.java

+package Entity;
+
+public class Point3D extends Vector3D{
+
+    /**
+     * Create a Point3D amd initializes it to zero
+     */
+    public Point3D() {
+    }
+
+    /**
+     * Creates a Point3D by copy a vector
+     * @param v
+     */
+    public Point3D(Vector3D v) {
+        super(v);
+    }
+
+    /**
+     * Create a Point3D with the supplied element values
+     * @param x
+     * first element
+     * @param y
+     * second element
+     * @param z
+     * third element
+     */
+    public Point3D(double x, double y, double z) {
+        super(x, y, z);
+    }
+}

src/main/java/Entity/Vector3D.java

+package Entity;
+
+public class Vector3D {
+
+    static private final double DOUBLE_PREC = 2.2204460492503131e-16;//Precision of a double
+
+    public double x;//first element
+    public double y;//second element
+    public double z;//third element
+
+    //Creates a 3-vector and initializes its elements to 0
+    public Vector3D() {
+    }
+
+    /**
+     * Creates a 3-vector by copy existing one
+     *
+     * @param v vector to be copied
+     */
+    public Vector3D(Vector3D v) {
+        set(v);
+    }
+
+    /**
+     * Creates a 3-vector with the supplied element values
+     *
+     * @param x first element
+     * @param y second element
+     * @param z third element
+     */
+    public Vector3D(double x, double y, double z) {
+        set(x, y, z);
+    }
+
+    /**
+     * Gets a single element of this vector. Element 0, 1, and 2 correspond to x,y and z
+     *
+     * @param i element index
+     * @return element value throws ArrayIndexOutOfBoundsException if i is not in range 0 to 2
+     */
+    public double get(int i) {
+        switch (i) {
+            case 0: {
+                return x;
+            }
+            case 1: {
+                return y;
+            }
+            case 2: {
+                return z;
+            }
+            default: {
+                throw new ArrayIndexOutOfBoundsException(i);
+            }
+        }
+    }
+
+    /**
+     * Sets a single element of this vector. Elements 0, 1, and 2 correspond to
+     * x, y, and z
+     *
+     * @param i     element index
+     * @param value element value
+     * @return element value throws ArrayIndexOutOfBoundsException if i is not in the range 0 to 2
+     */
+    public void set(int i, double value) {
+        switch (i) {
+            case 0: {
+                x = value;
+                break;
+            }
+            case 1: {
+                y = value;
+                break;
+            }
+            case 2: {
+                z = value;
+                break;
+            }
+            default: {
+                throw new ArrayIndexOutOfBoundsException(i);
+            }
+        }
+    }
+
+    /**
+     * Sets the values of this vector to those of v1
+     *
+     * @param v1 vector whose values are copied
+     */
+    public void set(Vector3D v1) {
+        this.x = v1.x;
+        this.y = v1.y;
+        this.z = v1.z;
+    }
+
+    /**
+     * Sets the values of the vector to the prescribed values
+     *
+     * @param x value for first element
+     * @param y value for second element
+     * @param z value for third element
+     */
+    public void set(double x, double y, double z) {
+        this.x = x;
+        this.y = y;
+        this.z = z;
+    }
+
+    /**
+     * Sets the elements of this vector to zero
+     */
+    public void setZero() {
+        x = 0;
+        y = 0;
+        z = 0;
+    }
+
+    /**
+     * Adds vector v1 to v2 and places the result in this vector
+     *
+     * @param v1 left-hand vector
+     * @param v2 right-hand vector
+     */
+    public void add(Vector3D v1, Vector3D v2) {
+        x = v1.x + v2.x;
+        y = v1.y + v2.y;
+        z = v1.z + v2.z;
+    }
+
+    /**
+     * Adds this vector to v and places the result in this vector
+     *
+     * @param v right-hand vector
+     */
+    public void add(Vector3D v) {
+        x += v.x;
+        y += v.y;
+        z += v.z;
+    }
+
+    /**
+     * Subs vector v1 from v2 and places the result in this vector
+     *
+     * @param v1 left-hand vector
+     * @param v2 right-hand vector
+     */
+    public void sub(Vector3D v1, Vector3D v2) {
+        x = v1.x - v2.x;
+        y = v1.y - v2.y;
+        z = v1.z - v2.z;
+    }
+
+    /**
+     * Subs this vector from v and places the result in this vector
+     *
+     * @param v right-hand vector
+     */
+    public void sub(Vector3D v) {
+        x -= v.x;
+        y -= v.y;
+        z -= v.z;
+    }
+
+    /**
+     * Scales the elements of this vector by s
+     *
+     * @param s scaling factor
+     */
+    public void scale(double s) {
+        x = s * x;
+        y = s * y;
+        z = s * z;
+    }
+
+    /**
+     * Scales the elements of vector v by s and place the results in this vector
+     *
+     * @param s scaling vector
+     * @param v vector to be scaled
+     */
+    public void scale(double s, Vector3D v) {
+        x = s * v.x;
+        y = s * v.y;
+        z = s * v.z;
+    }
+
+    /**
+     * Returns the 2 norm of this vector. This is the square root of the sum of the squares of the elements
+     *
+     * @return vector 2 norm
+     */
+    public double norm() {
+        return Math.sqrt(x * x + y * y + z * z);
+    }
+
+    /**
+     * Retruns the square of the 2 norm of this vector. this is the sum of the squares of the element
+     *
+     * @return square of the 2 norm
+     */
+    public double normSquared() {
+        return x * x + y * y + z * z;
+    }
+
+    /**
+     * Returns the Euclidean distance between this vector and vector v
+     *
+     * @param v vector destination
+     * @return distance between this vector and v
+     */
+    public double distance(Vector3D v) {
+        double dx = x - v.x;
+        double dy = y - v.y;
+        double dz = z - v.z;
+
+        return Math.sqrt(dx * dx + dy * dy + dz * dz);
+    }
+
+    /**
+     * Returns the squared of Euclidean distance between this vector and vector v
+     *
+     * @param v vector destination
+     * @return squared distance between this vector and v
+     */
+    public double distanceSquared(Vector3D v) {
+        double dx = x - v.x;
+        double dy = y - v.y;
+        double dz = z - v.z;
+
+        return dx * dx + dy * dy + dz * dz;
+    }
+
+    /**
+     * Returns the dot product of this vector and v1
+     *
+     * @param v right-hand vector
+     * @return dot product
+     */
+    public double dot(Vector3D v) {
+        return x * v.x + y * v.y + z * v.z;
+    }
+
+    /**
+     * Normalizes this vector in place
+     */
+    public void normalize() {
+        double lenSqr = x * x + y * y + z * z;
+        double err = lenSqr - 1;
+        if (err > (2 * DOUBLE_PREC) || err < -(2 * DOUBLE_PREC)) {
+            double len = Math.sqrt(lenSqr);
+            x /= len;
+            y /= len;
+            z /= len;
+        }
+    }
+
+    /**
+     * Computes the cross product of v1 and v2 and places the result in this vector
+     *
+     * @param v1 left-hand vector
+     * @param v2 right-hand vector
+     */
+    public void cross(Vector3D v1, Vector3D v2) {
+        double tmpx = v1.y * v2.z - v1.z * v2.y;
+        double tmpy = v1.z * v2.x - v1.x * v2.z;
+        double tmpz = v1.x * v2.y - v1.y - v2.x;
+
+        x = tmpx;
+        y = tmpy;
+        z = tmpz;
+    }
+
+    @Override
+    public String toString() {
+        return "Vector3D{" +
+                "x=" + x +
+                ", y=" + y +
+                ", z=" + z +
+                '}';
+    }
+}

src/main/java/Entity/Vertex.java

+package Entity;
+
+public class Vertex {
+
+    /**
+     * Spatial point associated with this vertex
+     */
+    public Point3D pnt;
+
+    /**
+     * Back index into an array
+     */
+    public int index;
+
+    /**
+     * List forward link
+     */
+    public Vertex prev;
+
+    /**
+     * List backward link
+     */
+    public Vertex next;
+
+    /**
+     * Current face that this vertex is outside of
+     */
+    public Face face;
+
+    /**
+     * Constructs a vertex and sets its coordinates to 0
+     */
+    public Vertex() {
+    }
+
+    /**
+     * Constructs a vertex with the specified coordinates and index
+     */
+    public Vertex(double x, double y, double z, int idx) {
+        pnt = new Point3D(x, y, z);
+        index = idx;
+    }
+}

src/main/java/Entity/VertexList.java

+package Entity;
+
+public class VertexList {
+
+    private Vertex head;
+
+    private Vertex tail;
+
+    /**
+     * Clears this list
+     */
+    public void clear() {
+        head = tail = null;
+    }
+
+    /**
+     * Adds a vertex to the end of this list
+     */
+    public void add(Vertex vtx) {
+        if (head == null) {
+            head = vtx;
+        } else {
+            tail.next = vtx;
+        }
+        vtx.prev = tail;
+        vtx.next = null;
+        tail = vtx;
+    }
+
+    /**
+     * Adds a chain of vertices to the end of this list
+     */
+    public void addAll(Vertex vtx) {
+        if (head == null) {
+            head = vtx;
+        } else {
+            tail.next = vtx;
+        }
+        vtx.prev = tail;
+        while (vtx.next != null) {
+            vtx = vtx.next;
+        }
+        tail = vtx;
+    }
+
+    /**
+     * Deletes a vertex from this list
+     */
+    public void delete(Vertex vtx) {
+        if (vtx.prev == null) {
+            head = vtx.next;
+        } else {
+            vtx.prev.next = vtx.next;
+        }
+        if (vtx.next == null) {
+            tail = vtx.prev;
+        } else {
+            vtx.next.prev = vtx.prev;
+        }
+    }
+
+    /**
+     * Deletes a chain of vertices from this list
+     */
+    public void delete(Vertex vtx1, Vertex vtx2) {
+        if (vtx1.prev == null) {
+            head = vtx2.next;
+        } else {
+            vtx1.prev.next = vtx2.next;
+        }
+        if (vtx2.next == null) {
+            tail = vtx1.prev;
+        } else {
+            vtx2.next.prev = vtx1.prev;
+        }
+    }
+
+    /**
+     * Inserts a vertex into this list before another specificed vertex
+     */
+    public void insertBefore(Vertex vtx, Vertex next) {
+        vtx.prev = next.prev;
+        if (next.prev == null) {
+            head = vtx;
+        } else {
+            next.prev.next = vtx;
+        }
+        vtx.next = next;
+        next.prev = vtx;
+    }
+
+    /**
+     * return the first element in this list
+     */
+    public Vertex first() {
+        return head;
+    }
+
+    /**
+     * Returns true if this list is empty
+     */
+    public boolean isEmpty() {
+        return head == null;
+    }
+}

src/main/java/Fleet_single_cam.java

+import Entity.Point3D;
 import org.opencv.core.Mat;
 import org.opencv.core.Size;
 import org.opencv.imgcodecs.Imgcodecs;
 import org.opencv.imgproc.Imgproc;
 
+import java.util.ArrayList;
 import java.util.Arrays;
 import java.util.HashMap;
+import java.util.List;
 
 public class Fleet_single_cam {
     private String id;
@@ -14,6 +17,7 @@ public class Fleet_single_cam {
     private int num_y;
     private int num_z;
     private boolean show;
+    private Point3D[] points;
     //    private
     HashMap<String, intArray> side;
 
@@ -32,6 +36,14 @@ public class Fleet_single_cam {
             return intArray.clone();
         }
 
+        public int getWidth() {
+            return intArray[0].length;
+        }
+
+        public int getHeight() {
+            return intArray.length;
+        }
+
         public void setIntArray(int[][] intArray) {
             this.intArray = intArray;
         }
@@ -126,6 +138,73 @@ public class Fleet_single_cam {
         this.side.get("bottom").setIntArray(fill_matrix(bottom));
     }
 
+    /**
+     * Create list point3d from 3 side
+     */
+    public void initPoint3d() {
+        //init point list
+        List<Point3D> point3dList = new ArrayList<>();
+
+        //temp pixel
+        int xx = 0;
+        int yy = 0;
+        int zz = 0;
+
+        //get side front, side, bottom
+        int[][] front = this.side.get("front").getIntArray();
+        int[][] side = this.side.get("side").getIntArray();
+        int[][] bottom = this.side.get("bottom").getIntArray();
+        //add point 0 in side front
+        zz = num_z + 1;
+        yy = num_y + 1;
+        for (int i = 0; i < front.length; i++) {
+            zz -= 1;
+            xx = 0;
+            for (int j = 0; j < front[i].length; j++) {
+                xx += 1;
+                //add if point == 0
+                if (front[i][j] == 0) {
+                    point3dList.add(new Point3D(xx, yy, zz));
+                }
+            }
+        }
+
+        //add point 0 in side side
+        zz = num_z + 1;
+        xx = 0;
+        for (int i = 0; i < side.length; i++) {
+            zz -= 1;
+            yy = 0;
+            for (int j = 0; j < side[i].length; j++) {
+                yy += 1;
+                //add if point == 0
+                if (side[i][j] == 0) {
+                    point3dList.add(new Point3D(xx, yy, zz));
+                }
+            }
+        }
+
+        //add point 0 in side bottom
+        zz = 0;
+        yy = num_y + 1;
+        for (int i = 0; i < bottom.length; i++) {
+            yy -= 1;
+            xx = 0;
+            for (int j = 0; j < bottom[i].length; j++) {
+                xx += 1;
+                //add if point == 0
+                if (bottom[i][j] == 0) {
+                    point3dList.add(new Point3D(xx, yy, zz));
+                }
+            }
+        }
+
+        points = point3dList.toArray(new Point3D[point3dList.size()]);
+    }
+
+    public Point3D[] getPoints() {
+        return points;
+    }
 
     private int[][] padding(int[][] matrix, int require_height, int require_width) {
         //get width, height
@@ -160,7 +239,6 @@ public class Fleet_single_cam {
 
         }
 
-
         return return_matrix;
 
     }

src/main/java/main.java

 import org.bytedeco.javacpp.Loader;
 import org.bytedeco.opencv.opencv_java;
 
+import java.util.Arrays;
+
 public class main {
     public static void main(String[] args) {
 
         Loader.load(opencv_java.class);
 
         //Khoi tạo 1 cam, nhận ảnh tĩnh vào
-        Fleet_single_cam cam = new Fleet_single_cam("a", "5b8ab6b219c9d6978fd827.jpg", 0.5, 5, 5, 4, false);
+        Fleet_single_cam cam1 = new Fleet_single_cam("a", "1da36bd1c4aa0bf452bb24.jpg", 0.5, 5, 5, 4, false);
+
+        //create front side, add 4 đỉnh của side front vào
+        cam1.add_side("front", new float[][]{
+                new float[]{681, 54},
+                new float[]{1250, 115},
+                new float[]{984, 528},
+                new float[]{679, 366}
+        });
+
+        //create mặt side, add 4 đỉnh của mặt side vào
+        cam1.add_side("side", new float[][]{
+                new float[]{8, 152},
+                new float[]{681, 54},
+                new float[]{679, 366},
+                new float[]{288, 545}
+        });
+
+        //create bottom side, add 4 đỉnh của side bottom vào
+        cam1.add_side("bottom", new float[][]{
+                new float[]{679, 366},
+                new float[]{984, 528},
+                new float[]{732, 955},
+                new float[]{288, 545}
+        });
+
+        cam1.refine_matrix();
+        cam1.initPoint3d();
+
+        //Khoi tạo 1 cam, nhận ảnh tĩnh vào
+        Fleet_single_cam cam2 = new Fleet_single_cam("a", "5b8ab6b219c9d6978fd827.jpg", 0.5, 5, 5, 4, false);
 
         //create front side, add 4 đỉnh của side front vào
-        cam.add_side("front", new float[][]{
+        cam2.add_side("front", new float[][]{
                 new float[]{687, 8},
                 new float[]{1264, 54},
                 new float[]{1027, 432},
@@ -18,7 +50,7 @@ public class main {
         });
 
         //create mặt side, add 4 đỉnh của mặt side vào
-        cam.add_side("side", new float[][]{
+        cam2.add_side("side", new float[][]{
                 new float[]{12, 132},
                 new float[]{687, 8},
                 new float[]{672, 305},
@@ -26,46 +58,40 @@ public class main {
         });
 
         //create bottom side, add 4 đỉnh của side bottom vào
-        cam.add_side("bottom", new float[][]{
+        cam2.add_side("bottom", new float[][]{
                 new float[]{672, 305},
                 new float[]{1027, 432},
                 new float[]{817, 923},
                 new float[]{275, 497}
         });
 
-        cam.refine_matrix();
+        cam2.refine_matrix();
+        cam2.initPoint3d();
+
+
+
+
+//        Point3d[] poly = Arrays.copyOf(cam1.getPoints(), cam1.getPoints().length+cam2.getPoints().length);
+//        System.arraycopy(cam2.getPoints(), 0, poly, cam1.getPoints().length, cam2.getPoints().length);
+//
+//        QuickHull3D hull = new QuickHull3D();
+//        hull.build(poly);
+//        System.out.println("Vertices:");
+//        Point3d[] vertices = hull.getVertices();
+//        for (int i = 0; i < vertices.length; i++) {
+//            Point3d pnt = vertices[i];
+//            System.out.println(pnt.x + " " + pnt.y + " " + pnt.z);
+//        }
+//
+//        System.out.println("Faces:");
+//        int[][] faceIndices = hull.getFaces();
+//        for (int i = 0; i < vertices.length; i++) {
+//            for (int k = 0; k < faceIndices[i].length; k++) {
+//                System.out.print(faceIndices[i][k] + " ");
+//            }
+//            System.out.println("");
+//        }
 
-        //print matrix
-        int[][] matrix = cam.side.get("front").getIntArray();
-        for (int i = 0; i < matrix.length; i++) {
-
-            for (int j = 0; j < matrix[0].length; j++) {
-                System.out.print(matrix[i][j] + " ");
-            }
-            System.out.println();
-        }
-
-        System.out.println();
-
-        int[][] matrix2 = cam.side.get("side").getIntArray();
-        for (int i = 0; i < matrix2.length; i++) {
-
-            for (int j = 0; j < matrix2[0].length; j++) {
-                System.out.print(matrix2[i][j] + " ");
-            }
-            System.out.println();
-        }
-
-        System.out.println();
-
-        int[][] matrix3 = cam.side.get("bottom").getIntArray();
-        for (int i = 0; i < matrix2.length; i++) {
-
-            for (int j = 0; j < matrix3[0].length; j++) {
-                System.out.print(matrix3[i][j] + " ");
-            }
-            System.out.println();
-        }
 
     }
 }

src/main/java/utils/QuickHull3d.java

+package utils;
+
+import Entity.*;
+
+import java.util.Vector;
+
+public class QuickHull3d {
+    /**
+     * Specifies that the distance tolerance should be computed automatically from the input point data
+     */
+    public static final double AUTOMATIC_TOLERANCE = -1;
+
+    protected int findIndex = -1;
+
+    //estimated size of the point set
+    protected double charLength;
+
+    protected Vertex[] pointBuffer = new Vertex[0];
+
+    protected int[] vertexPointIndices = new int[0];
+
+    private Face[] discardedFaces = new Face[3];
+
+    private Vertex[] maxVtxs = new Vertex[3];
+
+    private Vertex[] minVtxs = new Vertex[3];
+
+    protected Vector face = new Vector(16);
+
+    protected Vector horizon = new Vector(16);
+
+    private FaceList newFaces = new FaceList();
+
+    private VertexList unclaimed = new VertexList();
+
+    private VertexList claimed = new VertexList();
+
+    protected int numVertices;
+
+    protected int numFaces;
+
+    protected int numPoints;
+
+    protected double explicitTolerance = AUTOMATIC_TOLERANCE;
+
+    protected double tolerance;
+
+    private static final double DOUBLE_PREC = 2.2204460492503131e-16;
+
+    /**
+     * Create a convex hull object and initializes it to the convex hull of a set of points
+     * @param points
+     * input points
+     * @throws IllegalArgumentException
+     * the number of input points is less than four, or the point appear to be coincident, colinear, or coplanar
+     */
+    public QuickHull3d(Point3D[] points) throws IllegalArgumentException{
+        build(points, points.length);
+    }
+
+    /**
+     * Constructs the convex hull of a set of points
+     * @param points
+     * input points
+     * @param nump
+     * number of input poins
+     * @throws IllegalArgumentException
+     * the number of input points is less than four or greater than the length if points, or the points appear to be coincident, colinear, or coplanar
+     */
+    public void build(Point3D[] points, int nump) throws IllegalArgumentException{
+        if (nump < 4){
+            throw new IllegalArgumentException("Less than four input points specified");
+        }
+        if (points.length < nump){
+            throw new IllegalArgumentException("Point array too small for specified number of points");
+        }
+        initBuffers(nump);
+        setPoints(points, nump);
+        buildHull();
+    }
+
+    protected void initBuffers(int nump){
+        if (pointBuffer.length < nump){
+            Vertex[] newBuffer = new Vertex[nump];
+            vertexPointIndices = new int[nump];
+            for (int i = 0; i < pointBuffer.length; i++){
+                newBuffer[i] = pointBuffer[i];
+            }
+            for (int i = pointBuffer.length; i < nump; i++){
+                newBuffer[i] = new Vertex();
+            }
+            pointBuffer = newBuffer;
+        }
+        face.clear();
+        claimed.clear();
+        numFaces = 0;
+        numPoints = nump;
+    }
+
+    protected void setPoints(Point3D[] pnts, int nump) {
+        for (int i = 0; i < nump; i++){
+            Vertex vtx = pointBuffer[i];
+            vtx.pnt.set(pnts[i]);
+            vtx.index = i;
+        }
+    }
+
+    protected void buildHull(){
+        int cnt = 0;
+        Vertex eyeVtx;
+
+        computeMaxAndMin();
+        createInitialSimplex();
+        while ((eyeVtx = nextPointToAdd()) != null){
+            addPointToHull(eyeVtx);
+            cnt++;
+        }
+        reindexFacesAndVertices();
+    }
+
+    protected void computeMaxAndMin(){
+        //initialize max, min
+        Vector3D max = new Vector3D();
+        Vector3D min = new Vector3D();
+
+        for (int i=0;i<3;i++){
+            maxVtxs[i] = minVtxs[i] = pointBuffer[0];
+        }
+        max.set(pointBuffer[0].pnt);
+        min.set(pointBuffer[0].pnt);
+
+        //check all point to find max, min
+        for (int i=1;i<numPoints;i++){
+            Point3D pnt = pointBuffer[i].pnt;
+            //find maxVtxs[0] and minVtxs[0] , vectors with max x and min x
+            if (pnt.x >max.x){
+                max.x = pnt.x;
+                maxVtxs[0] = pointBuffer[i];
+            }else if (pnt.x < min.x){
+                min.x = pnt.x;
+                minVtxs[0] = pointBuffer[i];
+            }
+
+            //find maxVtxs[1] and minVtxs[1] , vectors with max y and min y
+            if (pnt.y >max.y){
+                max.y = pnt.y;
+                maxVtxs[1] = pointBuffer[i];
+            }else if (pnt.y < min.y){
+                min.y = pnt.y;
+                minVtxs[1] = pointBuffer[i];
+            }
+
+            //find maxVtxs[2] and minVtxs[2] , vectors with max z and min z
+            if (pnt.z >max.z){
+                max.z = pnt.z;
+                maxVtxs[2] = pointBuffer[i];
+            }else if (pnt.z < min.z){
+                min.z = pnt.z;
+                minVtxs[2] = pointBuffer[i];
+            }
+
+            charLength = Math.max(max.x - min.x, max.y - min.y);
+            charLength = Math.max(max.z - min.z, charLength);
+            if (explicitTolerance == AUTOMATIC_TOLERANCE){
+                tolerance = 3* DOUBLE_PREC * (Math.max(Math.abs(max.x), Math.abs(min.x)) + Math.max(Math.abs(max.y), Math.abs(min.y)) + Math.max(Math.abs(max.z), Math.abs(min.z)));
+            }else{
+                tolerance = explicitTolerance;
+            }
+        }
+    }
+
+    protected void createInitialSimplex() throws IllegalArgumentException{
+        double max = 0;
+        int imax = 0;
+
+        for (int i = 0; i< 3; i++){
+            double diff = maxVtxs[i].pnt.get(i)-minVtxs[i].pnt.get(i);
+            if (diff > max){
+                max = diff;
+                imax = i;
+            }
+        }
+
+        if (max <= tolerance){
+            throw new IllegalArgumentException("Input points appear to be conicident");
+        }
+
+        Vertex[] vtx = new Vertex[4];
+        //set first two vertices to be those with the greatest one dimensional separation
+
+        vtx[0] = maxVtxs[imax];
+        vtx[1] = minVtxs[imax];
+
+        // set third vertex to be the vertex farthest from the line between vtx0 and vtx1
+        Vector3D u01 = new Vector3D();
+        Vector3D diff02 = new Vector3D();
+        Vector3D nrml = new Vector3D();
+
+    }
+
+}

test_result.txt

+Vertices:
+5.0 6.0 3.0
+1.0 6.0 1.0
+5.0 6.0 1.0
+0.0 4.0 2.0
+0.0 1.0 1.0
+0.0 5.0 1.0
+1.0 5.0 0.0
+0.0 2.0 2.0
+5.0 5.0 0.0
+1.0 1.0 0.0
+5.0 1.0 0.0
+Faces:
+1 3 0
+9 6 8 10
+5 3 1
+5 1 6
+2 8 6 1
+2 1 0
+2 0 10 8
+7 10 0
+7 0 3
+4 9 10
+4 10 7
\ No newline at end of file