/**
* Copyright 2010 JogAmp Community. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without modification, are
* permitted provided that the following conditions are met:
*
* 1. Redistributions of source code must retain the above copyright notice, this list of
* conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright notice, this list
* of conditions and the following disclaimer in the documentation and/or other materials
* provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY JogAmp Community ``AS IS'' AND ANY EXPRESS OR IMPLIED
* WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
* FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL JogAmp Community OR
* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
* ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
* NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
* ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*
* The views and conclusions contained in the software and documentation are those of the
* authors and should not be interpreted as representing official policies, either expressed
* or implied, of JogAmp Community.
*/
package com.jogamp.opengl.math;
import java.util.ArrayList;
public class VectorUtil {
/** Zero vector */
public static final float[] ZERO = new float[] { 0f, 0f, 0f };
public enum Winding {
CW(-1), CCW(1);
public final int dir;
Winding(int dir) {
this.dir = dir;
}
}
public static final int COLLINEAR = 0;
/**
* Copies a vector of length 3
* @param dst output vector
* @param dstOffset offset of dst in array
* @param src input vector
* @param srcOffset offset of src in array
* @return copied output vector for chaining
*/
public static float[] copyVec3(final float[] dst, int dstOffset, final float[] src, int srcOffset)
{
System.arraycopy(src, srcOffset, dst, dstOffset, 3);
return dst;
}
/**
* Copies a vector of length 4
* @param dst output vector
* @param dstOffset offset of dst in array
* @param src input vector
* @param srcOffset offset of src in array
* @return copied output vector for chaining
*/
public static float[] copyVec4(final float[] dst, int dstOffset, final float[] src, int srcOffset)
{
System.arraycopy(src, srcOffset, dst, dstOffset, 4);
return dst;
}
/**
* Return true if both vectors are equal, no {@link FloatUtil#EPSILON} is taken into consideration.
*/
public static boolean equals(final float[] vec1, int vec1Offset, final float[] vec2, int vec2Offset) {
return vec1[0+vec1Offset] == vec2[0+vec2Offset] &&
vec1[1+vec1Offset] == vec2[1+vec2Offset] &&
vec1[2+vec1Offset] == vec2[2+vec2Offset];
}
/**
* Return true if both vectors are equal, i.e. their absolute delta < <code>epsilon</code>.
* @see FloatUtil#EPSILON
*/
public static boolean equals(final float[] vec1, int vec1Offset, final float[] vec2, int vec2Offset, final float epsilon) {
return Math.abs(vec1[0+vec1Offset] - vec2[0+vec2Offset]) < epsilon &&
Math.abs(vec1[1+vec1Offset] - vec2[1+vec2Offset]) < epsilon &&
Math.abs(vec1[2+vec1Offset] - vec2[2+vec2Offset]) < epsilon ;
}
/**
* Return true if vector is zero, no {@link FloatUtil#EPSILON} is taken into consideration.
*/
public static boolean isZero(final float[] vec, final int vecOffset) {
return 0f == vec[0+vecOffset] && 0f == vec[1+vecOffset] && 0f == vec[2+vecOffset];
}
/**
* Return true if vector is zero, i.e. it's absolute components < <code>epsilon</code>.
* @see FloatUtil#EPSILON
*/
public static boolean isZero(final float[] vec, final int vecOffset, final float epsilon) {
return isZero(vec[0+vecOffset], vec[1+vecOffset], vec[2+vecOffset], epsilon);
}
/**
* Return true if all three vector components are zero, i.e. it's their absolute value < <code>epsilon</code>.
* @see FloatUtil#EPSILON
*/
public static boolean isZero(final float x, final float y, final float z, final float epsilon) {
return Math.abs(x) < epsilon &&
Math.abs(y) < epsilon &&
Math.abs(z) < epsilon ;
}
/**
* Return the squared distance between the given two points described vector v1 and v2.
* <p>
* When comparing the relative distance between two points it is usually sufficient to compare the squared
* distances, thus avoiding an expensive square root operation.
* </p>
*/
public static float distanceSquared(final float[] v1, final float[] v2) {
final float dx = v1[0] - v2[0];
final float dy = v1[1] - v2[1];
final float dz = v1[2] - v2[2];
return dx * dx + dy * dy + dz * dz;
}
/**
* Return the distance between the given two points described vector v1 and v2.
*/
public static float distance(final float[] v1, final float[] v2) {
return FloatUtil.sqrt(distanceSquared(v1, v2));
}
/** compute the dot product of two points
* @param vec1 vector 1
* @param vec2 vector 2
* @return the dot product as float
*/
public static float dot(final float[] vec1, final float[] vec2)
{
return (vec1[0]*vec2[0] + vec1[1]*vec2[1] + vec1[2]*vec2[2]);
}
/**
* Compute the squared length of a vector, a.k.a the squared <i>norm</i>
*/
public static float lengthSquared(final float[] vec) {
return vec[0]*vec[0] + vec[1]*vec[1] + vec[2]*vec[2];
}
/**
* Compute the length of a vector, a.k.a the <i>norm</i>
*/
public static float length(final float[] vec) {
return FloatUtil.sqrt(lengthSquared(vec));
}
/**
* Normalize a vector
* @param result output vector
* @param vector input vector
* @return normalized output vector
*/
public static float[] normalize(final float[] result, final float[] vector) {
final float lengthSq = lengthSquared(vector);
if ( FloatUtil.isZero(lengthSq, FloatUtil.EPSILON) ) {
result[0] = 0f;
result[1] = 0f;
result[2] = 0f;
} else {
final float invSqr = 1f / FloatUtil.sqrt(lengthSq);
result[0] = vector[0] * invSqr;
result[1] = vector[1] * invSqr;
result[2] = vector[2] * invSqr;
}
return result;
}
/**
* Normalize a vector in place
* @param result output vector
* @param vector input vector
* @return normalized output vector
*/
public static float[] normalize(final float[] vector) {
final float lengthSq = lengthSquared(vector);
if ( FloatUtil.isZero(lengthSq, FloatUtil.EPSILON) ) {
vector[0] = 0f;
vector[1] = 0f;
vector[2] = 0f;
} else {
final float invSqr = 1f / FloatUtil.sqrt(lengthSq);
vector[0] *= invSqr;
vector[1] *= invSqr;
vector[2] *= invSqr;
}
return vector;
}
/**
* Scales a vector by param using given result float[]
* @param result vector for the result
* @param vector input vector
* @param scale single scale constant for all vector components
*/
public static float[] scale(final float[] result, final float[] vector, final float scale) {
result[0] = vector[0] * scale;
result[1] = vector[1] * scale;
result[2] = vector[2] * scale;
return result;
}
/** Scales a vector by param using given result float[]
* @param result vector for the result
* @param vector input vector
* @param scale 3 component scale constant for each vector component
* @return given result vector
*/
public static float[] scale(final float[] result, final float[] vector, final float[] scale)
{
result[0] = vector[0] * scale[0];
result[1] = vector[1] * scale[1];
result[2] = vector[2] * scale[2];
return result;
}
/**
* Adds two vectors
* @param v1 vector 1
* @param v2 vector 2
* @return v1 + v2
*/
public static float[] vectorAdd(final float[] result, final float[] v1, final float[] v2) {
result[0] = v1[0] + v2[0];
result[1] = v1[1] + v2[1];
result[2] = v1[2] + v2[2];
return result;
}
/**
* Subtracts two vectors
* @param v1 vector 1
* @param v2 vector 2
* @return v1 - v2
*/
public static float[] vectorSub(final float[] result, final float[] v1, final float[] v2) {
result[0] = v1[0] - v2[0];
result[1] = v1[1] - v2[1];
result[2] = v1[2] - v2[2];
return result;
}
/**
* cross product vec1 x vec2
* @param v1 vector 1
* @param v2 vector 2
* @return the resulting vector
*/
public static float[] cross(final float[] result, final float[] v1, final float[] v2)
{
result[0] = v1[1] * v2[2] - v1[2] * v2[1];
result[1] = v1[2] * v2[0] - v1[0] * v2[2];
result[2] = v1[0] * v2[1] - v1[1] * v2[0];
return result;
}
/** Column Matrix Vector multiplication
* @param colMatrix column matrix (4x4)
* @param vec vector(x,y,z)
* @return result
*/
public static float[] colMatrixVectorMult(final float[] result, final float[] colMatrix, final float[] vec)
{
result[0] = vec[0]*colMatrix[0] + vec[1]*colMatrix[4] + vec[2]*colMatrix[8] + colMatrix[12];
result[1] = vec[0]*colMatrix[1] + vec[1]*colMatrix[5] + vec[2]*colMatrix[9] + colMatrix[13];
result[2] = vec[0]*colMatrix[2] + vec[1]*colMatrix[6] + vec[2]*colMatrix[10] + colMatrix[14];
return result;
}
/** Matrix Vector multiplication
* @param rawMatrix column matrix (4x4)
* @param vec vector(x,y,z)
* @return result
*/
public static float[] rowMatrixVectorMult(final float[] result, final float[] rawMatrix, final float[] vec)
{
result[0] = vec[0]*rawMatrix[0] + vec[1]*rawMatrix[1] + vec[2]*rawMatrix[2] + rawMatrix[3];
result[1] = vec[0]*rawMatrix[4] + vec[1]*rawMatrix[5] + vec[2]*rawMatrix[6] + rawMatrix[7];
result[2] = vec[0]*rawMatrix[8] + vec[1]*rawMatrix[9] + vec[2]*rawMatrix[10] + rawMatrix[11];
return result;
}
/** Calculate the midpoint of two values
* @param p1 first value
* @param p2 second vale
* @return midpoint
*/
public static float mid(final float p1, final float p2)
{
return (p1+p2)/2.0f;
}
/**
* Calculate the midpoint of two points
* @param p1 first point
* @param p2 second point
* @return midpoint
*/
public static float[] mid(final float[] result, final float[] p1, final float[] p2)
{
result[0] = (p1[0] + p2[0])*0.5f;
result[1] = (p1[1] + p2[1])*0.5f;
result[2] = (p1[2] + p2[2])*0.5f;
return result;
}
/** Compute distance between 2 points
* @param p0 a ref point on the line
* @param vec vector representing the direction of the line
* @param point the point to compute the relative distance of
* @return distance float
*/
public static float computeLength(final float[] p0, final float[] point)
{
final float w0 = point[0]-p0[0];
final float w1 = point[1]-p0[1];
final float w2 = point[2]-p0[2];
return FloatUtil.sqrt(w0*w0 + w1*w1 + w2*w2);
}
/**Check equality of 2 vec3 vectors
* @param v1 vertex 1
* @param v2 vertex 2
* @return
*/
public static boolean checkEquality(final float[] v1, final float[] v2)
{
return Float.compare(v1[0], v2[0]) == 0 &&
Float.compare(v1[1], v2[1]) == 0 &&
Float.compare(v1[2], v2[2]) == 0 ;
}
/**Check equality of 2 vec2 vectors
* @param v1 vertex 1
* @param v2 vertex 2
* @return
*/
public static boolean checkEqualityVec2(final float[] v1, final float[] v2)
{
return Float.compare(v1[0], v2[0]) == 0 &&
Float.compare(v1[1], v2[1]) == 0 ;
}
/** Compute the determinant of 3 vectors
* @param a vector 1
* @param b vector 2
* @param c vector 3
* @return the determinant value
*/
public static float computeDeterminant(final float[] a, final float[] b, final float[] c)
{
return a[0]*b[1]*c[2] + a[1]*b[2]*c[0] + a[2]*b[0]*c[1] - a[0]*b[2]*c[1] - a[1]*b[0]*c[2] - a[2]*b[1]*c[0];
}
/** Check if three vertices are colliniear
* @param v1 vertex 1
* @param v2 vertex 2
* @param v3 vertex 3
* @return true if collinear, false otherwise
*/
public static boolean checkCollinear(final float[] v1, final float[] v2, final float[] v3)
{
return (computeDeterminant(v1, v2, v3) == VectorUtil.COLLINEAR);
}
/** Compute Vector
* @param vector storage for resulting Vector V1V2
* @param v1 vertex 1
* @param v2 vertex2 2
*/
public static void computeVector(final float[] vector, final float[] v1, final float[] v2) {
vector[0] = v2[0] - v1[0];
vector[1] = v2[1] - v1[1];
vector[2] = v2[2] - v1[2];
}
/** Check if vertices in triangle circumcircle
* @param a triangle vertex 1
* @param b triangle vertex 2
* @param c triangle vertex 3
* @param d vertex in question
* @return true if the vertex d is inside the circle defined by the
* vertices a, b, c. from paper by Guibas and Stolfi (1985).
*/
public static boolean inCircle(final Vert2fImmutable a, final Vert2fImmutable b, final Vert2fImmutable c, final Vert2fImmutable d) {
final float[] A = a.getCoord();
final float[] B = b.getCoord();
final float[] C = c.getCoord();
final float[] D = d.getCoord();
return (A[0] * A[0] + A[1] * A[1]) * triArea(B, C, D) -
(B[0] * B[0] + B[1] * B[1]) * triArea(A, C, D) +
(C[0] * C[0] + C[1] * C[1]) * triArea(A, B, D) -
(D[0] * D[0] + D[1] * D[1]) * triArea(A, B, C) > 0;
}
/** Computes oriented area of a triangle
* @param a first vertex
* @param b second vertex
* @param c third vertex
* @return compute twice the area of the oriented triangle (a,b,c), the area
* is positive if the triangle is oriented counterclockwise.
*/
public static float triArea(final Vert2fImmutable a, final Vert2fImmutable b, final Vert2fImmutable c){
final float[] A = a.getCoord();
final float[] B = b.getCoord();
final float[] C = c.getCoord();
return (B[0] - A[0]) * (C[1] - A[1]) - (B[1] - A[1]) * (C[0] - A[0]);
}
/** Computes oriented area of a triangle
* @param A first vertex
* @param B second vertex
* @param C third vertex
* @return compute twice the area of the oriented triangle (a,b,c), the area
* is positive if the triangle is oriented counterclockwise.
*/
public static float triArea(final float[] A, final float[] B, final float[] C){
return (B[0] - A[0]) * (C[1] - A[1]) - (B[1] - A[1])*(C[0] - A[0]);
}
/** Check if a vertex is in triangle using
* barycentric coordinates computation.
* @param a first triangle vertex
* @param b second triangle vertex
* @param c third triangle vertex
* @param p the vertex in question
* @return true if p is in triangle (a, b, c), false otherwise.
*/
public static boolean vertexInTriangle(final float[] a, final float[] b, final float[] c,
final float[] p,
final float[] ac, final float[] ab, final float[] ap){
// Compute vectors
computeVector(ac, a, c); //v0
computeVector(ab, a, b); //v1
computeVector(ap, a, p); //v2
// Compute dot products
final float dot00 = dot(ac, ac);
final float dot01 = dot(ac, ab);
final float dot02 = dot(ac, ap);
final float dot11 = dot(ab, ab);
final float dot12 = dot(ab, ap);
// Compute barycentric coordinates
final float invDenom = 1 / (dot00 * dot11 - dot01 * dot01);
final float u = (dot11 * dot02 - dot01 * dot12) * invDenom;
final float v = (dot00 * dot12 - dot01 * dot02) * invDenom;
// Check if point is in triangle
return (u >= 0) && (v >= 0) && (u + v < 1);
}
/**
* Check if one of three vertices are in triangle using
* barycentric coordinates computation.
* @param a first triangle vertex
* @param b second triangle vertex
* @param c third triangle vertex
* @param p1 the vertex in question
* @param p2 the vertex in question
* @param p3 the vertex in question
* @param tmpAC
* @param tmpAB
* @param tmpAP
* @return true if p1 or p2 or p3 is in triangle (a, b, c), false otherwise.
*/
public static boolean vertexInTriangle3(final float[] a, final float[] b, final float[] c,
final float[] p1, final float[] p2, final float[] p3,
final float[] tmpAC, final float[] tmpAB, final float[] tmpAP){
// Compute vectors
computeVector(tmpAC, a, c); //v0
computeVector(tmpAB, a, b); //v1
// Compute dot products
final float dotAC_AC = dot(tmpAC, tmpAC);
final float dotAC_AB = dot(tmpAC, tmpAB);
final float dotAB_AB = dot(tmpAB, tmpAB);
// Compute barycentric coordinates
final float invDenom = 1 / (dotAC_AC * dotAB_AB - dotAC_AB * dotAC_AB);
{
computeVector(tmpAP, a, p1); //v2
final float dotAC_AP1 = dot(tmpAC, tmpAP);
final float dotAB_AP1 = dot(tmpAB, tmpAP);
final float u1 = (dotAB_AB * dotAC_AP1 - dotAC_AB * dotAB_AP1) * invDenom;
final float v1 = (dotAC_AC * dotAB_AP1 - dotAC_AB * dotAC_AP1) * invDenom;
// Check if point is in triangle
if ( (u1 >= 0) && (v1 >= 0) && (u1 + v1 < 1) ) {
return true;
}
}
{
computeVector(tmpAP, a, p2); //v2
final float dotAC_AP2 = dot(tmpAC, tmpAP);
final float dotAB_AP2 = dot(tmpAB, tmpAP);
final float u = (dotAB_AB * dotAC_AP2 - dotAC_AB * dotAB_AP2) * invDenom;
final float v = (dotAC_AC * dotAB_AP2 - dotAC_AB * dotAC_AP2) * invDenom;
// Check if point is in triangle
if ( (u >= 0) && (v >= 0) && (u + v < 1) ) {
return true;
}
}
{
computeVector(tmpAP, a, p3); //v2
final float dotAC_AP3 = dot(tmpAC, tmpAP);
final float dotAB_AP3 = dot(tmpAB, tmpAP);
final float u = (dotAB_AB * dotAC_AP3 - dotAC_AB * dotAB_AP3) * invDenom;
final float v = (dotAC_AC * dotAB_AP3 - dotAC_AB * dotAC_AP3) * invDenom;
// Check if point is in triangle
if ( (u >= 0) && (v >= 0) && (u + v < 1) ) {
return true;
}
}
return false;
}
/** Check if points are in ccw order
* @param a first vertex
* @param b second vertex
* @param c third vertex
* @return true if the points a,b,c are in a ccw order
*/
public static boolean ccw(final Vert2fImmutable a, final Vert2fImmutable b, final Vert2fImmutable c){
return triArea(a,b,c) > 0;
}
/** Compute the winding of given points
* @param a first vertex
* @param b second vertex
* @param c third vertex
* @return Winding
*/
public static Winding getWinding(final Vert2fImmutable a, final Vert2fImmutable b, final Vert2fImmutable c) {
return triArea(a,b,c) > 0 ? Winding.CCW : Winding.CW ;
}
/** Computes the area of a list of vertices to check if ccw
* @param vertices
* @return positive area if ccw else negative area value
*/
public static float area(final ArrayList<? extends Vert2fImmutable> vertices) {
final int n = vertices.size();
float area = 0.0f;
for (int p = n - 1, q = 0; q < n; p = q++)
{
final float[] pCoord = vertices.get(p).getCoord();
final float[] qCoord = vertices.get(q).getCoord();
area += pCoord[0] * qCoord[1] - qCoord[0] * pCoord[1];
}
return area;
}
/** Compute the general winding of the vertices
* @param vertices array of Vertices
* @return CCW or CW {@link Winding}
*/
public static Winding getWinding(final ArrayList<? extends Vert2fImmutable> vertices) {
return area(vertices) >= 0 ? Winding.CCW : Winding.CW ;
}
/** Compute intersection between two segments
* @param a vertex 1 of first segment
* @param b vertex 2 of first segment
* @param c vertex 1 of second segment
* @param d vertex 2 of second segment
* @return the intersection coordinates if the segments intersect, otherwise returns null
*/
public static float[] seg2SegIntersection(final float[] result, final Vert2fImmutable a, final Vert2fImmutable b, final Vert2fImmutable c, final Vert2fImmutable d) {
final float determinant = (a.getX()-b.getX())*(c.getY()-d.getY()) - (a.getY()-b.getY())*(c.getX()-d.getX());
if (determinant == 0)
return null;
final float alpha = (a.getX()*b.getY()-a.getY()*b.getX());
final float beta = (c.getX()*d.getY()-c.getY()*d.getY());
final float xi = ((c.getX()-d.getX())*alpha-(a.getX()-b.getX())*beta)/determinant;
final float yi = ((c.getY()-d.getY())*alpha-(a.getY()-b.getY())*beta)/determinant;
final float gamma = (xi - a.getX())/(b.getX() - a.getX());
final float gamma1 = (xi - c.getX())/(d.getX() - c.getX());
if(gamma <= 0 || gamma >= 1) return null;
if(gamma1 <= 0 || gamma1 >= 1) return null;
result[0] = xi;
result[1] = yi;
result[2] = 0;
return result;
}
/** Compute intersection between two segments
* @param a vertex 1 of first segment
* @param b vertex 2 of first segment
* @param c vertex 1 of second segment
* @param d vertex 2 of second segment
* @return true if the segments intersect, otherwise returns false
*/
public static boolean testSeg2SegIntersection(final Vert2fImmutable a, final Vert2fImmutable b, final Vert2fImmutable c, final Vert2fImmutable d) {
final float[] A = a.getCoord();
final float[] B = b.getCoord();
final float[] C = c.getCoord();
final float[] D = d.getCoord();
final float determinant = (A[0]-B[0])*(C[1]-D[1]) - (A[1]-B[1])*(C[0]-D[0]);
if (determinant == 0) {
return false;
}
final float alpha = (A[0]*B[1]-A[1]*B[0]);
final float beta = (C[0]*D[1]-C[1]*D[1]);
final float xi = ((C[0]-D[0])*alpha-(A[0]-B[0])*beta)/determinant;
final float gamma = (xi - A[0])/(B[0] - A[0]);
final float gamma1 = (xi - C[0])/(D[0] - C[0]);
if(gamma <= 0 || gamma >= 1 || gamma1 <= 0 || gamma1 >= 1) {
return false;
}
return true;
}
/** Compute intersection between two lines
* @param a vertex 1 of first line
* @param b vertex 2 of first line
* @param c vertex 1 of second line
* @param d vertex 2 of second line
* @return the intersection coordinates if the lines intersect, otherwise
* returns null
*/
public static float[] line2lineIntersection(final float[] result, final Vert2fImmutable a, final Vert2fImmutable b, final Vert2fImmutable c, final Vert2fImmutable d) {
final float determinant = (a.getX()-b.getX())*(c.getY()-d.getY()) - (a.getY()-b.getY())*(c.getX()-d.getX());
if (determinant == 0)
return null;
final float alpha = (a.getX()*b.getY()-a.getY()*b.getX());
final float beta = (c.getX()*d.getY()-c.getY()*d.getY());
final float xi = ((c.getX()-d.getX())*alpha-(a.getX()-b.getX())*beta)/determinant;
final float yi = ((c.getY()-d.getY())*alpha-(a.getY()-b.getY())*beta)/determinant;
result[0] = xi;
result[1] = yi;
result[2] = 0;
return result;
}
/** Check if a segment intersects with a triangle
* @param a vertex 1 of the triangle
* @param b vertex 2 of the triangle
* @param c vertex 3 of the triangle
* @param d vertex 1 of first segment
* @param e vertex 2 of first segment
* @return true if the segment intersects at least one segment of the triangle, false otherwise
*/
public static boolean testTri2SegIntersection(final Vert2fImmutable a, final Vert2fImmutable b, final Vert2fImmutable c, final Vert2fImmutable d, final Vert2fImmutable e){
return testSeg2SegIntersection(a, b, d, e) ||
testSeg2SegIntersection(b, c, d, e) ||
testSeg2SegIntersection(a, c, d, e) ;
}
}