Distorted Android

///////////////////////////////////////////////////////////////////////////////////////////////////

// Copyright 2020 Leszek Koltunski                                                               //

//                                                                                               //

// This file is part of Magic Cube.                                                              //

//                                                                                               //

// Magic Cube is free software: you can redistribute it and/or modify                            //

// it under the terms of the GNU General Public License as published by                          //

// the Free Software Foundation, either version 2 of the License, or                             //

// (at your option) any later version.                                                           //

//                                                                                               //

// Magic Cube is distributed in the hope that it will be useful,                                 //

// but WITHOUT ANY WARRANTY; without even the implied warranty of                                //

// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the                                 //

// GNU General Public License for more details.                                                  //

//                                                                                               //

// You should have received a copy of the GNU General Public License                             //

// along with Magic Cube.  If not, see <http://www.gnu.org/licenses/>.                           //

///////////////////////////////////////////////////////////////////////////////////////////////////

package org.distorted.examples.meshfile;

import org.distorted.library.effect.VertexEffect;

import org.distorted.library.effect.VertexEffectDeform;

import org.distorted.library.effect.VertexEffectMove;

import org.distorted.library.effect.VertexEffectRotate;

import org.distorted.library.effect.VertexEffectScale;

import org.distorted.library.mesh.MeshBase;

import org.distorted.library.mesh.MeshJoined;

import org.distorted.library.mesh.MeshPolygon;

import org.distorted.library.type.Static1D;

import org.distorted.library.type.Static3D;

import org.distorted.library.type.Static4D;

///////////////////////////////////////////////////////////////////////////////////////////////////

public class CubitFactory

  {

  private static final float SQ2 = (float)Math.sqrt(2);

  private static final float SQ3 = (float)Math.sqrt(3);

  private static final float SQ6 = (float)Math.sqrt(6);

  private static final Static1D RADIUS = new Static1D(1);

  private static CubitFactory mThis;

///////////////////////////////////////////////////////////////////////////////////////////////////

  private CubitFactory()

    {

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  public static CubitFactory getInstance()

    {

    if( mThis==null ) mThis = new CubitFactory();

    return mThis;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// H - height of the band in the middle

// alpha - angle of the edge  [0,90]

// dist - often in a polygon the distance from edge to center is not 1, but something else.

// This is the distance.

// K - where to begin the second, much more flat part of the band. [0,1]

// N - number of bands. N>=3

//

// theory: two distinct parts to the band:

// 1) (0,B) - steep

// 2) (B,1) - flat

//

// In first part, we have y = g(x) ; in second - y = g(f(x)) where

//

// g(x) = sqrt( R^2 - (x-D)^2 ) - R*cos(alpha)

// f(x) = ((D-B)/(1-B)*x + B*(1-D)/(1-B)

// h(x) = R*(sin(alpha) - sin(x))

// R = H/(1-cos(alpha))

// D = H*sin(alpha)

// B = h(K*alpha)

//

// The N points are taken at:

//

// 1) in the second part, there are K2 = (N-3)/3 such points

// 2) in the first - K1 = (N-3) - K2

// 3) also, the 3 points 0,B,1

//

// so we have the sequence A[i] of N points

//

// 0

// h((i+1)*(1-K)*alpha/(K1+1)) (i=0,1,...,K1-1)

// B

// (1-B)*(i+1)/(K2+1) + B   (i=0,i,...,K2-1)

// 1

///////////////////////////////////////////////////////////////////////////////////////////////////

  private float f(float D, float B, float x)

    {

    return ((D-B)*x + B*(1-D))/(1-B);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  private float g(float R, float D, float x, float cosAlpha)

    {

    float d = x-D;

    return (float)(Math.sqrt(R*R-d*d)-R*cosAlpha);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  private float h(float R, float sinAlpha, float x)

    {

    return R*(sinAlpha-(float)Math.sin(x));

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  private float[] computeBands(float H, int alpha, float dist, float K, int N)

    {

    float[] bands = new float[2*N];

    bands[0] = 1.0f;

    bands[1] = 0.0f;

    float beta = (float)Math.atan(dist*Math.tan(Math.PI*alpha/180));

    float sinBeta = (float)Math.sin(beta);

    float cosBeta = (float)Math.cos(beta);

    float R = cosBeta<1.0f ? H/(1.0f-cosBeta) : 0.0f;

    float D = R*sinBeta;

    float B = h(R,sinBeta,K*beta);

    if( D>1.0f )

      {

      for(int i=1; i<N; i++)

        {

        bands[2*i  ] = (float)(N-1-i)/(N-1);

        bands[2*i+1] = H*(1-bands[2*i]);

        }

      }

    else

      {

      int K2 = (N-3)/3;

      int K1 = (N-3)-K2;

      for(int i=0; i<=K1; i++)

        {

        float angle = K*beta + (1-K)*beta*(K1-i)/(K1+1);

        float x = h(R,sinBeta,angle);

        bands[2*i+2] = 1.0f - x;

        bands[2*i+3] = g(R,D,x,cosBeta);

        }

      for(int i=0; i<=K2; i++)

        {

        float x = (1-B)*(i+1)/(K2+1) + B;

        bands[2*K1+2 + 2*i+2] = 1.0f - x;

        bands[2*K1+2 + 2*i+3] = g(R,D,f(D,B,x),cosBeta);

        }

      }

    return bands;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  private void roundCorners(MeshBase mesh, Static3D center, Static3D[] vertices, float strength, float regionRadius)

    {

    Static4D reg= new Static4D(0,0,0,regionRadius);

    float centX = center.get0();

    float centY = center.get1();

    float centZ = center.get2();

    for (Static3D vertex : vertices)

      {

      float x = strength*(centX - vertex.get0());

      float y = strength*(centY - vertex.get1());

      float z = strength*(centZ - vertex.get2());

      VertexEffect effect = new VertexEffectDeform(new Static3D(x,y,z), RADIUS, vertex, reg);

      mesh.apply(effect);

      }

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  MeshBase createFacesCube(int index)

    {

    final int MESHES=6;

    MeshBase[] meshes = new MeshPolygon[MESHES];

    int association = 1;

    float[] bands;

    float D = 0.027f;

    float E = 0.5f-D;

    float[] vertices = { -E,-E, +E,-E, +E,+E, -E,+E };

    int extraI, extraV;

    switch(index)

      {

      case 0 : bands = new float[] { 1.0f    ,-D,

                                     1.0f-D/2,-D*0.55f,

                                     1.0f-D  ,-D*0.25f,

                                     1.0f-2*D, 0.0f,

                                     0.50f   , 0.040f,

                                     0.0f    , 0.048f };

               extraI = 2;

               extraV = 2;

               break;

      case 1 : bands = new float[] { 1.0f       ,-D,

                                     1.0f-D*1.2f,-D*0.55f,

                                     1.0f-2*D   , 0.0f,

                                     0.50f      , 0.040f,

                                     0.0f       , 0.048f };

               extraI = 2;

               extraV = 2;

               break;

      case 2 : bands = new float[] { 1.0f       ,-D,

                                     1.0f-D*1.2f,-D*0.55f,

                                     1.0f-2*D   , 0.0f,

                                     0.50f      , 0.040f,

                                     0.0f       , 0.048f };

               extraI = 1;

               extraV = 2;

               break;

      default: bands = new float[] { 1.0f    ,-D,

                                     1.0f-2*D, 0.0f,

                                     0.50f   , 0.025f,

                                     0.0f    , 0.030f };

               extraI = 1;

               extraV = 1;

               break;

      }

    meshes[0] = new MeshPolygon(vertices,bands,extraI,extraV);

    meshes[0].setEffectAssociation(0,association,0);

    for(int i=1; i<MESHES; i++)

      {

      association <<=1;

      meshes[i] = meshes[0].copy(true);

      meshes[i].setEffectAssociation(0,association,0);

      }

    return new MeshJoined(meshes);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  MeshBase createFacesSkewbCorner()

    {

    MeshBase[] meshes = new MeshBase[6];

    float E = 0.5f;

    float F = SQ2/2;

    float[] vertices0 = { -E+E/4,E/4, E/4,-E+E/4, E/4,E/4};

    float[] bands0 = computeBands(0.03f,30,E/3,0.5f,7);

    meshes[0] = new MeshPolygon(vertices0, bands0, 3, 3);

    meshes[0].setEffectAssociation(0,1,0);

    meshes[1] = meshes[0].copy(true);

    meshes[1].setEffectAssociation(0,2,0);

    meshes[2] = meshes[0].copy(true);

    meshes[2].setEffectAssociation(0,4,0);

    float[] vertices1 = { 0,0, F,0, 7*F/8,(SQ3/8)*F, 5*F/8,(3*SQ3/8)*F, F/2,(SQ3/2)*F };

    float[] bands1 = computeBands(0,0,1,0,3);

    meshes[3] = new MeshPolygon(vertices1,bands1,1,5);

    meshes[3].setEffectAssociation(0,8,0);

    meshes[4] = meshes[3].copy(true);

    meshes[4].setEffectAssociation(0,16,0);

    meshes[5] = meshes[3].copy(true);

    meshes[5].setEffectAssociation(0,32,0);

    return new MeshJoined(meshes);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  MeshBase createFacesSkewbFace()

    {

    MeshBase[] meshes = new MeshBase[5];

    float E = SQ2/4;

    float[] vertices0 = { -E,-E, +E,-E, +E,+E, -E,+E };

    float[] bands0 = computeBands(0.05f,30,E/2,0.5f,7);

    meshes[0] = new MeshPolygon(vertices0, bands0, 3, 3);

    meshes[0].setEffectAssociation(0,1,0);

    float[] vertices1 = { -E,-SQ3*E, -E*0.7f,-SQ3*E, +E*0.7f,-SQ3*E, +E,-SQ3*E, 0,0 };

    float[] bands1 = computeBands(0,0,1,0,3);

    meshes[1] = new MeshPolygon(vertices1,bands1,0,0);

    meshes[1].setEffectAssociation(0,2,0);

    meshes[2] = meshes[1].copy(true);

    meshes[2].setEffectAssociation(0,4,0);

    meshes[3] = meshes[1].copy(true);

    meshes[3].setEffectAssociation(0,8,0);

    meshes[4] = meshes[1].copy(true);

    meshes[4].setEffectAssociation(0,16,0);

    return new MeshJoined(meshes);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  MeshBase createFacesOcta()

    {

    int association = 1;

    float C = 0.06f;

    float D = 0.031f;

    float E = SQ3/2;

    float F = 0.5f;

    float[] vertices = { -F,-E/3, +F,-E/3, 0.0f,2*E/3};

    float[] bands = new float[] { 1.0f    , 0,

                                  1.0f  -C, D*0.55f,

                                  1.0f-2*C, D*0.85f,

                                  1.0f-4*C, D*1.20f,

                                  0.5f    , D*1.40f,

                                  0.0f    , D*1.50f };

    MeshBase[] meshes = new MeshPolygon[8];

    meshes[0] = new MeshPolygon(vertices, bands, 2,2);

    meshes[0].setEffectAssociation(0,association,0);

    for(int i=1; i<8; i++)

      {

      association <<= 1;

      meshes[i] = meshes[0].copy(true);

      meshes[i].setEffectAssociation(0,association,0);

      }

    return new MeshJoined(meshes);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  MeshBase createFacesTetra()

    {

    MeshBase[] meshes = new MeshBase[4];

    int association = 1;

    float C = 0.06f;

    float D = 0.035f;

    float E = SQ3/2;

    float F = 0.5f;

    float[] vertices = { -F,-E/3, +F,-E/3, 0.0f,2*E/3};

    float[] bands = new float[] { 1.0f    , 0,

                                  1.0f  -C, D*0.50f,

                                  1.0f-2*C, D*0.80f,

                                  1.0f-4*C, D*1.10f,

                                  0.5f    , D*1.30f,

                                  0.0f    , D*1.35f };

    meshes[0] = new MeshPolygon(vertices, bands, 2,2);

    meshes[0].setEffectAssociation(0,association,0);

    for(int i=1; i<4; i++)

      {

      association <<= 1;

      meshes[i] = meshes[0].copy(true);

      meshes[i].setEffectAssociation(0,association,0);

      }

    return new MeshJoined(meshes);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  MeshBase createFacesDino()

    {

    final int MESHES=4;

    MeshBase[] meshes = new MeshPolygon[MESHES];

    float E = 0.5f*SQ2;

    float F = 0.5f;

    float[] vertices0 = { -F,F/3, 0,-2*F/3, +F,F/3 };

    float[] bands0 = computeBands(0.03f,45,F/3,0.2f,7);

    meshes[0] = new MeshPolygon(vertices0, bands0, 2, 5);

    meshes[0].setEffectAssociation(0,1,0);

    meshes[1] = meshes[0].copy(true);

    meshes[1].setEffectAssociation(0,2,0);

    float[] vertices1 = { -E/2,-E*(SQ3/6), E/2,-E*(SQ3/6), 0,E*(SQ3/3) };

    float[] bands1 = computeBands(0.02f,45,F/3,0.2f,3);

    meshes[2] = new MeshPolygon(vertices1, bands1, 1, 2);

    meshes[2].setEffectAssociation(0,4,0);

    meshes[3] = meshes[2].copy(true);

    meshes[3].setEffectAssociation(0,8,0);

    return new MeshJoined(meshes);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  MeshBase createFacesHelicopterCorner()

    {

    MeshBase[] meshes = new MeshBase[6];

    float E = 0.5f;

    float F = SQ2/4;

    float G = 1.0f/12;

    float[] vertices0 = { -E+E/4,E/4, E/4,-E+E/4, E/4,E/4};

    float[] bands0 = computeBands(0.03f,45,E/4,0.2f,7);

    meshes[0] = new MeshPolygon(vertices0, bands0, 3, 3);

    meshes[0].setEffectAssociation(0,1,0);

    meshes[1] = meshes[0].copy(true);

    meshes[1].setEffectAssociation(0,2,0);

    meshes[2] = meshes[0].copy(true);

    meshes[2].setEffectAssociation(0,4,0);

    float[] vertices1 = { -F,-G, 0,-G, +F,-G, 0,2*G };

    float[] bands1 = computeBands(0.00f,0,0,0.0f,3);

    meshes[3] = new MeshPolygon(vertices1,bands1,1,5);

    meshes[3].setEffectAssociation(0,8,0);

    meshes[4] = meshes[3].copy(true);

    meshes[4].setEffectAssociation(0,16,0);

    meshes[5] = meshes[3].copy(true);

    meshes[5].setEffectAssociation(0,32,0);

    return new MeshJoined(meshes);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  MeshBase createFacesHelicopterFace()

    {

    MeshBase[] meshes = new MeshBase[4];

    float E = 0.5f;

    float F = SQ2/4;

    float G = 1.0f/12;

    float[] vertices0 = { -E+E/4,E/4, E/4,-E+E/4, E/4,E/4};

    float[] bands0 = computeBands(0.03f,45,E/4,0.1f,7);

    meshes[0] = new MeshPolygon(vertices0, bands0, 3, 3);

    meshes[0].setEffectAssociation(0,1,0);

    float[] vertices1 = { -F,-G, +F,-G, 0,2*G};

    float[] bands1 = computeBands(0.01f,45,F,0.0f,3);

    meshes[1] = new MeshPolygon(vertices1, bands1, 1, 3);

    meshes[1].setEffectAssociation(0,2,0);

    float[] vertices2 = { -E/2,-F/3, +E/2,-F/3, 0,2*F/3};

    meshes[2] = new MeshPolygon(vertices2, bands1, 1, 3);

    meshes[2].setEffectAssociation(0,4,0);

    meshes[3] = meshes[2].copy(true);

    meshes[3].setEffectAssociation(0,8,0);

    return new MeshJoined(meshes);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  MeshBase createFacesRediEdge()

    {

    final int MESHES=6;

    float F = 0.25f;

    float[] bands0 = computeBands(0.03f,45,F,0.2f,7);

    float[] vertices0 = { -F,+F, -F,-F, 0, -2*F, +F,-F, +F,+F };

    MeshBase[] meshes = new MeshPolygon[MESHES];

    meshes[0] = new MeshPolygon(vertices0, bands0, 2, 2);

    meshes[0].setEffectAssociation(0,1,0);

    meshes[1] = meshes[0].copy(true);

    meshes[1].setEffectAssociation(0,2,0);

    float[] bands1 = computeBands(0.02f,45,F/2,0.2f,3);

    float[] vertices1 = { -F/2, +F/2, -F/2, -1.5f*F, 1.5f*F, +F/2 };

    meshes[2] = new MeshPolygon(vertices1, bands1, 1, 2);

    meshes[2].setEffectAssociation(0,4,0);

    meshes[3] = meshes[2].copy(true);

    meshes[3].setEffectAssociation(0,8,0);

    float X = 0.25f*SQ2;

    float Y = SQ6/16;

    float[] vertices2 = { -X, Y, -1.5f*X, -Y, +1.5f*X, -Y, +X, Y };

    meshes[4] = new MeshPolygon(vertices2, bands1, 1, 1);

    meshes[4].setEffectAssociation(0,16,0);

    meshes[5] = meshes[4].copy(true);

    meshes[5].setEffectAssociation(0,32,0);

    return new MeshJoined(meshes);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  MeshBase createFacesRediCorner()

    {

    final int MESHES=6;

    MeshBase[] meshes = new MeshBase[MESHES];

    float E = 0.5f;

    float[] vertices1 = { -E,-E, +E,-E, +E,+E, -E,+E };

    float[] bands1 = computeBands(0.04f,45,E,0.3f,6);

    meshes[0] = new MeshPolygon(vertices1,bands1,2,2);

    meshes[0].setEffectAssociation(0,1,0);

    meshes[1] = meshes[0].copy(true);

    meshes[1].setEffectAssociation(0,2,0);

    meshes[2] = meshes[0].copy(true);

    meshes[2].setEffectAssociation(0,4,0);

    float F = SQ2/2;

    float X = 0.5f;

    float G = 0.72f;

    float[] vertices2 = { -E,+F, -E+X,0, -E,-F, -E*G,-F, +E*G,-F, +E,-F, +E-X,0, +E,+F, +E*G,+F, -E*G,+F };

    float[] bands2 = computeBands(0.0f,0,1.0f,0.0f,2);

    meshes[3] = new MeshPolygon(vertices2,bands2,0,0);

    meshes[3].setEffectAssociation(0,8,0);

    meshes[4] = meshes[3].copy(true);

    meshes[4].setEffectAssociation(0,16,0);

    meshes[5] = meshes[3].copy(true);

    meshes[5].setEffectAssociation(0,32,0);

    return new MeshJoined(meshes);

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  VertexEffect[] createVertexEffectsCube()

    {

    Static3D axisY   = new Static3D(0,1,0);

    Static3D axisX   = new Static3D(1,0,0);

    Static3D center  = new Static3D(0,0,0);

    Static1D angle90 = new Static1D(90);

    Static1D angle180= new Static1D(180);

    Static1D angle270= new Static1D(270);

    VertexEffect[] effect = new VertexEffect[6];

    effect[0] = new VertexEffectMove(new Static3D(0,0,+0.5f));

    effect[1] = new VertexEffectRotate( angle180, axisX, center );

    effect[2] = new VertexEffectRotate( angle90 , axisX, center );

    effect[3] = new VertexEffectRotate( angle270, axisX, center );

    effect[4] = new VertexEffectRotate( angle270, axisY, center );

    effect[5] = new VertexEffectRotate( angle90 , axisY, center );

    effect[0].setMeshAssociation(63,-1);  // all 6 sides

    effect[1].setMeshAssociation(32,-1);  // back

    effect[2].setMeshAssociation( 8,-1);  // bottom

    effect[3].setMeshAssociation( 4,-1);  // top

    effect[4].setMeshAssociation( 2,-1);  // left

    effect[5].setMeshAssociation( 1,-1);  // right

    return effect;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  VertexEffect[] createVertexEffectsSkewbCorner()

    {

    float E = 0.5f;

    Static3D axisX  = new Static3D(1,0,0);

    Static3D axisY  = new Static3D(0,1,0);

    Static3D axis0  = new Static3D(-SQ2/2,0,SQ2/2);

    Static3D axis1  = new Static3D(+SQ3/3,+SQ3/3,+SQ3/3);

    Static1D angle1 = new Static1D(+90);

    Static1D angle2 = new Static1D(-90);

    Static1D angle3 = new Static1D(-15);

    Static1D angle4 = new Static1D((float)((180.0f/Math.PI)*Math.acos(SQ3/3)));

    Static1D angle5 = new Static1D(120);

    Static1D angle6 = new Static1D(240);

    Static3D center1= new Static3D(0,0,0);

    Static3D center2= new Static3D(-0.5f,-0.5f,-0.5f);

    Static3D move1  = new Static3D(-E/4,-E/4,0);

    Static3D move2  = new Static3D(-0.5f,-0.5f,-0.5f);

    VertexEffect[] effect = new VertexEffect[10];

    effect[0] = new VertexEffectMove(move1);

    effect[1] = new VertexEffectScale(new Static3D(1,1,-1));

    effect[2] = new VertexEffectRotate(angle1,axisX,center1);

    effect[3] = new VertexEffectRotate(angle2,axisY,center1);

    effect[4] = new VertexEffectMove(move2);

    effect[5] = new VertexEffectRotate(angle1,axisX,center2);

    effect[6] = new VertexEffectRotate(angle3,axisY,center2);

    effect[7] = new VertexEffectRotate(angle4,axis0,center2);

    effect[8] = new VertexEffectRotate(angle5,axis1,center2);

    effect[9] = new VertexEffectRotate(angle6,axis1,center2);

    effect[0].setMeshAssociation( 7,-1);  // meshes 0,1,2

    effect[1].setMeshAssociation( 6,-1);  // meshes 1,2

    effect[2].setMeshAssociation( 2,-1);  // mesh 1

    effect[3].setMeshAssociation( 4,-1);  // mesh 2

    effect[4].setMeshAssociation(56,-1);  // meshes 3,4,5

    effect[5].setMeshAssociation(56,-1);  // meshes 3,4,5

    effect[6].setMeshAssociation(56,-1);  // meshes 3,4,5

    effect[7].setMeshAssociation(56,-1);  // meshes 3,4,5

    effect[8].setMeshAssociation(16,-1);  // mesh 4

    effect[9].setMeshAssociation(32,-1);  // mesh 5

    return effect;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  VertexEffect[] createVertexEffectsSkewbFace()

    {

    Static3D center = new Static3D(0,0,0);

    Static3D axisX  = new Static3D(1,0,0);

    Static3D axisZ  = new Static3D(0,0,1);

    float angle = -(float)((180.0f/Math.PI)*Math.acos(SQ3/3));

    VertexEffect[] effect = new VertexEffect[6];

    effect[0] = new VertexEffectRotate( new Static1D(angle), axisX, center);

    effect[1] = new VertexEffectRotate( new Static1D(  135), axisZ, center);

    effect[2] = new VertexEffectRotate( new Static1D(   45), axisZ, center);

    effect[3] = new VertexEffectRotate( new Static1D(  -45), axisZ, center);

    effect[4] = new VertexEffectRotate( new Static1D( -135), axisZ, center);

    effect[5] = new VertexEffectMove( new Static3D(0,0,-0.5f) );

    effect[0].setMeshAssociation(30,-1);  // meshes 1,2,3,4

    effect[1].setMeshAssociation( 2,-1);  // mesh 1

    effect[2].setMeshAssociation( 5,-1);  // meshes 0,2

    effect[3].setMeshAssociation( 8,-1);  // mesh 3

    effect[4].setMeshAssociation(16,-1);  // mesh 4

    effect[5].setMeshAssociation(30,-1);  // meshes 1,2,3,4

    return effect;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  VertexEffect[] createVertexEffectsOcta()

    {

    Static1D alpha = new Static1D((float)(-(180/Math.PI)*Math.asin(SQ3/3)));

    Static1D angle1= new Static1D( 90);

    Static1D angle2= new Static1D(180);

    Static1D angle3= new Static1D(270);

    Static3D move1 = new Static3D(0,SQ2/2-SQ3/3,0);

    Static3D axisX = new Static3D(1,0,0);

    Static3D axisY = new Static3D(0,1,0);

    Static3D cent0 = new Static3D(0,0,0);

    Static3D cent1 = new Static3D(0,SQ2/2,0);

    Static3D flipY = new Static3D( 1,-1, 1);

    VertexEffect[] effect = new VertexEffect[6];

    effect[0] = new VertexEffectMove(move1);

    effect[1] = new VertexEffectRotate(alpha , axisX, cent1);

    effect[2] = new VertexEffectRotate(angle1, axisY, cent0);

    effect[3] = new VertexEffectRotate(angle2, axisY, cent0);

    effect[4] = new VertexEffectRotate(angle3, axisY, cent0);

    effect[5] = new VertexEffectScale(flipY);

    effect[2].setMeshAssociation ( 34,-1); // apply to meshes 1 & 5

    effect[3].setMeshAssociation ( 68,-1); // apply to meshes 2 & 6

    effect[4].setMeshAssociation (136,-1); // apply to meshes 3 & 7

    effect[5].setMeshAssociation (240,-1); // apply to meshes 4,5,6,7

    return effect;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  VertexEffect[] createVertexEffectsTetra()

    {

    Static3D flipZ = new Static3D( 1, 1,-1);

    Static1D alpha = new Static1D((float)(-(180/Math.PI)*Math.asin(SQ3/3)));

    Static1D angle1= new Static1D( 90);

    Static1D angle2= new Static1D(180);

    Static3D move1 = new Static3D(0,SQ2/4-SQ3/6,0);

    Static3D axisX = new Static3D(1,0,0);

    Static3D axisY = new Static3D(0,1,0);

    Static3D axisZ = new Static3D(0,0,1);

    Static3D cent0 = new Static3D(0,0,0);

    Static3D cent1 = new Static3D(0,SQ2/4,0);

    VertexEffect[] effect = new VertexEffect[6];

    effect[0] = new VertexEffectRotate(angle2, axisZ, cent0);

    effect[1] = new VertexEffectMove(move1);

    effect[2] = new VertexEffectRotate(alpha , axisX, cent1);

    effect[3] = new VertexEffectScale(flipZ);

    effect[4] = new VertexEffectRotate(angle1, axisY, cent0);

    effect[5] = new VertexEffectRotate(angle2, axisZ, cent0);

    effect[0].setMeshAssociation(15,-1); // meshes 0,1,2,3

    effect[1].setMeshAssociation(15,-1); // meshes 0,1,2,3

    effect[2].setMeshAssociation(15,-1); // meshes 0,1,2,3

    effect[3].setMeshAssociation(10,-1); // meshes 1 & 3

    effect[4].setMeshAssociation(12,-1); // meshes 2 & 3

    effect[5].setMeshAssociation(12,-1); // meshes 2 & 3

    return effect;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  VertexEffect[] createVertexEffectsDino()

    {

    float E = 0.5f*SQ2;

    float F = 0.5f;

    final float ANGLE = (float)((180/Math.PI)*(Math.atan(SQ2)));

    Static1D angle1 = new Static1D(-ANGLE);

    Static1D angle2 = new Static1D(+ANGLE);

    Static3D axisX  = new Static3D(1,0,0);

    Static3D axisY  = new Static3D(0,1,0);

    Static3D axisZ  = new Static3D(0,-1,1);

    Static3D center0= new Static3D(0,0,0);

    Static3D center1= new Static3D(0,-3*F,0);

    VertexEffect[] effect = new VertexEffect[10];

    effect[0] = new VertexEffectScale ( new Static3D(3,3,3) );

    effect[1] = new VertexEffectMove  ( new Static3D(0,-F,0) );

    effect[2] = new VertexEffectRotate( new Static1D(90), axisX, center0 );

    effect[3] = new VertexEffectScale ( new Static3D(1,-1,1) );

    effect[4] = new VertexEffectMove  ( new Static3D(3*E/2,E*(SQ3/2)-3*F,0) );

    effect[5] = new VertexEffectRotate( new Static1D(+90), axisY, center1 );

    effect[6] = new VertexEffectScale ( new Static3D(-1,1,1) );

    effect[7] = new VertexEffectRotate( new Static1D( 45), axisX, center1 );

    effect[8] = new VertexEffectRotate( angle1           , axisZ, center1 );

    effect[9] = new VertexEffectRotate( angle2           , axisZ, center1 );

    effect[0].setMeshAssociation(15,-1);  // apply to meshes 0,1,2,3

    effect[1].setMeshAssociation( 3,-1);  // apply to meshes 0,1

    effect[2].setMeshAssociation( 2,-1);  // apply to mesh 1

    effect[3].setMeshAssociation( 2,-1);  // apply to mesh 0

    effect[4].setMeshAssociation(12,-1);  // apply to meshes 2,3

    effect[5].setMeshAssociation(12,-1);  // apply to meshes 2,3

    effect[6].setMeshAssociation( 8,-1);  // apply to mesh 3

    effect[7].setMeshAssociation(12,-1);  // apply to meshes 2,3

    effect[8].setMeshAssociation( 4,-1);  // apply to mesh 2

    effect[9].setMeshAssociation( 8,-1);  // apply to mesh 3

    return effect;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  VertexEffect[] createVertexEffectsHelicopterCorner()

    {

    float E = 0.5f;

    Static3D axisX  = new Static3D(1,0,0);

    Static3D axisY  = new Static3D(0,1,0);

    Static3D axis0  = new Static3D(-SQ2/2,0,SQ2/2);

    Static3D axis1  = new Static3D(+SQ3/3,+SQ3/3,+SQ3/3);

    Static1D angle1 = new Static1D(+90);

    Static1D angle2 = new Static1D(-90);

    Static1D angle3 = new Static1D(-135);

    Static1D angle4 = new Static1D(90);

    Static1D angle5 = new Static1D(120);

    Static1D angle6 = new Static1D(240);

    Static3D center1= new Static3D(0,0,0);

    Static3D center2= new Static3D(-0.25f,-0.25f,-0.25f);

    Static3D move1  = new Static3D(-E/4,-E/4,0);

    Static3D move2  = new Static3D(-0.25f,(-1.0f/6)-0.25f,-0.25f);

    VertexEffect[] effect = new VertexEffect[10];

    effect[0] = new VertexEffectMove(move1);

    effect[1] = new VertexEffectScale(new Static3D(1,1,-1));

    effect[2] = new VertexEffectRotate(angle1,axisX,center1);

    effect[3] = new VertexEffectRotate(angle2,axisY,center1);

    effect[4] = new VertexEffectMove(move2);

    effect[5] = new VertexEffectRotate(angle1,axisX,center2);

    effect[6] = new VertexEffectRotate(angle3,axisY,center2);

    effect[7] = new VertexEffectRotate(angle4,axis0,center2);

    effect[8] = new VertexEffectRotate(angle5,axis1,center2);

    effect[9] = new VertexEffectRotate(angle6,axis1,center2);

    effect[0].setMeshAssociation( 7,-1);  // meshes 0,1,2

    effect[1].setMeshAssociation( 6,-1);  // meshes 1,2

    effect[2].setMeshAssociation( 2,-1);  // mesh 1

    effect[3].setMeshAssociation( 4,-1);  // mesh 2

    effect[4].setMeshAssociation(56,-1);  // meshes 3,4,5

    effect[5].setMeshAssociation(56,-1);  // meshes 3,4,5

    effect[6].setMeshAssociation(56,-1);  // meshes 3,4,5

    effect[7].setMeshAssociation(56,-1);  // meshes 3,4,5

    effect[8].setMeshAssociation(16,-1);  // mesh 4

    effect[9].setMeshAssociation(32,-1);  // mesh 5

    return effect;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  VertexEffect[] createVertexEffectsHelicopterFace()

    {

    float E = 0.5f;

    float F = SQ2/4;

    Static3D move0  = new Static3D(-E/4, -E/4, 0);

    Static3D move1  = new Static3D(-(SQ2/24)-E/2, -(SQ2/24)-E/2, 0);

    Static3D move2  = new Static3D(-E/2, F/3, 0);

    Static3D move3  = new Static3D(+E/2, F/3, 0);

    Static3D move4  = new Static3D(+E/3,+E/3, 0);

    Static1D angle1 = new Static1D(135);

    Static1D angle2 = new Static1D(90);

    Static1D angle3 = new Static1D(-90);

    Static1D angle4 = new Static1D(-135);

    Static3D axisX  = new Static3D(1,0,0);

    Static3D axisY  = new Static3D(0,1,0);

    Static3D axisZ  = new Static3D(0,0,1);

    Static3D axis1  = new Static3D(1,-1,0);

    Static3D center = new Static3D(0,0,0);

    Static3D center1= new Static3D(-E/2,-E/2,0);

    VertexEffect[] effect = new VertexEffect[10];

    effect[0] = new VertexEffectMove(move0);

    effect[1] = new VertexEffectRotate(angle1, axisZ, center);

    effect[2] = new VertexEffectMove(move1);

    effect[3] = new VertexEffectRotate(angle2, axis1, center1);

    effect[4] = new VertexEffectMove(move2);

    effect[5] = new VertexEffectMove(move3);

    effect[6] = new VertexEffectRotate(angle3, axisZ, center);

    effect[7] = new VertexEffectRotate(angle4, axisX, center);

    effect[8] = new VertexEffectRotate(angle1, axisY, center);

    effect[9] = new VertexEffectMove(move4);

    effect[0].setMeshAssociation( 1,-1);  // mesh 0

    effect[1].setMeshAssociation( 2,-1);  // mesh 1

    effect[2].setMeshAssociation( 2,-1);  // mesh 1

    effect[3].setMeshAssociation( 2,-1);  // mesh 1

    effect[4].setMeshAssociation( 4,-1);  // mesh 2

    effect[5].setMeshAssociation( 8,-1);  // mesh 3

    effect[6].setMeshAssociation( 8,-1);  // mesh 3

    effect[7].setMeshAssociation( 4,-1);  // mesh 2

    effect[8].setMeshAssociation( 8,-1);  // mesh 3

    effect[9].setMeshAssociation(15,-1);  // meshes 0,1,2,3

    return effect;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  VertexEffect[] createVertexEffectsRediEdge()

    {

    Static3D move0 = new Static3D(0.0f, -0.5f, 0.0f);

    Static3D move1 = new Static3D(0.25f, -0.25f, 0.0f);

    Static3D move2 = new Static3D(0.5f, 0.0f, 0.0f);

    Static3D move3 = new Static3D(0.0f, (SQ3-6)/8, (SQ3-6)/8);

    Static3D flipZ = new Static3D(1,1,-1);

    Static3D flipX = new Static3D(-1,1,1);

    Static3D scale = new Static3D(2,2,2);

    Static3D cent0 = new Static3D(0,0, 0);

    Static3D cent1 = new Static3D(0,0, -1.5f);

    Static3D axisX = new Static3D(1,0, 0);

    Static3D axisY = new Static3D(0,1, 0);

    Static3D axis  = new Static3D(0,SQ2/2,-SQ2/2);

    Static1D angle1= new Static1D(90);

    Static1D angle2= new Static1D(45);

    Static1D angle3= new Static1D( (float)(180/Math.PI*Math.acos(SQ3/3)) );

    VertexEffect[] effect = new VertexEffect[12];

    effect[0] = new VertexEffectScale(scale);

    effect[1] = new VertexEffectMove(move0);

    effect[2] = new VertexEffectScale(flipZ);

    effect[3] = new VertexEffectRotate(angle1,axisX,cent0);

    effect[4] = new VertexEffectMove(move1);

    effect[5] = new VertexEffectRotate(angle1,axisY,cent0);

    effect[6] = new VertexEffectMove(move2);

    effect[7] = new VertexEffectScale(flipX);

    effect[8] = new VertexEffectRotate(angle2,axisX,cent0);

    effect[9] = new VertexEffectMove(move3);

    effect[10]= new VertexEffectRotate(angle3,axis ,cent1);

    effect[11]= new VertexEffectScale(flipX);

    effect[0].setMeshAssociation(63,-1);  // meshes 0,1,2,3,4,5

    effect[1].setMeshAssociation( 3,-1);  // meshes 0,1

    effect[2].setMeshAssociation( 2,-1);  // mesh 1

    effect[3].setMeshAssociation( 2,-1);  // mesh 1

    effect[4].setMeshAssociation(12,-1);  // meshes 2,3

    effect[5].setMeshAssociation(60,-1);  // meshes 2,3,4,5

    effect[6].setMeshAssociation(12,-1);  // meshes 2,3

    effect[7].setMeshAssociation( 8,-1);  // mesh 3

    effect[8].setMeshAssociation(48,-1);  // meshes 4,5

    effect[9].setMeshAssociation(48,-1);  // meshes 4,5

    effect[10].setMeshAssociation(48,-1); // meshes 4,5

    effect[11].setMeshAssociation(32,-1); // mesh 5

    return effect;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  VertexEffect[] createVertexEffectsRediCorner()

    {

    Static3D axisY   = new Static3D(0,1,0);

    Static3D axisX   = new Static3D(1,0,0);

    Static3D axisZ   = new Static3D(0,0,1);

    Static3D center  = new Static3D(0,0,0);

    Static1D angle90 = new Static1D(90);

    Static1D angle270= new Static1D(270);

    Static1D angle45 = new Static1D(-45);

    VertexEffect[] effect = new VertexEffect[6];

    effect[0] = new VertexEffectMove(new Static3D(0,0,+0.5f));

    effect[1] = new VertexEffectRotate( angle270, axisX, center );

    effect[2] = new VertexEffectRotate( angle90 , axisY, center );

    effect[3] = new VertexEffectRotate( angle45 , axisX, center );

    effect[4] = new VertexEffectRotate( angle90 , axisY, center );

    effect[5] = new VertexEffectRotate( angle270, axisZ, center );

    effect[0].setMeshAssociation( 7,-1);  // 0,1,2

    effect[1].setMeshAssociation( 2,-1);  // 1

    effect[2].setMeshAssociation( 4,-1);  // 2

    effect[3].setMeshAssociation(56,-1);  // 3

    effect[4].setMeshAssociation(16,-1);  // 4

    effect[5].setMeshAssociation(32,-1);  // 5

    return effect;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// OBJECTS

///////////////////////////////////////////////////////////////////////////////////////////////////

// CUBE

  MeshBase createCubeMesh(int index)

    {

    MeshBase mesh = createFacesCube(index);

    VertexEffect[] effects = createVertexEffectsCube();

    for( VertexEffect effect : effects ) mesh.apply(effect);

    Static3D roundingCenter  = new Static3D(0,0,0);

    Static3D[] vertices = new Static3D[8];

    vertices[0] = new Static3D(+0.5f,+0.5f,+0.5f);

    vertices[1] = new Static3D(+0.5f,+0.5f,-0.5f);

    vertices[2] = new Static3D(+0.5f,-0.5f,+0.5f);

    vertices[3] = new Static3D(+0.5f,-0.5f,-0.5f);

    vertices[4] = new Static3D(-0.5f,+0.5f,+0.5f);

    vertices[5] = new Static3D(-0.5f,+0.5f,-0.5f);

    vertices[6] = new Static3D(-0.5f,-0.5f,+0.5f);

    vertices[7] = new Static3D(-0.5f,-0.5f,-0.5f);

    roundCorners(mesh,roundingCenter,vertices,0.06f,0.12f);

    return mesh;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// SKEWB

  MeshBase createSkewbCornerMesh()

    {

    MeshBase mesh = createFacesSkewbCorner();

    VertexEffect[] effects = createVertexEffectsSkewbCorner();

    for( VertexEffect effect : effects ) mesh.apply(effect);

    float E = 0.5f;

    Static3D roundingCenter = new Static3D(-E/2,-E/2,-E/2);

    Static3D[] verticesType1 = new Static3D[1];

    verticesType1[0] = new Static3D(0.0f,0.0f,0.0f);

    roundCorners(mesh,roundingCenter,verticesType1,0.08f,0.15f);

    Static3D[] verticesType2 = new Static3D[3];

    verticesType2[0] = new Static3D(-E, 0, 0);

    verticesType2[1] = new Static3D( 0,-E, 0);

    verticesType2[2] = new Static3D( 0, 0,-E);

    roundCorners(mesh,roundingCenter,verticesType2,0.08f,0.20f);

    return mesh;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  MeshBase createSkewbFaceMesh()

    {

    MeshBase mesh = createFacesSkewbFace();

    VertexEffect[] effects = createVertexEffectsSkewbFace();

    for( VertexEffect effect : effects ) mesh.apply(effect);

    Static3D roundingCenter = new Static3D(0,0,-0.2f);

    float E = SQ2/4;

    Static3D[] vertices = new Static3D[4];

    vertices[0] = new Static3D(-E*SQ2,      0, 0);

    vertices[1] = new Static3D(+E*SQ2,      0, 0);

    vertices[2] = new Static3D(     0, -E*SQ2, 0);

    vertices[3] = new Static3D(     0, +E*SQ2, 0);

    roundCorners(mesh,roundingCenter,vertices,0.10f,0.10f);

    return mesh;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// SKEWB DIAMOND / PYRAMINX

  MeshBase createOctaMesh()

    {

    MeshBase mesh = createFacesOcta();

    VertexEffect[] effects = createVertexEffectsOcta();

    for( VertexEffect effect : effects ) mesh.apply(effect);

    Static3D roundingCenter = new Static3D(0,0,0);

    Static3D[] vertices = new Static3D[6];

    vertices[0] = new Static3D(    0, SQ2/2,    0 );

    vertices[1] = new Static3D( 0.5f,     0, 0.5f );

    vertices[2] = new Static3D(-0.5f,     0, 0.5f );

    vertices[3] = new Static3D(    0,-SQ2/2,    0 );

    vertices[4] = new Static3D(-0.5f,     0,-0.5f );

    vertices[5] = new Static3D( 0.5f,     0,-0.5f );

    roundCorners(mesh,roundingCenter,vertices,0.06f,0.20f);

    return mesh;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  MeshBase createTetraMesh()

    {

    MeshBase mesh = createFacesTetra();

    VertexEffect[] effects = createVertexEffectsTetra();

    for( VertexEffect effect : effects ) mesh.apply(effect);

    Static3D roundingCenter = new Static3D(0,0,0);

    Static3D[] verticesRound = new Static3D[4];

    verticesRound[0] = new Static3D(-0.5f,+SQ2/4,   0 );

    verticesRound[1] = new Static3D(+0.5f,+SQ2/4,   0 );

    verticesRound[2] = new Static3D(    0,-SQ2/4,+0.5f);

    verticesRound[3] = new Static3D(    0,-SQ2/4,-0.5f);

    roundCorners(mesh,roundingCenter,verticesRound,0.08f,0.15f);

    return mesh;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// DINO

  MeshBase createDinoMesh()

    {

    MeshBase mesh = createFacesDino();

    VertexEffect[] effects = createVertexEffectsDino();

    for( VertexEffect effect : effects ) mesh.apply(effect);

    float F = 0.5f;

    Static3D roundingCenter = new Static3D(0.0f, -1.5f*F, -1.5f*F);

    Static3D[] verticesRound = new Static3D[4];

    verticesRound[0] = new Static3D(     0,-3*F,    0 );

    verticesRound[1] = new Static3D(     0,   0, -3*F );

    verticesRound[2] = new Static3D(  -3*F,   0,    0 );

    verticesRound[3] = new Static3D(  +3*F,   0,    0 );

    roundCorners(mesh,roundingCenter,verticesRound,0.10f,0.40f);

    return mesh;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// Helicopter

  MeshBase createHelicopterCornerMesh()

    {

    MeshBase mesh = createFacesHelicopterCorner();

    VertexEffect[] effects = createVertexEffectsHelicopterCorner();

    for( VertexEffect effect : effects ) mesh.apply(effect);

    float E = 0.5f;

    Static3D roundingCenter = new Static3D(-E/2,-E/2,-E/2);

    Static3D[] verticesType1 = new Static3D[1];

    verticesType1[0] = new Static3D(0.0f,0.0f,0.0f);

    roundCorners(mesh,roundingCenter,verticesType1,0.08f,0.15f);

    Static3D[] verticesType2 = new Static3D[3];

    verticesType2[0] = new Static3D(-E, 0, 0);

    verticesType2[1] = new Static3D( 0,-E, 0);

    verticesType2[2] = new Static3D( 0, 0,-E);

    roundCorners(mesh,roundingCenter,verticesType2,0.10f,0.20f);

    return mesh;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  MeshBase createHelicopterFaceMesh()

    {

    MeshBase mesh = createFacesHelicopterFace();

    VertexEffect[] effects = createVertexEffectsHelicopterFace();

    for( VertexEffect effect : effects ) mesh.apply(effect);

    float E = 0.5f;

    Static3D roundingCenter = new Static3D(-E/2 + E/3,-E/2 + E/3,-E/2);

    Static3D[] verticesType1 = new Static3D[1];

    verticesType1[0] = new Static3D(E/3,E/3,0.0f);

    roundCorners(mesh,roundingCenter,verticesType1,0.06f,0.15f);

    Static3D[] verticesType2 = new Static3D[2];

    verticesType2[0] = new Static3D(-E+E/3, E/3  , 0);

    verticesType2[1] = new Static3D( E/3  ,-E+E/3, 0);

    roundCorners(mesh,roundingCenter,verticesType2,0.10f,0.20f);

    return mesh;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

// Redi cube

  MeshBase createRediEdgeMesh()

    {

    MeshBase mesh = createFacesRediEdge();

    VertexEffect[] effects = createVertexEffectsRediEdge();

    for( VertexEffect effect : effects ) mesh.apply(effect);

    Static3D center = new Static3D(0.0f,-0.75f,-0.75f);

    Static3D[] vertices = new Static3D[4];

    vertices[0] = new Static3D( 0.5f, 0.0f, 0.0f);

    vertices[1] = new Static3D(-0.5f, 0.0f, 0.0f);

    vertices[2] = new Static3D(0.0f, 0.0f,-1.5f);

    vertices[3] = new Static3D(0.0f,-1.5f, 0.0f);

    roundCorners(mesh,center,vertices,0.06f,0.20f);

    return mesh;

    }

///////////////////////////////////////////////////////////////////////////////////////////////////

  MeshBase createRediCornerMesh()

    {

    MeshBase mesh = createFacesRediCorner();

    VertexEffect[] effects = createVertexEffectsRediCorner();

    for( VertexEffect effect : effects ) mesh.apply(effect);

    Static3D center = new Static3D(0,0,0);

    Static3D[] vertices = new Static3D[8];

    vertices[0] = new Static3D(+0.5f,+0.5f,+0.5f);

    vertices[1] = new Static3D(+0.5f,+0.5f,-0.5f);

    vertices[2] = new Static3D(+0.5f,-0.5f,+0.5f);

    vertices[3] = new Static3D(+0.5f,-0.5f,-0.5f);

    vertices[4] = new Static3D(-0.5f,+0.5f,+0.5f);

    vertices[5] = new Static3D(-0.5f,+0.5f,-0.5f);

    vertices[6] = new Static3D(-0.5f,-0.5f,+0.5f);

    vertices[7] = new Static3D(-0.5f,-0.5f,-0.5f);

    roundCorners(mesh,center,vertices,0.06f,0.12f);

    return mesh;

    }

  }