Distorted Android

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

// Copyright 2018 Leszek Koltunski                                                               //

//                                                                                               //

// This file is part of Distorted.                                                               //

//                                                                                               //

// Distorted 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.                                                           //

//                                                                                               //

// Distorted 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 Distorted.  If not, see <http://www.gnu.org/licenses/>.                            //

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

package org.distorted.library.mesh;

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

/**

 * Create a Mesh which approximates a sphere.

 * <p>

 * Do so by dividing each of the 20 faces of the regular icosahedron into smaller triangles and inflating

 * those to lay on the surface of the sphere.

 */

public class MeshSphere extends MeshBase

  {

  private static final int NUMFACES = 20;

  private static final double sqrt2 = Math.sqrt(2.0);

  private static final double P = Math.PI;

  private static final double A = 0.463647609; // arctan(0.5), +-latitude of the 10 'middle' vertices

                                               // https://en.wikipedia.org/wiki/Regular_icosahedron

  // An array of 20 entries, each describing a single face of the regular icosahedron in an (admittedly)

  // weird fashion.

  // Each face of a regular icosahedron is a equilateral triangle, with 2 vertices on the same latitude.

  // Single row is (longitude of V1, longitude of V2, (common) latitude of V1 and V2, latitude of V3)

  // longitude of V3 is simply midpoint of V1 and V2 so we don't have to specify it here.

  private static final double FACES[][] =      {

                                                   { 0.0*P, 0.4*P,  A, 0.5*P },

                                                   { 0.4*P, 0.8*P,  A, 0.5*P },

                                                   { 0.8*P, 1.2*P,  A, 0.5*P },  // 5 'top' faces with

                                                   { 1.2*P, 1.6*P,  A, 0.5*P },  // the North Pole

                                                   { 1.6*P, 2.0*P,  A, 0.5*P },

                                                   { 0.0*P, 0.4*P,  A,    -A },

                                                   { 0.4*P, 0.8*P,  A,    -A },

                                                   { 0.8*P, 1.2*P,  A,    -A },  // 5 faces mostly above

                                                   { 1.2*P, 1.6*P,  A,    -A },  // the equator

                                                   { 1.6*P, 2.0*P,  A,    -A },

                                                   { 0.2*P, 0.6*P, -A,     A },

                                                   { 0.6*P, 1.0*P, -A,     A },

                                                   { 1.0*P, 1.4*P, -A,     A },  // 5 faces mostly below

                                                   { 1.4*P, 1.8*P, -A,     A },  // the equator

                                                   { 1.8*P, 0.2*P, -A,     A },

                                                   { 0.2*P, 0.6*P, -A,-0.5*P },

                                                   { 0.6*P, 1.0*P, -A,-0.5*P },

                                                   { 1.0*P, 1.4*P, -A,-0.5*P },  // 5 'bottom' faces with

                                                   { 1.4*P, 1.8*P, -A,-0.5*P },  // the South Pole

                                                   { 1.8*P, 0.2*P, -A,-0.5*P },

                                               };

  private int currentVert;

  private int numVertices;

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

// Each of the 20 faces of the icosahedron requires (level*level + 4*level) vertices for the face

// itself and a join to the next face (which requires 2 vertices). We don't need the join in case

// of the last, 20th face, thus the -2.

// (level*level +4*level) because there are level*level little triangles, each requiring new vertex,

// plus 2 extra vertices to start off a row and 2 to move to the next row (or the next face in case

// of the last row) and there are 'level' rows.

//

// Now to this we need to add 6*(level-1) vertices for the internal seams in the three triangles

// in the back ( 2,7,16 in the list above ): 3 triangles, level-1 rows of more than 1 triangle in

// each, 2 extra seam vertices in each row.

  private void computeNumberOfVertices(int level)

    {

    numVertices = NUMFACES*level*(level+4) -2  + 6*(level-1);

    currentVert = 0;

    }

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

  private int convertAng(double radian)

    {

    return (int)(radian*180.0/P);

    }

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

  private void repeatVertex(float[] attribs, int diff)

    {

    //android.util.Log.e("sphere", "repeat last!");

    if( currentVert>0 )

      {

      attribs[VERT_ATTRIBS*currentVert + POS_ATTRIB  ] = attribs[VERT_ATTRIBS*(currentVert-diff) + POS_ATTRIB  ];

      attribs[VERT_ATTRIBS*currentVert + POS_ATTRIB+1] = attribs[VERT_ATTRIBS*(currentVert-diff) + POS_ATTRIB+1];

      attribs[VERT_ATTRIBS*currentVert + POS_ATTRIB+2] = attribs[VERT_ATTRIBS*(currentVert-diff) + POS_ATTRIB+2];

      attribs[VERT_ATTRIBS*currentVert + NOR_ATTRIB  ] = attribs[VERT_ATTRIBS*(currentVert-diff) + NOR_ATTRIB  ];

      attribs[VERT_ATTRIBS*currentVert + NOR_ATTRIB+1] = attribs[VERT_ATTRIBS*(currentVert-diff) + NOR_ATTRIB+1];

      attribs[VERT_ATTRIBS*currentVert + NOR_ATTRIB+2] = attribs[VERT_ATTRIBS*(currentVert-diff) + NOR_ATTRIB+2];

      attribs[VERT_ATTRIBS*currentVert + INF_ATTRIB  ] = attribs[VERT_ATTRIBS*(currentVert-diff) + INF_ATTRIB  ];

      attribs[VERT_ATTRIBS*currentVert + INF_ATTRIB+1] = attribs[VERT_ATTRIBS*(currentVert-diff) + INF_ATTRIB+1];

      attribs[VERT_ATTRIBS*currentVert + INF_ATTRIB+2] = attribs[VERT_ATTRIBS*(currentVert-diff) + INF_ATTRIB+2];

      attribs[VERT_ATTRIBS*currentVert + TEX_ATTRIB  ] = attribs[VERT_ATTRIBS*(currentVert-diff) + TEX_ATTRIB  ];

      attribs[VERT_ATTRIBS*currentVert + TEX_ATTRIB+1] = attribs[VERT_ATTRIBS*(currentVert-diff) + TEX_ATTRIB+1];

      currentVert++;

      }

    }

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

// Supposed to return the latitude of the point between two points on the sphere with latitudes

// lat1 and lat2, so if for example quot=0.2, then it will return the latitude of something 20%

// along the way from lat1 to lat2.

//

// This is approximation only - in general it is of course not true that the midpoint of two points

// on a unit sphere with spherical coords (A1,B1) and (A2,B2) is ( (A1+A2)/2, (B1+B2)/2 ) - take

// (0,0) and (PI, epsilon) as a counterexample.

//

// Here however, the latitudes we are interested at are the latitudes of the vertices of a regular

// icosahedron - i.e. +=A and +=PI/2, whose longitudes are close, and we don't really care if the

// split into smaller triangles is exact.

//

// quot better be between 0.0 and 1.0.

// this is 'directed' i.e. from lat1 to lat2.

  private double midLatitude(double lat1, double lat2, double quot)

    {

    return lat1*(1.0-quot)+lat2*quot;

    }

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

// Same in case of longitude. This is for our needs exact, because we are ever only calling this with

// two longitudes of two vertices with the same latitude. Additional problem: things can wrap around

// the circle.

// this is 'undirected' i.e. we don't assume from lon1 to lon2 - just along the smaller arc joining

// lon1 to lon2.

  private double midLongitude(double lon1, double lon2, double quot)

    {

    double min, max;

    if( lon1<lon2 ) { min=lon1; max=lon2; }

    else            { min=lon2; max=lon1; }

    double diff = max-min;

    if( diff>P ) { diff=2*P-diff; min=max; }

    double ret = min+quot*diff;

    if( ret>=2*P ) ret-=2*P;

    return ret;

    }

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

// linear map (column,row, level):

//

// (      0,       0, level) -> (lonV1,latV12)

// (      0, level-1, level) -> (lonV3,latV3 )

// (level-1,       0, level) -> (lonV2,latV12)

  private void addVertex(float[] attribs, int column, int row, int level,

                         double lonV1, double lonV2, double latV12, double latV3, boolean lastInRow)

    {

    double quotX = (double)column/level;

    double quotY = (double)row   /level;

    double quotZ;

    if( latV12*latV3 < 0.0 )  // equatorial triangle

      {

      quotZ = quotX + 0.5*quotY;

      }

    else                      // polar triangle

      {

      quotZ = (quotY==1.0 ? 0.0 : quotX / (1.0-quotY));

      }

    double longitude = midLongitude(lonV1, lonV2, quotZ );

    double latitude  = midLatitude(latV12, latV3, quotY );

    //android.util.Log.e("sphere", "newVertex: long:"+lonPoint+" lat:"+latPoint+" column="+column+" row="+row);

    double sinLON = Math.sin(longitude);

    double cosLON = Math.cos(longitude);

    double sinLAT = Math.sin(latitude);

    double cosLAT = Math.cos(latitude);

    float x = (float)(cosLAT*sinLON / sqrt2);

    float y = (float)(sinLAT        / sqrt2);

    float z = (float)(cosLAT*cosLON / sqrt2);

    double texX = 0.5 + longitude/(2*P);

    if( texX>=1.0 ) texX-=1.0;

    //android.util.Log.e("tex", "longitude = "+((int)(180.0*longitude/P))+" texX="+texX );

    double texY = 0.5 + latitude/P;

    attribs[VERT_ATTRIBS*currentVert + POS_ATTRIB  ] = x;  //

    attribs[VERT_ATTRIBS*currentVert + POS_ATTRIB+1] = y;  //

    attribs[VERT_ATTRIBS*currentVert + POS_ATTRIB+2] = z;  //

                                                           //  In case of this Mesh so it happens that

    attribs[VERT_ATTRIBS*currentVert + NOR_ATTRIB  ] = x;  //  the vertex coords, normal vector, and

    attribs[VERT_ATTRIBS*currentVert + NOR_ATTRIB+1] = y;  //  inflate vector have identical (x,y,z).

    attribs[VERT_ATTRIBS*currentVert + NOR_ATTRIB+2] = z;  //

                                                           //  TODO: think about some more efficient

    attribs[VERT_ATTRIBS*currentVert + INF_ATTRIB  ] = x;  //  representation.

    attribs[VERT_ATTRIBS*currentVert + INF_ATTRIB+1] = y;  //

    attribs[VERT_ATTRIBS*currentVert + INF_ATTRIB+2] = z;  //

    attribs[VERT_ATTRIBS*currentVert + TEX_ATTRIB  ] = (float)texX;

    attribs[VERT_ATTRIBS*currentVert + TEX_ATTRIB+1] = (float)texY;

    currentVert++;

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

    // Problem: on the 'change of date' line in the back of the sphere, some triangles see texX

    // coords suddenly jump from 1-epsilon to 0+epsilon, which looks like a seam with a narrow copy

    // of the whole texture there.

    // Solution: each such 'jump' triangle, if it is the last in a row, should have the texX of its

    // last (and maybe forelast as well) vertex remapped to 1.0.

    // If such triangle is not the last in its row, we need to add two extra vertices between it and

    // the next one, remap the old ones' texX to 1.0, and set the two new ones' texX to 0.0.

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

    if( currentVert>=3 )

      {

      double tex1 = attribs[VERT_ATTRIBS*(currentVert-2) + TEX_ATTRIB];

      double tex2 = attribs[VERT_ATTRIBS*(currentVert-3) + TEX_ATTRIB];

      double y1   = attribs[VERT_ATTRIBS*(currentVert-2) + INF_ATTRIB + 1];

      double y2   = attribs[VERT_ATTRIBS*(currentVert-3) + INF_ATTRIB + 1];

      if( tex1!=tex2 || y1!=y2 )  // if the triangle is not degenerate

        {

        double diff1 = Math.abs(texX-tex1);

        double diff2 = Math.abs(texX-tex2);

        if( diff1>0.5 || diff2>0.5 )    // a jump in texture coords which can only happen along the

          {                             // 'date change' line. Have to correct!

          if( lastInRow )

            {

                            attribs[VERT_ATTRIBS*(currentVert-1) + TEX_ATTRIB] = 1.0f;

            if( tex1<tex2 ) attribs[VERT_ATTRIBS*(currentVert-2) + TEX_ATTRIB] = 1.0f;

            }

          else

            {

            if( latitude> -A )  // top two triangles being corrected

              {

              if (2*column+row-1 == level)  // last such triangle in a row; have to introduce extra 2 vertices.

                {

                /*

                android.util.Log.e("sphere", "LAST max diff exceeded: " + convertAng(longitude) + " " + convertAng(latitude) + " texX=" + texX);

                android.util.Log.d("sphere", " tex1=" + tex1 + " tex2=" + tex2 + " y1=" + y1 + " y2=" + y2);

                android.util.Log.d("sphere", " latV12=" + latV12 + " latV3=" + latV3);

                */

                repeatVertex(attribs, 2);

                repeatVertex(attribs, 2);

                attribs[VERT_ATTRIBS*(currentVert-1) + TEX_ATTRIB] = 0.0f;

                attribs[VERT_ATTRIBS*(currentVert-2) + TEX_ATTRIB] = 0.0f;

                attribs[VERT_ATTRIBS*(currentVert-3) + TEX_ATTRIB] = 1.0f;

                if (tex1 < tex2) attribs[VERT_ATTRIBS*(currentVert-4) + TEX_ATTRIB] = 1.0f;

                }

              if (2*column+row == level)    // not the last; just remap current vertex' texX to 1.0.

                {

                /*

                android.util.Log.e("sphere", "NOT LAST max diff exceeded: " + convertAng(longitude) + " " + convertAng(latitude) + " texX=" + texX);

                android.util.Log.d("sphere", " tex1=" + tex1 + " tex2=" + tex2 + " y1=" + y1 + " y2=" + y2);

                android.util.Log.d("sphere", " latV12=" + latV12 + " latV3=" + latV3);

                */

                attribs[VERT_ATTRIBS*(currentVert-1) + TEX_ATTRIB] = 1.0f;

                }

              }

            else // bottom triangle

              {

              /*

              android.util.Log.e("sphere", "BOTTOM LAST max diff exceeded: " + convertAng(longitude) + " " + convertAng(latitude) + " texX=" + texX);

              android.util.Log.d("sphere", " tex1=" + tex1 + " tex2=" + tex2 + " y1=" + y1 + " y2=" + y2);

              android.util.Log.d("sphere", " latV12=" + latV12 + " latV3=" + latV3);

              */

              repeatVertex(attribs, 2);

              repeatVertex(attribs, 2);

              attribs[VERT_ATTRIBS*(currentVert-3) + TEX_ATTRIB] = 1.0f;

              }

            }

          }

        }

      }

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

    // End problem

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

    }

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

  private void buildFace(float[] attribs, int level, int face, double lonV1, double lonV2, double latV12, double latV3)

    {

    for(int row=0; row<level; row++)

      {

      for (int column=0; column<level-row; column++)

        {

        addVertex(attribs, column, row  , level, lonV1, lonV2, latV12, latV3, false);

        if (column==0 && !(face==0 && row==0 ) ) repeatVertex(attribs,1);

        addVertex(attribs, column, row+1, level, lonV1, lonV2, latV12, latV3, false);

        }

      addVertex(attribs, level-row, row , level, lonV1, lonV2, latV12, latV3, true);

      if( row!=level-1 || face!=NUMFACES-1 ) repeatVertex(attribs,1);

      }

    }

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

// PUBLIC API

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

  /**

   * Creates the underlying grid of vertices with the usual attribs which approximates a sphere.

   * <p>

   * When level=1, it outputs the 12 vertices of a regular icosahedron.

   * When level=N, it divides each of the 20 icosaherdon's triangular faces into N^2 smaller triangles

   * (by dividing each side into N equal segments) and 'inflates' the internal vertices so that they

   * touch the sphere.

   *

   * @param level Specifies the approximation level. Valid values: level ≥ 1

   */

  public MeshSphere(int level)

    {

    super(1.0f);

    computeNumberOfVertices(level);

    float[] attribs= new float[VERT_ATTRIBS*numVertices];

    for(int face=0; face<NUMFACES; face++ )

      {

      buildFace(attribs, level, face, FACES[face][0], FACES[face][1], FACES[face][2], FACES[face][3]);

      }

    if( currentVert!=numVertices )

      android.util.Log.d("MeshSphere", "currentVert= " +currentVert+" numVertices="+numVertices );

    setAttribs(attribs);

    }

  }