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.VertexEffectQuaternion;

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;

import java.util.ArrayList;

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

class FactoryCubit

  {

  static final float SQ5   = (float)Math.sqrt(5);

  static final float SIN18 = (SQ5-1)/4;

  static final float COS18 = (float)(0.25f*Math.sqrt(10.0f+2.0f*SQ5));

  private static final float[] mBuffer = new float[3];

  private static final float[] mQuat1  = new float[4];

  private static final float[] mQuat2  = new float[4];

  private static final float[] mQuat3  = new float[4];

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

  private static FactoryCubit mThis;

  private static class FaceInfo

    {

    float[] vertices;

    float vx,vy,vz;

    float scale;

    float qx,qy,qz,qw;

    boolean flip;

    }

  private static final ArrayList<FaceInfo> mFaceInfo = new ArrayList<>();

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

  private FactoryCubit()

    {

    }

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

  public static FactoryCubit getInstance()

    {

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

    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));

    }

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

  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 = (int)((N-3)*K);

      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);

        }

      }

    bands[2*N-2] = 0.0f;

    bands[2*N-1] =    H;

    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);

      }

    }

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

  private boolean areColinear(float[][] vertices, int index1, int index2, int index3)

    {

    float x1 = vertices[index1][0];

    float y1 = vertices[index1][1];

    float z1 = vertices[index1][2];

    float x2 = vertices[index2][0];

    float y2 = vertices[index2][1];

    float z2 = vertices[index2][2];

    float x3 = vertices[index3][0];

    float y3 = vertices[index3][1];

    float z3 = vertices[index3][2];

    float v1x = x2-x1;

    float v1y = y2-y1;

    float v1z = z2-z1;

    float v2x = x3-x1;

    float v2y = y3-y1;

    float v2z = z3-z1;

    float A = (float)Math.sqrt( (v1x*v1x+v1y*v1y+v1z*v1z) / (v2x*v2x+v2y*v2y+v2z*v2z) );

//android.util.Log.e("D", "("+x1+","+y1+","+z1+") , ("+x2+","+y2+","+z2+") , ("+x3+","+y3+","+z3+")" );

//boolean result = (v1x==A*v2x && v1y==A*v2y && v1z==A*v2z);

//android.util.Log.e("D", "are those colinear? : "+result);

    return (v1x==A*v2x && v1y==A*v2y && v1z==A*v2z);

    }

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

  private void computeNormalVector(float[][] vertices, int index1, int index2, int index3)

    {

    float x1 = vertices[index1][0];

    float y1 = vertices[index1][1];

    float z1 = vertices[index1][2];

    float x2 = vertices[index2][0];

    float y2 = vertices[index2][1];

    float z2 = vertices[index2][2];

    float x3 = vertices[index3][0];

    float y3 = vertices[index3][1];

    float z3 = vertices[index3][2];

    float v1x = x2-x1;

    float v1y = y2-y1;

    float v1z = z2-z1;

    float v2x = x3-x1;

    float v2y = y3-y1;

    float v2z = z3-z1;

    mBuffer[0] = v1y*v2z - v2y*v1z;

    mBuffer[1] = v1z*v2x - v2z*v1x;

    mBuffer[2] = v1x*v2y - v2x*v1y;

    }

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

// return quat1*quat2

  private static void quatMultiply( float[] quat1, float[] quat2, float[] result )

    {

    float qx = quat1[0];

    float qy = quat1[1];

    float qz = quat1[2];

    float qw = quat1[3];

    float rx = quat2[0];

    float ry = quat2[1];

    float rz = quat2[2];

    float rw = quat2[3];

    result[0] = rw*qx - rz*qy + ry*qz + rx*qw;

    result[1] = rw*qy + rz*qx + ry*qw - rx*qz;

    result[2] = rw*qz + rz*qw - ry*qx + rx*qy;

    result[3] = rw*qw - rz*qz - ry*qy - rx*qx;

    }

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

  private void fitInSquare(FaceInfo info, float[][] vert3D)

    {

    float minX = Float.MAX_VALUE;

    float maxX =-Float.MAX_VALUE;

    float minY = Float.MAX_VALUE;

    float maxY =-Float.MAX_VALUE;

    for (float[] vert : vert3D)

      {

      float x = vert[0];

      float y = vert[1];

      if (x > maxX) maxX = x;

      if (x < minX) minX = x;

      if (y > maxY) maxY = y;

      if (y < minY) minY = y;

      }

    info.scale = Math.max(maxX-minX,maxY-minY);

    int len = vert3D.length;

    info.vertices = new float[2*len];

    for( int vertex=0; vertex<len; vertex++ )

      {

      info.vertices[2*vertex  ] = vert3D[vertex][0] / info.scale;

      info.vertices[2*vertex+1] = vert3D[vertex][1] / info.scale;

      }

    info.flip = false;

    }

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

  private void constructNew(FaceInfo info, final float[][] vert3D)

    {

    // compute center of gravity

    info.vx = 0.0f;

    info.vy = 0.0f;

    info.vz = 0.0f;

    int len = vert3D.length;

    for (float[] vert : vert3D)

      {

      info.vx += vert[0];

      info.vy += vert[1];

      info.vz += vert[2];

      }

    info.vx /= len;

    info.vy /= len;

    info.vz /= len;

    // move all vertices so that their center of gravity is at (0,0,0)

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

      {

      vert3D[i][0] -= info.vx;

      vert3D[i][1] -= info.vy;

      vert3D[i][2] -= info.vz;

      }

    // find 3 non-colinear vertices

    int foundIndex = -1;

    for(int vertex=2; vertex<len; vertex++)

      {

      if( !areColinear(vert3D,0,1,vertex) )

        {

        foundIndex = vertex;

        break;

        }

      }

    // compute the normal vector

    if( foundIndex==-1 )

      {

      throw new RuntimeException("all vertices colinear");

      }

    computeNormalVector(vert3D,0,1,foundIndex);

    // rotate so that the normal vector becomes (0,0,1)

    float axisX = -mBuffer[1];

    float axisY =  mBuffer[0];

    float axisZ = 0.0f;

    float vecLen = mBuffer[0]*mBuffer[0] + mBuffer[1]*mBuffer[1] + mBuffer[2]*mBuffer[2];

    vecLen = (float)Math.sqrt(vecLen);

    mBuffer[0] /= vecLen;

    mBuffer[1] /= vecLen;

    mBuffer[2] /= vecLen;

    float axiLen = axisX*axisX + axisY*axisY + axisZ*axisZ;

    axiLen = (float)Math.sqrt(axiLen);

    axisX /= axiLen;

    axisY /= axiLen;

    axisZ /= axiLen;

    float cosTheta = mBuffer[2];

    float sinTheta = axiLen / vecLen;

    mQuat1[0] = axisX*sinTheta;

    mQuat1[1] = axisY*sinTheta;

    mQuat1[2] = axisZ*sinTheta;

    mQuat1[3] = cosTheta;

    mQuat2[0] = axisX*sinTheta;

    mQuat2[1] = axisY*sinTheta;

    mQuat2[2] = axisZ*sinTheta;

    mQuat2[3] = -cosTheta;

    for (float[] vert : vert3D)

      {

      quatMultiply(mQuat1, vert, mQuat3);

      quatMultiply(mQuat3, mQuat2, vert);

      }

    // fit the whole thing in a square and remember the scale & 2D vertices

    fitInSquare(info, vert3D);

    // remember the rotation

    info.qx = mQuat1[0];

    info.qy = mQuat1[1];

    info.qz = mQuat1[2];

    info.qw =-mQuat1[3];

    }

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

  private float computeCos(float x1, float y1, float x2, float y2, float len1, float len2)

    {

    return (x1*x2+y1*y2) / (len1*len2);

    }

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

// sin of (signed!) angle between vectors (x1,y1) and (x2,y2), counterclockwise!

  private float computeSin(float x1, float y1, float x2, float y2, float len1, float len2)

    {

    return (x2*y1-x1*y2) / (len1*len2);

    }

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

  private void rotateAllVertices(float[] result, int len, float[] vertices, float sin, float cos)

    {

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

      {

      result[2*i  ] = vertices[2*i  ]*cos - vertices[2*i+1]*sin;

      result[2*i+1] = vertices[2*i  ]*sin + vertices[2*i+1]*cos;

      }

    }

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

  private boolean isScaledVersionOf(float[] v1, float[] v2, int len)

    {

    float EPSILON = 0.001f;

    float scale = v1[0]!=0.0f ? v2[0]/v1[0] : v2[1]/v1[1];

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

      {

      float horz = v2[2*i  ] - scale*v1[2*i  ];

      float vert = v2[2*i+1] - scale*v1[2*i+1];

      if( horz>EPSILON || horz<-EPSILON || vert>EPSILON || vert<-EPSILON ) return false;

      }

    return true;

    }

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

  private void mirrorAllVertices(float[] output, int len, float[] input)

    {

    for(int vertex=0; vertex<len; vertex++)

      {

      output[2*vertex  ] = input[2*vertex  ];

      output[2*vertex+1] =-input[2*vertex+1];

      }

    }

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

  private void correctInfo(FaceInfo info, float[] rotatedVertices, int len, float[] originalVertices, float sin, float cos, boolean flip)

    {

    info.flip = flip;

    System.arraycopy(originalVertices, 0, info.vertices, 0, 2*len);

    float scale = rotatedVertices[0]!=0.0f ? originalVertices[0]/rotatedVertices[0] :

                                             originalVertices[1]/rotatedVertices[1];

    info.scale *= scale;

    mQuat1[0] = 0.0f;

    mQuat1[1] = 0.0f;

    mQuat1[2] = sin;

    mQuat1[3] = cos;

    mQuat2[0] = info.qx;

    mQuat2[1] = info.qy;

    mQuat2[2] = info.qz;

    mQuat2[3] = info.qw;

    quatMultiply( mQuat1, mQuat2, mQuat3 );

    info.qx = mQuat3[0];

    info.qy = mQuat3[1];

    info.qz = mQuat3[2];

    info.qw = mQuat3[3];

    }

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

  private boolean foundVertex(FaceInfo info, float[] buffer, int len, boolean inverted, float[] vertices, float[] vert2D, float lenVert)

    {

    for(int vertex=0; vertex<len; vertex++)

      {

      float xR = vertices[2*vertex  ];

      float yR = vertices[2*vertex+1];

      float lenRotV = (float)Math.sqrt(xR*xR+yR*yR);

      float cos = computeCos(xR,yR,vert2D[0],vert2D[1], lenRotV, lenVert);

      float sin = computeSin(xR,yR,vert2D[0],vert2D[1], lenRotV, lenVert);

      rotateAllVertices(buffer,len,vertices,sin,cos);

      if( isScaledVersionOf(buffer,vert2D,len) )

        {

        correctInfo(info,buffer,len,vert2D,sin,cos,inverted);

        return true;

        }

      }

    return false;

    }

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

  private boolean tryFindingRotation(final FaceInfo info, final float[] vert2D)

    {

    int len = vert2D.length/2;

    if( len == info.vertices.length/2 )

      {

      float[] tmp1 = new float[2*len];

      float lenVert = (float)Math.sqrt(vert2D[0]*vert2D[0] + vert2D[1]*vert2D[1]);

      if( foundVertex(info,tmp1,len,false,info.vertices,vert2D,lenVert) ) return true;

      float[] tmp2 = new float[2*len];

      mirrorAllVertices(tmp2,len,info.vertices);

      if( foundVertex(info,tmp1,len,true ,tmp2         ,vert2D,lenVert) ) return true;

      }

    return false;

    }

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

  private float[][] constructVert(float[][] vertices, int[] index)

    {

    int len = index.length;

    float[][] ret = new float[len][4];

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

      {

      ret[i][0] = vertices[index[i]][0];

      ret[i][1] = vertices[index[i]][1];

      ret[i][2] = vertices[index[i]][2];

      ret[i][3] = 1.0f;

      }

    return ret;

    }

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

  private void prepareFaceInfo( final float[][] vertices, final int[][] indexes)

    {

    mFaceInfo.clear();

    int numFaces = indexes.length;

    FaceInfo info;

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

      {

      FaceInfo newInfo = new FaceInfo();

      int[] index = indexes[face];

      float[][] vert = constructVert(vertices,index);

      constructNew(newInfo,vert);

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

        {

        info = mFaceInfo.get(previous);

        if( tryFindingRotation(info,newInfo.vertices) ) break;

        }

      mFaceInfo.add(newInfo);

      }

    }

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

  MeshBase createRoundedSolid(final float[][] vertices, final int[][] vertIndexes, final float[][] bands, final int[] bandIndexes)

    {

    int EFFECTS_PER_FACE = 3;

    prepareFaceInfo(vertices,vertIndexes);

    int numFaces = vertIndexes.length;

    float[] band, bandsComputed;

    MeshBase[] meshes = new MeshBase[numFaces];

    FaceInfo info;

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

      {

      info = mFaceInfo.get(face);

      band = bands[bandIndexes[face]];

      bandsComputed = computeBands( band[0], (int)band[1], band[2], band[3], (int)band[4]);

      meshes[face] = new MeshPolygon(info.vertices,bandsComputed,(int)band[5],(int)band[6]);

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

      }

    MeshBase mesh = new MeshJoined(meshes);

    VertexEffect[] effects = new VertexEffect[EFFECTS_PER_FACE*numFaces];

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

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

      {

      int assoc = (1<<face);

      info = mFaceInfo.get(face);

      Static3D move3D= new Static3D(info.vx,info.vy,info.vz);

      Static3D scale = new Static3D(info.scale,info.scale, info.flip ? -info.scale : info.scale);

      Static4D quat  = new Static4D(info.qx,info.qy,info.qz,info.qw);

      effects[EFFECTS_PER_FACE*face  ] = new VertexEffectScale(scale);

      effects[EFFECTS_PER_FACE*face+1] = new VertexEffectQuaternion(quat,center);

      effects[EFFECTS_PER_FACE*face+2] = new VertexEffectMove(move3D);

      effects[EFFECTS_PER_FACE*face  ].setMeshAssociation(assoc,-1);

      effects[EFFECTS_PER_FACE*face+1].setMeshAssociation(assoc,-1);

      effects[EFFECTS_PER_FACE*face+2].setMeshAssociation(assoc,-1);

      }

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

    return mesh;

    }

  }