TwistyPuzzleLib

import org.distorted.objectlib.main.Movement;

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

// 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.objectlib.main;

import org.distorted.library.type.Static2D;

import org.distorted.library.type.Static3D;

import org.distorted.library.type.Static4D;

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

public abstract class Movement

  {

  // it doesn't matter where we touch a face - the list of enabled rotAxis will always be the same

  public static final int TYPE_NOT_SPLIT    = 0;

  // each face is split into several parts by lines coming from its center to the midpoints of each edge

  public static final int TYPE_SPLIT_EDGE   = 1;

  // each face is split into several parts by lines coming from its center to the vertices

  public static final int TYPE_SPLIT_CORNER = 2;

  public static final int MOVEMENT_HEXAHEDRON   = 6;

  public static final int MOVEMENT_TETRAHEDRON  = 4;

  public static final int MOVEMENT_OCTAHEDRON   = 8;

  public static final int MOVEMENT_DODECAHEDRON =12;

  public static final int MOVEMENT_SHAPECHANGE  = 0;

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

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

  private final int mNumFaceAxis;

  private final float[] mPoint, mCamera, mTouch;

  private final float[] mPoint2D, mMove2D;

  private final int[] mEnabledRotAxis;

  private final float[] mDistanceCenterFace3D;

  private final Static3D[] mFaceAxis;

  private int mLastTouchedFace;

  private float[][][] mCastedRotAxis;

  private Static4D[][] mCastedRotAxis4D;

  private float[][] mTouchBorders, mA, mB;

  private final int mType;

  private final int[][][] mEnabled;

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

  abstract int returnPart(int type, int face, float[] touchPoint);

  abstract boolean isInsideFace(int face, float[] point);

  public abstract float returnRotationFactor(int[] numLayers, int row);

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

  Movement(Static3D[] rotAxis, Static3D[] faceAxis, float[][] cuts, boolean[][] rotatable,

           float[] distance3D, float size, int type, int[][][] enabled)

    {

    mPoint = new float[3];

    mCamera= new float[3];

    mTouch = new float[3];

    mPoint2D = new float[2];

    mMove2D  = new float[2];

    mType = type;

    mEnabled = enabled;

    mFaceAxis   = faceAxis;

    mNumFaceAxis= mFaceAxis.length;

    mEnabledRotAxis = new int[rotAxis.length+1];

    mDistanceCenterFace3D = distance3D; // distance from the center of the object to each of its faces

    computeCastedAxis(rotAxis);

    computeBorders(cuts,rotatable,size);

    computeLinear(rotAxis,faceAxis);

    }

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

// mCastedRotAxis[1][2]{0,1} are the 2D coords of the 2nd rotAxis cast onto the face defined by the

// 1st faceAxis.

  private void computeCastedAxis(Static3D[] rotAxis)

    {

    mCastedRotAxis   = new float[mNumFaceAxis][rotAxis.length][2];

    mCastedRotAxis4D = new Static4D[mNumFaceAxis][rotAxis.length];

    float fx,fy,fz,f;

    for( int casted=0; casted<rotAxis.length; casted++)

      {

      Static3D a = rotAxis[casted];

      mPoint[0]= a.get0();

      mPoint[1]= a.get1();

      mPoint[2]= a.get2();

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

        {

        convertTo2Dcoords( mPoint, face, mCastedRotAxis[face][casted]);

        normalize2D(mCastedRotAxis[face][casted]);

        fx = mFaceAxis[face].get0();

        fy = mFaceAxis[face].get1();

        fz = mFaceAxis[face].get2();

        f  = mPoint[0]*fx + mPoint[1]*fy + mPoint[2]*fz;

        mCastedRotAxis4D[face][casted] = new Static4D( mPoint[0]-f*fx, mPoint[1]-f*fy, mPoint[2]-f*fz, 0);

        }

      }

    }

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

  private void normalize2D(float[] vect)

    {

    float len = (float)Math.sqrt(vect[0]*vect[0] + vect[1]*vect[1]);

    vect[0] /= len;

    vect[1] /= len;

    }

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

// find the casted axis with which our move2D vector forms an angle closest to 90 deg.

  private int computeRotationIndex(int faceAxis, float[] move2D, int[] enabled)

    {

    float cosAngle, minCosAngle = Float.MAX_VALUE;

    int minIndex=0, index;

    float m0 = move2D[0];

    float m1 = move2D[1];

    float len = (float)Math.sqrt(m0*m0 + m1*m1);

    if( len!=0.0f )

      {

      m0 /= len;

      m1 /= len;

      }

    else

      {

      m0 = 1.0f;  // arbitrarily

      m1 = 0.0f;  //

      }

    int numAxis = enabled[0];

    for(int axis=1; axis<=numAxis; axis++)

      {

      index = enabled[axis];

      cosAngle = m0*mCastedRotAxis[faceAxis][index][0] + m1*mCastedRotAxis[faceAxis][index][1];

      if( cosAngle<0 ) cosAngle = -cosAngle;

      if( cosAngle<minCosAngle )

        {

        minCosAngle=cosAngle;

        minIndex = index;

        }

      }

    return minIndex;

    }

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

// in the center of the face offset is always 0 regardless of the axis

  private float computeOffset(float[] point, float[] axis)

    {

    return point[0]*axis[0] + point[1]*axis[1];

    }

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

  private boolean faceIsVisible(int index)

    {

    Static3D faceAxis = mFaceAxis[index];

    float castCameraOnAxis = mCamera[0]*faceAxis.get0() + mCamera[1]*faceAxis.get1() + mCamera[2]*faceAxis.get2();

    return castCameraOnAxis > mDistanceCenterFace3D[index];

    }

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

// given precomputed mCamera and mPoint, respectively camera and touch point positions in ScreenSpace,

// compute point 'output[]' which:

// 1) lies on a face of the Object, i.e. surface defined by (axis, distance from (0,0,0))

// 2) is co-linear with mCamera and mPoint

//

// output = camera + alpha*(point-camera), where alpha = [dist-axis*camera] / [axis*(point-camera)]

  private void castTouchPointOntoFace(int index, float[] output)

    {

    Static3D faceAxis = mFaceAxis[index];

    float d0 = mPoint[0]-mCamera[0];

    float d1 = mPoint[1]-mCamera[1];

    float d2 = mPoint[2]-mCamera[2];

    float a0 = faceAxis.get0();

    float a1 = faceAxis.get1();

    float a2 = faceAxis.get2();

    float denom = a0*d0 + a1*d1 + a2*d2;

    if( denom != 0.0f )

      {

      float axisCam = a0*mCamera[0] + a1*mCamera[1] + a2*mCamera[2];

      float alpha = (mDistanceCenterFace3D[index]-axisCam)/denom;

      output[0] = mCamera[0] + d0*alpha;

      output[1] = mCamera[1] + d1*alpha;

      output[2] = mCamera[2] + d2*alpha;

      }

    }

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

// Convert the 3D point3D into a 2D point on the same face surface, but in a different

// coordinate system: a in-plane 2D coord where the origin is in the point where the axis intersects

// the surface, and whose Y axis points 'north' i.e. is in the plane given by the 3D origin, the

// original 3D Y axis and our 2D in-plane origin.

// If those 3 points constitute a degenerate triangle which does not define a plane - which can only

// happen if axis is vertical (or in theory when 2D origin and 3D origin meet, but that would have to

// mean that the distance between the center of the Object and its faces is 0) - then we arbitrarily

// decide that 2D Y = (0,0,-1) in the North Pole and (0,0,1) in the South Pole)

  private void convertTo2Dcoords(float[] point3D, int index , float[] output)

    {

    Static3D faceAxis = mFaceAxis[index];

    float y0,y1,y2; // base Y vector of the 2D coord system

    float a0 = faceAxis.get0();

    float a1 = faceAxis.get1();

    float a2 = faceAxis.get2();

    if( a0==0.0f && a2==0.0f )

      {

      y0=0; y1=0; y2=-a1;

      }

    else if( a1==0.0f )

      {

      y0=0; y1=1; y2=0;

      }

    else

      {

      float norm = (float)(-a1/Math.sqrt(1-a1*a1));

      y0 = norm*a0; y1= norm*(a1-1/a1); y2=norm*a2;

      }

    float x0 = y1*a2 - y2*a1;  //

    float x1 = y2*a0 - y0*a2;  // (2D coord baseY) x (axis) = 2D coord baseX

    float x2 = y0*a1 - y1*a0;  //

    float originAlpha = point3D[0]*a0 + point3D[1]*a1 + point3D[2]*a2;

    float origin0 = originAlpha*a0; // coords of the point where axis

    float origin1 = originAlpha*a1; // intersects surface plane i.e.

    float origin2 = originAlpha*a2; // the origin of our 2D coord system

    float v0 = point3D[0] - origin0;

    float v1 = point3D[1] - origin1;

    float v2 = point3D[2] - origin2;

    output[0] = v0*x0 + v1*x1 + v2*x2;

    output[1] = v0*y0 + v1*y1 + v2*y2;

    }

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

  private float[] computeBorder(float[] cuts, boolean[] rotatable, float size)

    {

    if( cuts==null ) return null;

    int len = cuts.length;

    float[] border = new float[len];

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

      {

      if( !rotatable[i] )

        {

        border[i] = i>0 ? border[i-1] : -Float.MAX_VALUE;

        }

      else

        {

        if( rotatable[i+1] ) border[i] = cuts[i]/size;

        else

          {

          int found = -1;

          for(int j=i+2; j<=len; j++)

            {

            if( rotatable[j] )

              {

              found=j;

              break;

              }

            }

          border[i] = found>0 ? (cuts[i]+cuts[found-1])/(2*size) : Float.MAX_VALUE;

          }

        }

      }

    return border;

    }

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

// size, not numLayers (see Master Skewb where size!=numLayers) - also cuboids.

  void computeBorders(float[][] cuts, boolean[][] rotatable, float size)

    {

    int numCuts = cuts.length;

    mTouchBorders = new float[numCuts][];

    for(int axis=0; axis<numCuts; axis++)

      {

      mTouchBorders[axis] = computeBorder(cuts[axis],rotatable[axis],size);

      }

    }

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

  private int computeSign(Static3D a, Static3D b)

    {

    float a1 = a.get0();

    float a2 = a.get1();

    float a3 = a.get2();

    float b1 = b.get0();

    float b2 = b.get1();

    float b3 = b.get2();

    return a1*b1+a2*b2+a3*b3 < 0 ? 1:-1;

    }

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

  private float crossProductLen(Static3D a, Static3D b)

    {

    float a1 = a.get0();

    float a2 = a.get1();

    float a3 = a.get2();

    float b1 = b.get0();

    float b2 = b.get1();

    float b3 = b.get2();

    float x1 = a2*b3-a3*b2;

    float x2 = a3*b1-a1*b3;

    float x3 = a1*b2-a2*b1;

    return (float)Math.sqrt(x1*x1 + x2*x2 + x3*x3);

    }

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

// compute the array of 'A' and 'B' coeffs of the Ax+B linear function by which we need to multiply

// the 3D 'cuts' to translate it from 3D (i.e. with respect to the rotAxis) to 2D in-face (i.e. with

// respect to the 2D rotAxis cast into a particular face)

  private void computeLinear(Static3D[] rotAxis, Static3D[] faceAxis)

    {

    int numFaces = faceAxis.length;

    int numRot   = rotAxis.length;

    mA = new float[numFaces][numRot];

    mB = new float[numFaces][numRot];

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

      for(int j=0; j<numRot; j++)

        {

        mA[i][j] = crossProductLen(faceAxis[i],rotAxis[j]);

        if( mA[i][j]!=0.0f )

          {

          float coeff = (float)Math.sqrt(1/(mA[i][j]*mA[i][j]) -1);

          int sign = computeSign(faceAxis[i],rotAxis[j]);

          mB[i][j] = sign*coeff*mDistanceCenterFace3D[i];

          }

        else mB[i][j] = 0.0f;

        }

    }

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

  private int computeRowFromOffset(int face, int axisIndex, float offset)

    {

    float[] borders = mTouchBorders[axisIndex];

    if( borders==null ) return 0;

    int len = borders.length;

    float A = mA[face][axisIndex];

    if( A!=0.0f )

      {

      float B = mB[face][axisIndex];

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

        {

        float translated = B + borders[i]/A;

        if( offset<translated ) return i;

        }

      }

    return len;

    }

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

  void computeEnabledAxis(int face, float[] touchPoint, int[] enabled)

    {

    int part = returnPart(mType,face,touchPoint);

    int num = mEnabled[face][0].length;

    enabled[0] = num;

    System.arraycopy(mEnabled[face][part], 0, enabled, 1, num);

    }

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

// PUBLIC API

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

  public boolean faceTouched(Static4D rotatedTouchPoint, Static4D rotatedCamera, float objectRatio)

    {

    mPoint[0]  = rotatedTouchPoint.get0()/objectRatio;

    mPoint[1]  = rotatedTouchPoint.get1()/objectRatio;

    mPoint[2]  = rotatedTouchPoint.get2()/objectRatio;

    mCamera[0] = rotatedCamera.get0()/objectRatio;

    mCamera[1] = rotatedCamera.get1()/objectRatio;

    mCamera[2] = rotatedCamera.get2()/objectRatio;

    for( mLastTouchedFace=0; mLastTouchedFace<mNumFaceAxis; mLastTouchedFace++)

      {

      if( faceIsVisible(mLastTouchedFace) )

        {

        castTouchPointOntoFace(mLastTouchedFace, mTouch);

        convertTo2Dcoords(mTouch, mLastTouchedFace, mPoint2D);

        if( isInsideFace(mLastTouchedFace,mPoint2D) ) return true;

        }

      }

    return false;

    }

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

  public Static2D newRotation(Static4D rotatedTouchPoint, float objectRatio)

    {

    mPoint[0] = rotatedTouchPoint.get0()/objectRatio;

    mPoint[1] = rotatedTouchPoint.get1()/objectRatio;

    mPoint[2] = rotatedTouchPoint.get2()/objectRatio;

    castTouchPointOntoFace(mLastTouchedFace, mTouch);

    convertTo2Dcoords(mTouch, mLastTouchedFace, mMove2D);

    mMove2D[0] -= mPoint2D[0];

    mMove2D[1] -= mPoint2D[1];

    computeEnabledAxis(mLastTouchedFace, mPoint2D, mEnabledRotAxis);

    int rotIndex = computeRotationIndex(mLastTouchedFace, mMove2D, mEnabledRotAxis);

    float offset = computeOffset(mPoint2D, mCastedRotAxis[mLastTouchedFace][rotIndex]);

    int row      = computeRowFromOffset(mLastTouchedFace,rotIndex,offset);

    return new Static2D(rotIndex,row);

    }

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

  public Static4D getCastedRotAxis(int rotIndex)

    {

    return mCastedRotAxis4D[mLastTouchedFace][rotIndex];

    }

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

  public int getTouchedFace()

    {

    return mLastTouchedFace;

    }

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

  public float[] getTouchedPoint3D()

    {

    return mTouch;

    }

  }

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

// 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.objectlib.main;

import org.distorted.library.type.Static3D;

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

// Cuboids

public class MovementCuboids extends Movement

{

  private final float[] mDist3D;

  public static final Static3D[] FACE_AXIS = new Static3D[]

         {

           new Static3D(1,0,0), new Static3D(-1,0,0),

           new Static3D(0,1,0), new Static3D(0,-1,0),

           new Static3D(0,0,1), new Static3D(0,0,-1)

         };

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

  public MovementCuboids(Static3D[] rotAxis, float[][] cuts, boolean[][] rotatable, float size, int type,

                         int[][][] enabled, float[] dist3D)

    {

    super(rotAxis, FACE_AXIS, cuts, rotatable, dist3D, size, type, enabled);

    mDist3D = dist3D;

    }

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

  int returnPart(int type, int face, float[] touchPoint)

    {

    return 0;

    }

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

  public float returnRotationFactor(int[] numLayers, int row)

    {

    return 1.0f;

    }

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

  boolean isInsideFace(int face, float[] p)

    {

    switch(face/2)

      {

      case 0: return ( p[0]<=mDist3D[4] && p[0]>=-mDist3D[4] && p[1]<=mDist3D[2] && p[1]>=-mDist3D[2] );

      case 1: return ( p[0]<=mDist3D[0] && p[0]>=-mDist3D[0] && p[1]<=mDist3D[4] && p[1]>=-mDist3D[4] );

      case 2: return ( p[0]<=mDist3D[0] && p[0]>=-mDist3D[0] && p[1]<=mDist3D[2] && p[1]>=-mDist3D[2] );

      }

    return false;

    }

}

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

// 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.objectlib.main;

import static org.distorted.objectlib.main.TwistyObject.SQ5;

import org.distorted.library.type.Static3D;

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

// Dodecahedral objects: map the 2D swipes of user's fingers to 3D rotations

public class MovementDodecahedron extends Movement

{

  public static final float C2       = (SQ5+3)/4;

  public static final float LEN      = (float)(Math.sqrt(1.25f+0.5f*SQ5));

  public static final float SIN54    = (SQ5+1)/4;

  public static final float COS54    = (float)(Math.sqrt(10-2*SQ5)/4);

  public  static final float DIST3D = (float)Math.sqrt(0.625f+0.275f*SQ5);

  private static final float DIST2D = (SIN54/COS54)/2;

  private static final float[] D3D  = { DIST3D,DIST3D,DIST3D,DIST3D,DIST3D,DIST3D,

                                        DIST3D,DIST3D,DIST3D,DIST3D,DIST3D,DIST3D };

  public static final Static3D[] FACE_AXIS = new Static3D[]

         {

           new Static3D(    C2/LEN, SIN54/LEN,    0      ),

           new Static3D(    C2/LEN,-SIN54/LEN,    0      ),

           new Static3D(   -C2/LEN, SIN54/LEN,    0      ),

           new Static3D(   -C2/LEN,-SIN54/LEN,    0      ),

           new Static3D( 0        ,    C2/LEN, SIN54/LEN ),

           new Static3D( 0        ,    C2/LEN,-SIN54/LEN ),

           new Static3D( 0        ,   -C2/LEN, SIN54/LEN ),

           new Static3D( 0        ,   -C2/LEN,-SIN54/LEN ),

           new Static3D( SIN54/LEN,    0     ,    C2/LEN ),

           new Static3D( SIN54/LEN,    0     ,   -C2/LEN ),

           new Static3D(-SIN54/LEN,    0     ,    C2/LEN ),

           new Static3D(-SIN54/LEN,    0     ,   -C2/LEN )

         };

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

  public MovementDodecahedron(Static3D[] rotAxis, float[][] cuts, boolean[][] rotatable, float size, int type, int[][][] enabled)

    {

    super(rotAxis, FACE_AXIS, cuts,rotatable,D3D, size, type, enabled);

    }

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

  public float returnRotationFactor(int[] numLayers, int row)

    {

    return 1.0f;

    }

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

// return angle (in radians) that the line connecting the center C of the pentagonal face and the

// first vertex of the pentagon makes with a vertical line coming upwards from the center C.

  private float returnAngle(int face)

    {

    switch(face)

      {

      case  0:

      case  2:

      case  6:

      case  7: return 0.0f;

      case  1:

      case  3:

      case  4:

      case  5: return (float)(36*Math.PI/180);

      case  9:

      case 10: return (float)(54*Math.PI/180);

      case  8:

      case 11: return (float)(18*Math.PI/180);

      }

    return 0.0f;

    }

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

// The pair (distance,angle) defines a point P in R^2 in polar coordinate system. Let V be the vector

// from the center of the coordinate system to P.

// Let P' be the point defined by polar (distance,angle+PI/2). Let Lh be the half-line starting at

// P' and going in the direction of V.

// Return true iff point 'point' lies on the left of Lh, i.e. when we rotate (using the center of

// the coordinate system as the center of rotation) 'point' and Lh in such a way that Lh points

// directly upwards, is 'point' on the left or the right of it?

  private boolean isOnTheLeft(float[] point, float distance, float angle)

    {

    float sin = (float)Math.sin(angle);

    float cos = (float)Math.cos(angle);

    float vx = point[0] + sin*distance;

    float vy = point[1] - cos*distance;

    return vx*sin < vy*cos;

    }

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

  int returnPart(int type, int face, float[] point)

    {

    switch(type)

      {

      case TYPE_SPLIT_EDGE  : return partEdge(point,face);

      case TYPE_SPLIT_CORNER: return partCorner(point,face);

      default               : return 0;

      }

    }

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

// Return 0,1,2,3,4 - the vertex of the pentagon to which point 'point' is the closest, if the

// 'point' is inside the pentagon - or -1 otherwise.

// The 'first' vertex is the one we meet the first when we rotate clockwise starting from 12:00.

// This vertex makes angle 'returnAngle()' with the line coming out upwards from the center of the

// pentagon.

// Distance from the center to a vertex of the pentagon = 1/(6*COS54)

  int partEdge(float[] point, int face)

    {

    float angle = returnAngle(face);

    float A = (float)(Math.PI/5);

    for(int i=0; i<5; i++)

      {

      if( isOnTheLeft(point, DIST2D, (9-2*i)*A-angle) ) return -1;

      }

    if( isOnTheLeft(point, 0, 2.5f*A-angle) )

      {

      if( isOnTheLeft(point, 0, 3.5f*A-angle) )

        {

        return isOnTheLeft(point, 0, 5.5f*A-angle) ? 3 : 4;

        }

      else return 0;

      }

    else

      {

      if( isOnTheLeft(point, 0, 4.5f*A-angle) )

        {

        return 2;

        }

      else

        {

        return isOnTheLeft(point, 0, 6.5f*A-angle) ? 1 : 0;

        }

      }

    }

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

// TODO - no such object yet

  int partCorner(float[] point, int face)

    {

    return 0;

    }

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

  boolean isInsideFace(int face, float[] p)

    {

    float angle = returnAngle(face);

    float A = (float)(Math.PI/5);

    for(int i=0; i<5; i++)

      {

      if( isOnTheLeft(p, DIST2D, (9-2*i)*A-angle) ) return false;

      }

    return true;

    }

}

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

// 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.objectlib.main;

import org.distorted.library.type.Static3D;

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

// Hexahedral objects: map the 2D swipes of user's fingers to 3D rotations

public class MovementHexahedron extends Movement

{

  private static final float DIST3D = 0.5f;

  private static final float DIST2D = 0.5f;

  private static final float[] D3D  = { DIST3D,DIST3D,DIST3D,DIST3D,DIST3D,DIST3D };

  public static final Static3D[] FACE_AXIS = new Static3D[]

         {

           new Static3D(1,0,0), new Static3D(-1,0,0),

           new Static3D(0,1,0), new Static3D(0,-1,0),

           new Static3D(0,0,1), new Static3D(0,0,-1)

         };

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

  public MovementHexahedron(Static3D[] rotAxis, float[][] cuts, boolean[][] rotatable, float size, int type, int[][][] enabled)

    {

    super(rotAxis, FACE_AXIS, cuts, rotatable, D3D, size, type, enabled);

    }

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

//  corner    edge

//  \ 0 /     3 | 0

// 3 \ / 1  ___ | ___

//   / \        |

//  / 2 \     2 | 1

  int returnPart(int type, int face, float[] touchPoint)

    {

    switch(type)

      {

      case TYPE_NOT_SPLIT   : return 0;

      case TYPE_SPLIT_EDGE  : boolean e0 = touchPoint[0] > 0;

                              boolean e1 = touchPoint[1] > 0;

                              return e0 ? (e1 ? 0:1) : (e1 ? 3:2);

      case TYPE_SPLIT_CORNER: boolean c0 = touchPoint[1] >= touchPoint[0];

                              boolean c1 = touchPoint[1] >=-touchPoint[0];

                              return c0 ? (c1 ? 0:3) : (c1 ? 1:2);

      }

    return 0;

    }

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

  public float returnRotationFactor(int[] numLayers, int row)

    {

    return 1.0f;

    }

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

  boolean isInsideFace(int face, float[] p)

    {

    return ( p[0]<=DIST2D && p[0]>=-DIST2D && p[1]<=DIST2D && p[1]>=-DIST2D );

    }

}

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

// 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.objectlib.main;

import org.distorted.library.type.Static3D;

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

// Octahedral objects: map the 2D swipes of user's fingers to 3D rotations

public class MovementOctahedron extends Movement

{

  private static final float DIST3D = SQ6/6;

  private static final float DIST2D = SQ3/6;

  private static final float[] D3D  = { DIST3D,DIST3D,DIST3D,DIST3D,DIST3D,DIST3D,DIST3D,DIST3D };

  public static final Static3D[] FACE_AXIS = new Static3D[]

         {

           new Static3D(+SQ6/3,+SQ3/3,     0), new Static3D(-SQ6/3,-SQ3/3,     0),

           new Static3D(-SQ6/3,+SQ3/3,     0), new Static3D(+SQ6/3,-SQ3/3,     0),

           new Static3D(     0,+SQ3/3,+SQ6/3), new Static3D(     0,-SQ3/3,-SQ6/3),

           new Static3D(     0,+SQ3/3,-SQ6/3), new Static3D(     0,-SQ3/3,+SQ6/3)

         };

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

  public MovementOctahedron(Static3D[] rotAxis, float[][] cuts, boolean[][] rotatable, float size, int type, int[][][] enabled)

    {

    super(rotAxis, FACE_AXIS, cuts, rotatable, D3D, size, type, enabled);

    }

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

// corner    edge

//   |       \ 0 /

// 2 | 0      \ /

//  / \      2 | 1

// / 1 \       |

  int returnPart(int type, int face, float[] touchPoint)

    {

    switch(type)

      {

      case TYPE_NOT_SPLIT   : return 0;

      case TYPE_SPLIT_EDGE  : float y1 = (face%2 == 0 ? touchPoint[1] : -touchPoint[1]);

                              float x1 = touchPoint[0];

                              boolean e0 = x1>0;

                              boolean e1 = y1>(+SQ3/3)*x1;

                              boolean e2 = y1>(-SQ3/3)*x1;

                              if(  e1 && e2 ) return 0;

                              if( !e1 && e0 ) return 1;

                              if( !e0 &&!e2 ) return 2;

      case TYPE_SPLIT_CORNER: float y2 = (face%2 == 0 ? touchPoint[1] : -touchPoint[1]);

                              float x2 = touchPoint[0];

                              boolean c0 = x2>0;

                              boolean c1 = y2>(+SQ3/3)*x2;

                              boolean c2 = y2>(-SQ3/3)*x2;

                              if(  c0 && c2 ) return 0;

                              if( !c1 &&!c2 ) return 1;

                              if( !c0 && c1 ) return 2;

      }

    return 0;

    }

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

  public float returnRotationFactor(int[] numLayers, int row)

    {

    return 1.0f;

    }

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

  boolean isInsideFace(int face, float[] p)

    {

    float y = (face%2 == 0 ? p[1] : -p[1]);

    float x = p[0];

    return (y >= -DIST2D) && (y <= DIST2D*(2-6*x)) && (y <= DIST2D*(2+6*x));

    }

}

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

// 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.objectlib.main;

import org.distorted.library.type.Static3D;

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

// Tetrahedral objects: map the 2D swipes of user's fingers to 3D rotations

public class MovementTetrahedron extends Movement

{

  private static final float DIST3D = SQ6/12;

  private static final float DIST2D = SQ3/6;

  private static final float[] D3D  = { DIST3D,DIST3D,DIST3D,DIST3D };

  public static final Static3D[] FACE_AXIS = new Static3D[]

         {

           new Static3D(     0,+SQ3/3,+SQ6/3),

           new Static3D(     0,+SQ3/3,-SQ6/3),

           new Static3D(-SQ6/3,-SQ3/3,     0),

           new Static3D(+SQ6/3,-SQ3/3,     0),

         };

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

  public MovementTetrahedron(Static3D[] rotAxis, float[][] cuts, boolean[][] rotatable, float size, int type, int[][][] enabled)

    {

    super(rotAxis, FACE_AXIS, cuts, rotatable, D3D, size, type, enabled);

    }

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

// corner    edge

//   |       \ 0 /

// 2 | 0      \ /

//  / \      2 | 1

// / 1 \       |

  int returnPart(int type, int face, float[] touchPoint)

    {

    switch(type)

      {

      case TYPE_NOT_SPLIT   : return 0;

      case TYPE_SPLIT_EDGE  : float y1 = (face > 1 ? touchPoint[1] : -touchPoint[1]);

                              float x1 = touchPoint[0];

                              boolean e0 = x1>0;

                              boolean e1 = y1>(+SQ3/3)*x1;

                              boolean e2 = y1>(-SQ3/3)*x1;

                              if(  e1 && e2 ) return 0;

                              if( !e1 && e0 ) return 1;

                              if( !e0 &&!e2 ) return 2;

      case TYPE_SPLIT_CORNER: float y2 = (face > 1 ? touchPoint[1] : -touchPoint[1]);

                              float x2 = touchPoint[0];

                              boolean c0 = x2>0;

                              boolean c1 = y2>(+SQ3/3)*x2;

                              boolean c2 = y2>(-SQ3/3)*x2;

                              if(  c0 && c2 ) return 0;

                              if( !c1 &&!c2 ) return 1;

                              if( !c0 && c1 ) return 2;

      }

    return 0;

    }

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

// Jing has nL=2

  public float returnRotationFactor(int[] numLayers, int row)

    {

    int numL = numLayers[0];

    return numL==2 ? 1.0f : ((float)numL)/(numL-row);

    }

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

  boolean isInsideFace(int face, float[] p)

    {

    float y = (face > 1 ? p[1] : -p[1]);

    float x = p[0];

    return (y >= -DIST2D) && (y <= DIST2D*(2-6*x)) && (y <= DIST2D*(2+6*x));

    }

}

        if( object!=null && mMovement!=null && mMovement.faceTouched(rotatedTouchPoint,rotatedCamera,object.getObjectRatio() ) )

      Static2D res = mMovement.newRotation(rotatedTouchPoint,object.getObjectRatio());

import static org.distorted.objectlib.main.Movement.MOVEMENT_TETRAHEDRON;

import static org.distorted.objectlib.main.Movement.MOVEMENT_HEXAHEDRON;

import static org.distorted.objectlib.main.Movement.MOVEMENT_OCTAHEDRON;

import static org.distorted.objectlib.main.Movement.MOVEMENT_DODECAHEDRON;

import static org.distorted.objectlib.main.Movement.MOVEMENT_SHAPECHANGE;

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

  float getObjectRatio()

    {

    return mObjectScreenRatio*mInitScreenRatio;

    }