Magic Cube

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

// 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.objects;

import org.distorted.library.type.Static2D;

import org.distorted.library.type.Static3D;

import org.distorted.library.type.Static4D;

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

public abstract class RubikObjectMovement

  {

  private int mLastTouchedAxis;

  private float[] mPoint, mCamera, mTouch;

  private float[] mPoint2D, mMove2D;

  private float[][][] mCastAxis;

  private int mLastTouchedLR;

  private int mNumAxis, mNumFacesPerAxis;

  private float mDistanceCenterFace3D, mDistanceCenterFace2D;

  private Static3D[] mAxis;

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

  abstract boolean isInsideFace(float[] point);

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

  RubikObjectMovement(Static3D[] axis, int numFacesPerAxis, float distance3D, float distance2D)

    {

    mPoint = new float[3];

    mCamera= new float[3];

    mTouch = new float[3];

    mPoint2D = new float[2];

    mMove2D  = new float[2];

    mAxis = axis;

    mNumAxis = mAxis.length;

    mNumFacesPerAxis = numFacesPerAxis;

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

    mDistanceCenterFace2D = distance2D; // distance from the center of a face to its edge

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

    // 1st pair (axis,lr)

    mCastAxis = new float[mNumAxis*mNumFacesPerAxis][mNumAxis][2];

    for( int casted=0; casted<mNumAxis; casted++)

      {

      Static3D a = mAxis[casted];

      mPoint[0]= a.get0();

      mPoint[1]= a.get1();

      mPoint[2]= a.get2();

      for( int surface=0; surface<mNumAxis; surface++)

        for(int lr=0; lr<mNumFacesPerAxis; lr++)

          {

          int index = surface*mNumFacesPerAxis + lr;

          if( casted!=surface )

            {

            convertTo2Dcoords( mPoint, mAxis[surface], lr, mPoint2D);

            mCastAxis[index][casted][0] = mPoint2D[0];

            mCastAxis[index][casted][1] = mPoint2D[1];

            normalize2D(mCastAxis[index][casted]);

            }

          else

            {

            mCastAxis[index][casted][0] = 0;

            mCastAxis[index][casted][1] = 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 axis, int lr, float[] move2D)

    {

    float cosAngle, minCosAngle = Float.MAX_VALUE;

    int minIndex=-1;

    int index = axis*mNumFacesPerAxis + lr;

    float m0 = move2D[0];

    float m1 = move2D[1];

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

    m0 /= len;

    m1 /= len;

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

      {

      if( axis != i )

        {

        cosAngle = m0*mCastAxis[index][i][0] +  m1*mCastAxis[index][i][1];

        if( cosAngle<0 ) cosAngle = -cosAngle;

        if( cosAngle<minCosAngle )

          {

          minCosAngle=cosAngle;

          minIndex = i;

          }

        }

      }

    return minIndex;

    }

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

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

    {

    return point[0]*axis[0] + point[1]*axis[1] + mDistanceCenterFace2D;

    }

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

  private boolean faceIsVisible(Static3D axis, int lr)

    {

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

    return (2*lr-1)*castCameraOnAxis > mDistanceCenterFace3D;

    }

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

// 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)) [and this

//    distance is +-mDistanceCenterFace, depending if it is the face on the left or the right end of

//    the axis] (lr=0 or 1, so (2lr-1)*mDistanceCenterFace)

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

//

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

  private void castTouchPointOntoFace(Static3D axis, int lr, float[] output)

    {

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

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

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

    float a0 = axis.get0();

    float a1 = axis.get1();

    float a2 = axis.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 distance = (2*lr-1)*mDistanceCenterFace3D;

      float alpha = (distance-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, Static3D axis, int lr, float[] output)

    {

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

    float a0 = axis.get0();

    float a1 = axis.get1();

    float a2 = axis.get2();

    if( lr==0 )

      {

      a0=-a0; a1=-a1; a2=-a2;

      }

    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;

    }

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

// PUBLIC API

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

  public boolean faceTouched(Static4D rotatedTouchPoint, Static4D rotatedCamera)

    {

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

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

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

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

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

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

    for( mLastTouchedAxis=0; mLastTouchedAxis<mNumAxis; mLastTouchedAxis++)

      {

      for( mLastTouchedLR=0; mLastTouchedLR<mNumFacesPerAxis; mLastTouchedLR++)

        {

        if( faceIsVisible(mAxis[mLastTouchedAxis], mLastTouchedLR) )

          {

          castTouchPointOntoFace(mAxis[mLastTouchedAxis], mLastTouchedLR, mTouch);

          convertTo2Dcoords(mTouch, mAxis[mLastTouchedAxis], mLastTouchedLR, mPoint2D);

          if( isInsideFace(mPoint2D) ) return true;

          }

        }

      }

    return false;

    }

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

  public Static2D newRotation(Static4D rotatedTouchPoint)

    {

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

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

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

    castTouchPointOntoFace(mAxis[mLastTouchedAxis], mLastTouchedLR, mTouch);

    convertTo2Dcoords(mTouch, mAxis[mLastTouchedAxis], mLastTouchedLR, mMove2D);

    mMove2D[0] -= mPoint2D[0];

    mMove2D[1] -= mPoint2D[1];

    int rotIndex = computeRotationIndex(mLastTouchedAxis, mLastTouchedLR, mMove2D);

    int index    = mLastTouchedAxis*mNumFacesPerAxis+mLastTouchedLR;

    float offset = computeOffset(mPoint2D, mCastAxis[index][rotIndex]);

    return new Static2D(rotIndex,offset);

    }

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

  public int getTouchedFace()

    {

    return mNumFacesPerAxis==2 ? 2*mLastTouchedAxis + 1 - mLastTouchedLR : mLastTouchedAxis;

    }

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

// TODO

  public int getTouchedCubit()

    {

    return 0;

    }

  }