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 Movement

  {

  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;

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

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

  abstract void computeEnabledAxis(int face, float[] touchPoint, int[] enabledAxis);

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

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

  Movement(Static3D[] rotAxis, Static3D[] faceAxis, float[][] cuts, boolean[][] rotatable, float distance3D, int size)

    {

    mPoint = new float[3];

    mCamera= new float[3];

    mTouch = new float[3];

    mPoint2D = new float[2];

    mMove2D  = new float[2];

    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(distance3D,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, mFaceAxis[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(Static3D faceAxis)

    {

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

    return 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))

// 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 faceAxis, float[] output)

    {

    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-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 faceAxis, float[] output)

    {

    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, int size)

    {

    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)

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

    {

    int numCuts = cuts.length;

    mTouchBorders = new float[numCuts][];

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

      {

      mTouchBorders[i] = computeBorder(cuts[i],rotatable[i],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(float distance3D, 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*distance3D*coeff;

          }

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

        }

    }

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

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

    {

    float[] borders = mTouchBorders[axisIndex];

    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;

    }

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

// 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(mFaceAxis[mLastTouchedFace]) )

        {

        castTouchPointOntoFace(mFaceAxis[mLastTouchedFace], mTouch);

        convertTo2Dcoords(mTouch, mFaceAxis[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(mFaceAxis[mLastTouchedFace], mTouch);

    convertTo2Dcoords(mTouch, mFaceAxis[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;

    }

  }