Magic Cube

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

// Copyright 2022 Leszek Koltunski                                                               //

//                                                                                               //

// This file is part of Magic Cube.                                                              //

//                                                                                               //

// along with the code. If not, check https://distorted.org/magic/License-Magic-Cube.html        //

package org.distorted.bandaged;

import org.distorted.library.type.Static4D;

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

  private float mObjectRatio;

  private final Static3D[] mFaceAxis;

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

// 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)

// (ax,ay,az) - vector normal to the face surface.

  void convertTo2Dcoords(float[] point3D, float ax, float ay, float az , float[] output)

    {

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

    if( ax==0.0f && az==0.0f )

      {

      y0=0; y1=0; y2=-ay;

      }

    else if( ay==0.0f )

      {

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

      }

    else

      {

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

      y0 = norm*ax; y1= norm*(ay-1/ay); y2=norm*az;

      }

    float x0 = y1*az - y2*ay;  //

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

    float x2 = y0*ay - y1*ax;  //

    float originAlpha = point3D[0]*ax + point3D[1]*ay + point3D[2]*az;

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

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

    float origin2 = originAlpha*az; // 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;

    }

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

// 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)]

    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];

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

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

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

      }

    }

  private boolean faceIsVisible(int face)

    {

    Static3D faceAxis = mFaceAxis[face];

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

  private boolean objectTouched(Static4D rotatedTouchPoint, Static4D rotatedCamera)

    {

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

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

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

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

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

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

    for( mLastTouchedFace=0; mLastTouchedFace<6; mLastTouchedFace++)

      {

      if( faceIsVisible(mLastTouchedFace) )

        {

        castTouchPointOntoFace(mLastTouchedFace, mTouch);

        float ax = mFaceAxis[mLastTouchedFace].get0();

        float ay = mFaceAxis[mLastTouchedFace].get1();

        float az = mFaceAxis[mLastTouchedFace].get2();

        convertTo2Dcoords(mTouch, ax,ay,az, mPoint2D);

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

      }

    return false;

    }

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

// PUBLIC API

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

    mCamera= new float[3];

    mTouch = new float[3];

    mPoint2D = new float[2];

    double halfFOV = fov * (Math.PI/360);

    float tanHalf = (float)Math.tan(halfFOV);

    float dist = 0.5f/tanHalf;

    CAMERA_POINT = new Static4D(0,0,dist,0);

    }

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

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

  public void setObjectRatio(float ratio)

    {

    mObjectRatio = ratio;

    }

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

// return the index of the cubit touched; if none, return -1.

  public int cubitTouched(float x, float y, Static4D quat)

    {

    Static4D touchPoint = new Static4D(x, y, 0, 0);

    Static4D rotatedTouchPoint= QuatHelper.rotateVectorByInvertedQuat(touchPoint, quat);

    Static4D rotatedCamera= QuatHelper.rotateVectorByInvertedQuat(CAMERA_POINT, quat);

    boolean touched = objectTouched(rotatedTouchPoint,rotatedCamera);

    if( !touched ) return -1;

}