pinball/base/EMath.cpp

/***************************************************************************
                          EMath.cpp  -  description
                             -------------------
    begin                : Sat Jan 29 2000
    copyright            : (C) 2000 by
    email                :
 ***************************************************************************/

#include <math.h>
#include <stdlib.h>

#include "Private.h"
#include "EMath.h"

#if EM_USE_FAST_FLOAT2INT
IntOrFloat gBias; //.i = (23 + 127) << 23;
#endif

const Matrix EMath::identityMatrix =
{
	{
  	/* 3x3 identity */
   	{ 1.0f, 0.0f, 0.0f },
   	{ 0.0f, 1.0f, 0.0f },
   	{ 0.0f, 0.0f, 1.0f },
  },
	/* zero translation */
	{ 0.0f, 0.0f, 0.0f }
};

EMath::EMath() {
}

EMath::~EMath() {
}

// void EMath::applyMatrix(const Matrix & mtx, const Vertex3D & vtxIn, Vertex3D & vtxOut) {
//   vtxOut.x = vtxIn.x * mtx.v[0][0] + vtxIn.y * mtx.v[0][1] + vtxIn.z * mtx.v[0][2] + mtx.t[0];
//   vtxOut.y = vtxIn.x * mtx.v[1][0] + vtxIn.y * mtx.v[1][1] + vtxIn.z * mtx.v[1][2] + mtx.t[1];
//   vtxOut.z = vtxIn.x * mtx.v[2][0] + vtxIn.y * mtx.v[2][1] + vtxIn.z * mtx.v[2][2] + mtx.t[2];
// }

void EMath::applyMatrixTrans(const Matrix & mtx, const Vertex3D & vtxIn, Vertex3D & vtxOut) {
	vtxOut.x = vtxIn.x + mtx.t[0];
	vtxOut.y = vtxIn.y + mtx.t[1];
	vtxOut.z = vtxIn.z + mtx.t[2];
}

void EMath::crossProduct(const Vertex3D & vtxA, const Vertex3D & vtxB, Vertex3D & vtxOut) {
	vtxOut.x = (vtxA.y * vtxB.z) - (vtxA.z * vtxB.y);
	vtxOut.y = (vtxA.z * vtxB.x) - (vtxA.x * vtxB.z);
	vtxOut.z = (vtxA.x * vtxB.y) - (vtxA.y * vtxB.x);
}

float EMath::dotProduct(const Vertex3D & vtxA, const Vertex3D & vtxB) {
	return vtxA.x * vtxB.x + vtxA.y * vtxB.y + vtxA.z * vtxB.z;
}

float EMath::emAcos(float f) {
	return (float) acos(EM_PI_2*f);
}

float EMath::emAtan(float f) {
	return (float)atan(EM_PI_2*f);
}

float EMath::emCos(float f) {
	return (float)cos(EM_PI_2*f);
}

float EMath::emRand() {
	return ((float)(rand()-(RAND_MAX/2))/(RAND_MAX/2));
}

float EMath::emSin(float f) {
	return (float)sin(EM_PI_2*f);
}

float EMath::emSqrt(float f) {
	return (float)sqrt(f);
}

float EMath::emTan(float f) {
	return (float)tan(EM_PI_2*f);
}

float EMath::emPow(float x, float y) {
	return (float)pow(x, y);
}

/* */
void EMath::getTransformationMatrix(Matrix & mtx, const Vertex3D & vtxT, 
                                    const Vertex3D & vtxR, const Vertex3D & vtxS) {
	float sin_x = EMath::emSin(vtxR.x);
  float cos_x = EMath::emCos(vtxR.x);

  float sin_y = EMath::emSin(vtxR.y);
  float cos_y = EMath::emCos(vtxR.y);

  float sin_z = EMath::emSin(vtxR.z);
  float cos_z = EMath::emCos(vtxR.z);

  float sinx_siny = sin_x * sin_y;
  float cosx_siny = cos_x * sin_y;

  mtx.v[0][0] = cos_y * cos_z * vtxS.x;
  mtx.v[0][1] = cos_y * sin_z;
  mtx.v[0][2] = -sin_y;

  mtx.v[1][0] = (sinx_siny * cos_z) - (cos_x * sin_z);
  mtx.v[1][1] = (sinx_siny * sin_z) + (cos_x * cos_z) * vtxS.y;
  mtx.v[1][2] = sin_x * cos_y;

  mtx.v[2][0] = (cosx_siny * cos_z) + (sin_x * sin_z);
  mtx.v[2][1] = (cosx_siny * sin_z) - (sin_x * cos_z);
  mtx.v[2][2] = cos_x * cos_y * vtxS.z;

  mtx.t[0] = vtxT.x;
  mtx.t[1] = vtxT.y;
  mtx.t[2] = vtxT.z;
}

void EMath::getTransformationMatrix(Matrix & mtx, const Vertex3D & vtxT, 
                                    const Quaternion & qRot, const Vertex3D & vtxS) {
  // a lean function for filling m[16] with
  // a 4x4 transformation matrix based on 
  // translation v and rotation q
  // This routine would likely be used by an opengl
  // programmer calling glmultmatrix()
  mtx.v[0][0] = 1 - 2*(qRot.y*qRot.y + qRot.z*qRot.z) * vtxS.x;
  mtx.v[0][1] = 2*(qRot.x*qRot.y + qRot.w*qRot.z);
  mtx.v[0][2] = 2*(qRot.x*qRot.z - qRot.w*qRot.y);

  mtx.v[1][0] = 2*(qRot.x*qRot.y - qRot.w*qRot.z);	
  mtx.v[1][1] = 1 - 2*(qRot.x*qRot.x + qRot.z*qRot.z) * vtxS.y;
  mtx.v[1][2] = 2*(qRot.y*qRot.z + qRot.w*qRot.x);

  mtx.v[2][0] = 2*(qRot.x*qRot.z + qRot.w*qRot.y); 
  mtx.v[2][1] = 2*(qRot.y*qRot.z - qRot.w*qRot.x); 
  mtx.v[2][2] = 1-2*(qRot.x*qRot.x + qRot.y*qRot.y) * vtxS.z;
  /*
  mtx.v[0][0] = 1 - 2*(qRot.y*qRot.y + qRot.z*qRot.z);
  mtx.v[1][0] = 2*(qRot.x*qRot.y + qRot.w*qRot.z);
  mtx.v[2][0] = 2*(qRot.x*qRot.z - qRot.w*qRot.y);

  mtx.v[0][1] = 2*(qRot.x*qRot.y - qRot.w*qRot.z);	
  mtx.v[1][1] = 1 - 2*(qRot.x*qRot.x + qRot.z*qRot.z);
  mtx.v[2][1] = 2*(qRot.y*qRot.z + qRot.w*qRot.x);

  mtx.v[0][2] = 2*(qRot.x*qRot.z + qRot.w*qRot.y); 
  mtx.v[1][2] = 2*(qRot.y*qRot.z - qRot.w*qRot.x); 
  mtx.v[2][2] = 1-2*(qRot.x*qRot.x + qRot.y*qRot.y);
*/
  mtx.t[0] = vtxT.x;
  mtx.t[1] = vtxT.y;
  mtx.t[2] = vtxT.z;
}


/* Stolen from allegro. Thanks!! */
void EMath::inverse(const Matrix & mtx, Matrix & inv) {
	Matrix mtxTmp = mtx;
	inv = identityMatrix;

  int cc;
  int rowMax; // Points to max abs value row in this column
  int row;
  float tmp;

  // Go through columns
  for (int c=0; c<3; c++) {
    // Find the row with max value in this column
    rowMax = c;
    for (int r=c+1; r<3; r++) {
      if (fabs(mtxTmp.v[c][r]) > fabs(mtxTmp.v[c][rowMax])) {
        rowMax = r;
      }
    }

    // If the max value here is 0, we can't invert.  Return identity.
    if (mtx.v[rowMax][c] == 0.0f) {
			inv = identityMatrix;
      return;
		}

    // Swap row "rowMax" with row "c"
    for (cc=0; cc<3; cc++) {
      tmp = mtxTmp.v[cc][c];
      mtxTmp.v[cc][c] = mtxTmp.v[cc][rowMax];
      mtxTmp.v[cc][rowMax] = tmp;
      tmp = inv.v[cc][c];
      inv.v[cc][c] = inv.v[cc][rowMax];
      inv.v[cc][rowMax] = tmp;
    }

    // Now everything we do is on row "c".
    // Set the max cell to 1 by dividing the entire row by that value
    tmp = mtxTmp.v[c][c];
    for (cc=0; cc<3; cc++) {
      mtxTmp.v[cc][c] /= tmp;
      inv.v[cc][c] /= tmp;
    }

    // Now do the other rows, so that this column only has a 1 and 0's
    for (row = 0; row < 3; row++) {
      if (row != c) {
        tmp = mtxTmp.v[c][row];
        for (cc=0; cc<3; cc++) {
          mtxTmp.v[cc][row] -= mtxTmp.v[cc][c] * tmp;
          inv.v[cc][row] -= inv.v[cc][c] * tmp;
        }
      }
    }
    
  }
  
  inv.t[0] = -mtx.t[0];
  inv.t[1] = -mtx.t[1];
  inv.t[2] = -mtx.t[2];
}

/* mtxA or mtxB NOT allowed to be the same as out.
 */
void EMath::matrixMulti(const Matrix & mtxA, const Matrix & mtxB, Matrix & mtxOut) {
  for (int a=0; a<3; a++) {
    for (int b=0; b<3; b++) {
      mtxOut.v[a][b] =
	(mtxA.v[0][b] * mtxB.v[a][0]) +
	(mtxA.v[1][b] * mtxB.v[a][1]) +
	(mtxA.v[2][b] * mtxB.v[a][2]);
    }
    
    mtxOut.t[a] =
      (mtxA.t[0] * mtxB.v[a][0]) +
      (mtxA.t[1] * mtxB.v[a][1]) +
      (mtxA.t[2] * mtxB.v[a][2]) +
      mtxB.t[a];
  }
}


void EMath::planeLineIntersection(const Vertex3D & nrml, float dist, 
				  const Vertex3D & vtxA, const Vertex3D & vtxB, Vertex3D & vtxDiff) {
  // returns the point where the line p1-p2 intersects the plane n&d
  EMath::subst(vtxB, vtxA, vtxDiff);
  float dot = EMath::dotProduct(nrml, vtxDiff);
  float k = -(dist + EMath::dotProduct(nrml, vtxA) ) / dot;
  EMath::scaleVertex(vtxDiff, k);
  EMath::add(vtxA, vtxDiff);
}


/* */
void EMath::normalizeVector(Vertex3D & vtx) {
  float length_1;
  float length = EMath::vectorLength(vtx);
  if (EM_ZERO(length)) {
    vtx.x = 0.0f;
    vtx.y = 1.0f;
    vtx.z = 0.0f;
    return;
  }
  length_1 = 1.0f / length;
  vtx.x *= length_1;
  vtx.y *= length_1;
  vtx.z *= length_1;
}

/* */
void EMath::scaleVector(Vertex3D & vtx, float sc) {
  vtx.x *= sc;
  vtx.y *= sc;
  vtx.z *= sc;
}

/* Projection of vector A onto B. */
float EMath::projection(const Vertex3D & vtxA, const Vertex3D & vtxB, Vertex3D & vtxOut) {
  float k =(vtxA.x * vtxB.x  +  vtxA.y * vtxB.y  +  vtxA.z * vtxB.z) /
		(vtxB.x * vtxB.x  +  vtxB.y * vtxB.y  +  vtxB.z * vtxB.z);
  
  vtxOut.x = k * vtxB.x;
  vtxOut.y = k * vtxB.y;
  vtxOut.z = k * vtxB.z;
  
  return k;
}

float EMath::perpendicular(const Vertex3D & vtxA, const Vertex3D & vtxB, Vertex3D & vtxOut) {
  float k =(vtxA.x * vtxB.x  +  vtxA.y * vtxB.y  +  vtxA.z * vtxB.z) /
    (vtxB.x * vtxB.x  +  vtxB.y * vtxB.y  +  vtxB.z * vtxB.z);
  
  vtxOut.x = vtxA.x - k * vtxB.x;
  vtxOut.y = vtxA.y - k * vtxB.y;
  vtxOut.z = vtxA.z - k * vtxB.z;
  
  return k;
}

/* */
float EMath::polygonZNormal(const Vertex3D & edgeA, const Vertex3D & edgeB, 
			    const Vertex3D & edgeC) {
  return ((edgeB.x - edgeA.x) * (edgeC.y - edgeB.y)) - ((edgeC.x - edgeB.x) * (edgeB.y - edgeA.y));
}


/* First the projection of vtxIn onto vtxWall is counted.
 * the reflection is then vtxOut = vtxIn - 2*vtxPro.
 * If k > 0 the vtxIn vector is comming from behind the wall and
 * no reflection is made. */
void EMath::reflection(const Vertex3D & vtxIn, const Vertex3D & vtxWall, Vertex3D & vtxOut, 
		       bool bBehind) {
  Vertex3D vtxPro;
  float k =(vtxIn.x * vtxWall.x  +  vtxIn.y * vtxWall.y  +  vtxIn.z * vtxWall.z) /
    (vtxWall.x * vtxWall.x  +  vtxWall.y * vtxWall.y  +  vtxWall.z * vtxWall.z);
  
  if ( k < 0 || bBehind)	{
    vtxPro.x = k * vtxWall.x;
    vtxPro.y = k * vtxWall.y;
    vtxPro.z = k * vtxWall.z;
    
    vtxOut.x = - vtxPro.x - vtxPro.x + vtxIn.x;
    vtxOut.y = - vtxPro.y - vtxPro.y + vtxIn.y;
    vtxOut.z = - vtxPro.z - vtxPro.z + vtxIn.z;
  }
}

/* First the projection of vtxIn onto vtxWall is counted.
 * the reflection is then vtxOut = vtxIn - 2*vtxPro.
 * If k > 0 the vtxIn vector is comming from behind the wall and
 * no reflection is made. */
void EMath::reflectionDamp(const Vertex3D & vtxIn, const Vertex3D & vtxWall, Vertex3D & vtxOut, 
			   float damp, float extra, float scale, bool bBehind) {
  Vertex3D vtxPro;
  float k =(vtxIn.x * vtxWall.x  +  vtxIn.y * vtxWall.y  +  vtxIn.z * vtxWall.z) /
    (vtxWall.x * vtxWall.x  +  vtxWall.y * vtxWall.y  +  vtxWall.z * vtxWall.z);
  
  if ( k < 0 || bBehind) {
    vtxPro.x = k * vtxWall.x;
    vtxPro.y = k * vtxWall.y;
    vtxPro.z = k * vtxWall.z;
    
    vtxOut.x = (vtxIn.x - vtxPro.x - vtxPro.x * damp + vtxWall.x * extra) * scale;
    vtxOut.y = (vtxIn.y - vtxPro.y - vtxPro.y * damp + vtxWall.y * extra) * scale;
    vtxOut.z = (vtxIn.z - vtxPro.z - vtxPro.z * damp + vtxWall.z * extra) * scale;
  }
}

/*
float EMath::vectorLength(const Vertex3D & vtx) {
return EMath::emSqrt(vtx.x * vtx.x + vtx.y * vtx.y + vtx.z * vtx.z);
}

float EMath::vectorLengthSqr(const Vertex3D & vtx) {
return (vtx.x * vtx.x + vtx.y * vtx.y + vtx.z * vtx.z);
}
*/

/* */
float EMath::volume(const Vertex3D & vtxA, const Vertex3D & vtxB, const Vertex3D & vtxC) {
  return vtxA.x*( vtxB.y*vtxC.z - vtxB.z*vtxC.y ) - 
    vtxA.y*( vtxB.x*vtxC.z - vtxB.z*vtxC.x ) + 
    vtxA.z*( vtxB.x*vtxC.y - vtxB.y*vtxC.x );
}

void EMath::rotationArc(const Vertex3D & vtxa, const Vertex3D & vtxb, Quaternion & qOut) {
  Vertex3D vtxA = vtxa;
  Vertex3D vtxB = vtxb;
  EMath::normalizeVector(vtxA);
  EMath::normalizeVector(vtxB);
  Vertex3D vtxCross;
  EMath::crossProduct(vtxA, vtxB, vtxCross);
  float dot = EMath::dotProduct(vtxA, vtxB);
  float sq = EMath::emSqrt((1+dot)*2);
  qOut.x = vtxCross.x / sq;
  qOut.y = vtxCross.y / sq;
  qOut.z = vtxCross.z / sq;
  qOut.w = sq / 2.0f;
}

void EMath::quaternionMulti(const Quaternion & qA, const Quaternion & qB, Quaternion & qOut) {
  qOut.w = qA.w*qB.w - qA.x*qB.x - qA.y*qB.y - qA.z*qB.z; 
  qOut.x = qA.w*qB.x + qA.x*qB.w + qA.y*qB.z - qA.z*qB.y; 
  qOut.y = qA.w*qB.y - qA.x*qB.z + qA.y*qB.w + qA.z*qB.x; 
  qOut.z = qA.w*qB.z + qA.x*qB.y - qA.y*qB.x + qA.z*qB.w; 
}

float EMath::quadratic(float f0, float f1, float f2, float t) {
  // this was a beizer curve
  // float t1 = 1.0f - t;
  // return t1*t1*f0 + 2.0f*t*t1*f1 + t*t*f2;
  float df1 = f1 - f0;
  float df2 = f2 - f1;
  float ddf = df2 - df1;
  return f0 + t*df1 + 0.5f*t*(t-1.0f)*ddf;
}

float EMath::cubic(float f0, float f1, float f2, float f3, float t) {
  float df1 = f1 - f0;
  float df2 = f2 - f1;
  float df3 = f3 - f2;
  float ddf1 = df2 - df1;
  float ddf2 = df3 - df2;
  float dddf = ddf2 - ddf1;
  return f0 + t*df1 + 0.5*t*(t-1.0f)*ddf1 + 0.166667f*t*(t-1.0f)*(t-2.0f)*dddf;
}