// Smooth Flow Camera based on Pascals Triangle.
// Author - James Scandrett
// 22nd July 2005

#declare camloc = <-30,4,-30>;
#declare order = 14;
#declare camwid = 2;

// {Power, P1, P2, P3, P4, P5, P6, P7, P8},
#declare pascals = array[14][15] {
    {1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {3, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {4, 1, 3, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {5, 1, 4, 6, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
    {6, 1, 5, 10, 10, 5, 1, 0, 0, 0, 0, 0, 0, 0, 0},
    {7, 1, 6, 15, 20, 15, 6, 1, 0, 0, 0, 0, 0, 0, 0},
    {8, 1, 7, 21, 35, 35, 21, 7, 1, 0, 0, 0, 0, 0, 0},
    {9, 1, 8, 28, 56, 70, 56, 28, 8, 1, 0, 0, 0, 0, 0},
    {10, 1, 9, 36, 84, 126, 126, 84, 36, 9, 1, 0, 0, 0, 0},
    {11, 1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1, 0, 0, 0},
    {12, 1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1, 0, 0},
    {13, 1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1, 0},
    {14, 1, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1},
    }

#declare cpoint = 19;
#declare camlocs = array[14][4] {
    {carpos[cpoint * 0][1],  carpos[cpoint * 0][2], carpos[cpoint * 0][3], 5},
    {carpos[cpoint * 1][1],  carpos[cpoint * 1][2], carpos[cpoint * 1][3], 5},
    {carpos[cpoint * 2][1],  carpos[cpoint * 2][2], carpos[cpoint * 2][3], 5},
    {carpos[cpoint * 3][1],  carpos[cpoint * 3][2], carpos[cpoint * 3][3], 5},
    {carpos[cpoint * 4][1],  carpos[cpoint * 4][2], carpos[cpoint * 4][3], 15},
    {carpos[cpoint * 5][1],  carpos[cpoint * 5][2], carpos[cpoint * 5][3], 15},
    {carpos[cpoint * 6][1],  carpos[cpoint * 6][2], carpos[cpoint * 6][3], 15},
    {carpos[cpoint * 7][1],  carpos[cpoint * 7][2], carpos[cpoint * 7][3], 15},
    {carpos[cpoint * 8][1],  carpos[cpoint * 8][2], carpos[cpoint * 8][3], 15},
    {carpos[cpoint * 9][1],  carpos[cpoint * 9][2], carpos[cpoint * 9][3], 15},
    {carpos[cpoint * 10][1],  carpos[cpoint * 10][2], carpos[cpoint * 10][3], 5},
    {carpos[cpoint * 11][1],  carpos[cpoint * 11][2], carpos[cpoint * 11][3], 5},
    {carpos[cpoint * 12][1],  carpos[cpoint * 12][2], carpos[cpoint * 12][3], 5},
    {carpos[cpoint * 13][1],  carpos[cpoint * 13][2], carpos[cpoint * 13][3], 5},
  }


#declare transit = clock / finaltime;

// Assume pow(0,0) = 1

#declare point = 0;
#declare sumxpoint = 0;
#declare sumypoint = 0;
#declare sumzpoint = 0;
#declare sumcangle = 0;
#while (point < order)
    #if (clock = 0)
        #declare xpoint = pascals[order - 1][point + 1] * camlocs[point][0] * pow(1 - transit,order - (point + 1));
        #declare ypoint = pascals[order - 1][point + 1] * camlocs[point][1] * pow(1 - transit,order - (point + 1));
        #declare zpoint = pascals[order - 1][point + 1] * camlocs[point][2] * pow(1 - transit,order - (point + 1));
        #declare cangle = pascals[order - 1][point + 1] * camlocs[point][3] * pow(1 - transit,order - (point + 1));
      #else
        #declare xpoint = pascals[order - 1][point + 1] * camlocs[point][0] * pow(transit,point) * pow(1 - transit,order - (point + 1));
        #declare ypoint = pascals[order - 1][point + 1] * camlocs[point][1] * pow(transit,point) * pow(1 - transit,order - (point + 1));
        #declare zpoint = pascals[order - 1][point + 1] * camlocs[point][2] * pow(transit,point) * pow(1 - transit,order - (point + 1));
        #declare cangle = pascals[order - 1][point + 1] * camlocs[point][3] * pow(transit,point) * pow(1 - transit,order - (point + 1));
    #end

    #declare sumxpoint = sumxpoint + xpoint;
    #declare sumypoint = sumypoint + ypoint;
    #declare sumzpoint = sumzpoint + zpoint;
    #declare sumcangle = sumcangle + cangle;
    #declare point = point + 1;
#end

#declare camlook = <sumxpoint, sumypoint, sumzpoint>;
#declare camseparation = VDist (camloc, camlook);
#declare camangle = degrees(atan(sumcangle/camseparation));

camera {
  location camloc
  look_at camlook
  angle abs(camangle)
}