Function SphRatio

general.cpp:582–603

// proportion (0.0-1.0) along the great circle path between them.

void SphRatio(real lon1, real lat1, real lon2, real lat2, real rRatio,
  real *lon, real *lat)
{
  real x1, y1, z1, x2, y2, z2, x, y, z, len, ang, adj, ang2;

  SphToRec(1.0, lon1, lat1, &x1, &y1, &z1);
  SphToRec(1.0, lon2, lat2, &x2, &y2, &z2);
  if (rRatio != 0.5) {
    // Bisecting an arc is easy, however other proportions require extra math.
    len = RLength3(x2 - x1, y2 - y1, z2 - z1) / 2.0;
    ang = RAsinD(len);
    adj = 1.0 / RTanD(ang);
    rRatio = (rRatio - 0.5) / 0.5;
    ang2 = rRatio * ang;
    rRatio = adj * RTanD(ang2);
    rRatio = (rRatio / 2.0) + 0.5;
  }
  x = x1 + (x2 - x1) * rRatio;
  y = y1 + (y2 - y1) * rRatio;
  z = z1 + (z2 - z1) * rRatio;
  RecToSph3(x, y, z, lon, lat);
}


// Given a planet and sign, determine whether: The planet rules the sign or