@Override
protected void applyTransformation() {
// Everything here is stored in double precision because single precision floating point causes
// a major
// overflow. Number3D still stores internally in single precision so all the calculation will be
// done in here
// until Number3D is completely overhauled. Theory behind math in this method can be looked up
// easily on
// Wikipedia.
// Angle in radians (interpolated time from 0 to 1 results in radian angle 0 to 2PI)
double angle =
(mDirection == OrbitDirection.CLOCKWISE ? -1 : 1) * mAngle * mInterpolatedTime * PI_DIV_180;
// Calculate the distances of periapsis and apoapsis to the focal point.
double periapsisRadius = mPeriapsis.distanceTo(mFocalPoint);
double apoapsisRadius = periapsisRadius * (1 + mEccentricity) / (1 - mEccentricity);
// Get the apoapsis point which will be needed to calculate the center point of the ellipse.
// NOTE: Discard least significant digits after 8th decimal places to lower the computational
// error epsilon.
double uAx = (Math.round(mFocalPoint.x * 1e8) - Math.round(mPeriapsis.x * 1e8)) / 1e8;
double uAy = (Math.round(mFocalPoint.y * 1e8) - Math.round(mPeriapsis.y * 1e8)) / 1e8;
double uAz = (Math.round(mFocalPoint.z * 1e8) - Math.round(mPeriapsis.z * 1e8)) / 1e8;
double mod = Math.sqrt(uAx * uAx + uAy * uAy + uAz * uAz);
if (mod != 0 && mod != 1) {
mod = 1 / mod;
uAx *= mod;
uAy *= mod;
uAz *= mod;
}
double apoapsisDir_x = Math.round(uAx * apoapsisRadius * 1e8) / 1e8;
double apoapsisDir_y = Math.round(uAy * apoapsisRadius * 1e8) / 1e8;
double apoapsisDir_z = Math.round(uAz * apoapsisRadius * 1e8) / 1e8;
double apoapsisPos_x = Math.round((apoapsisDir_x + mFocalPoint.x) * 1e8) / 1e8;
double apoapsisPos_y = Math.round((apoapsisDir_y + mFocalPoint.y) * 1e8) / 1e8;
double apoapsisPos_z = Math.round((apoapsisDir_z + mFocalPoint.z) * 1e8) / 1e8;
// Midpoint between apoapsis and periapsis is the center of the ellipse.
double center_x = Math.round(((mPeriapsis.x + apoapsisPos_x) / 2) * 1e8) / 1e8;
double center_y = Math.round(((mPeriapsis.y + apoapsisPos_y) / 2) * 1e8) / 1e8;
double center_z = Math.round(((mPeriapsis.z + apoapsisPos_z) / 2) * 1e8) / 1e8;
// Calculate semiminor axis length.
double b = Math.sqrt(periapsisRadius * apoapsisRadius);
// Direction vector to periapsis from the center point and ascending node from the center point
double semimajorAxis_x = Math.round((mPeriapsis.x - center_x) * 1e8) / 1e8;
double semimajorAxis_y = Math.round((mPeriapsis.y - center_y) * 1e8) / 1e8;
double semimajorAxis_z = Math.round((mPeriapsis.z - center_z) * 1e8) / 1e8;
double unitSemiMajorAxis_x = semimajorAxis_x;
double unitSemiMajorAxis_y = semimajorAxis_y;
double unitSemiMajorAxis_z = semimajorAxis_z;
mod =
Math.sqrt(
semimajorAxis_x * semimajorAxis_x
+ semimajorAxis_y * semimajorAxis_y
+ semimajorAxis_z * semimajorAxis_z);
if (mod != 0 && mod != 1) {
mod = 1 / mod;
unitSemiMajorAxis_x *= mod;
unitSemiMajorAxis_y *= mod;
unitSemiMajorAxis_z *= mod;
}
// Translate normal vector to the center point.
Vector3 unitNormal = mNormal.clone();
unitNormal.normalize();
double uNx = Math.round(unitNormal.x * 1e8) / 1e8;
double uNy = Math.round(unitNormal.y * 1e8) / 1e8;
double uNz = Math.round(unitNormal.z * 1e8) / 1e8;
double normalCenter_x = center_x + uNx;
double normalCenter_y = center_y + uNy;
double normalCenter_z = center_z + uNz;
mod =
Math.sqrt(
normalCenter_x * normalCenter_x
+ normalCenter_y * normalCenter_y
+ normalCenter_z * normalCenter_z);
if (mod != 0 && mod != 1) {
mod = 1 / mod;
normalCenter_x *= mod;
normalCenter_y *= mod;
normalCenter_z *= mod;
}
// We can calculate the semiminor axis from unit vector of cross product of semimajor axis and
// the normal.
Vector3 unitSemiminorAxis =
Vector3.crossAndCreate(
new Vector3(unitSemiMajorAxis_x, unitSemiMajorAxis_y, unitSemiMajorAxis_z),
new Vector3(normalCenter_x, normalCenter_y, normalCenter_z));
Vector3 semiminorAxis = Vector3.scaleAndCreate(unitSemiminorAxis, (float) b);
// Parametric equation for ellipse in 3D space.
double x = center_x + (Math.cos(angle) * semimajorAxis_x) + (Math.sin(angle) * semiminorAxis.x);
double y = center_y + (Math.cos(angle) * semimajorAxis_y) + (Math.sin(angle) * semiminorAxis.y);
double z = center_z + (Math.cos(angle) * semimajorAxis_z) + (Math.sin(angle) * semiminorAxis.z);
mTransformable3D.setPosition((float) x, (float) y, (float) z);
}
