/// <summary>
/// A direction interpolated between the two given directions.
/// </summary>
/// <param name="slon">Start longitude.</param>
/// <param name="slat">Start latitude.</param>
/// <param name="elon">End longitude.</param>
/// <param name="elat">End latitude.</param>
/// <param name="t">Interpolation.</param>
/// <param name="lon">Output longitude.</param>
/// <param name="lat">Output latitude.</param>
public virtual void InterpolateDirection(double slon, double slat, double elon, double elat, double t, ref double lon, ref double lat)
{
var s = new Vector3d(Math.Cos(slon) * Math.Cos(slat), Math.Sin(slon) * Math.Cos(slat), Math.Sin(slat));
var e = new Vector3d(Math.Cos(elon) * Math.Cos(elat), Math.Sin(elon) * Math.Cos(elat), Math.Sin(elat));
var v = (s * (1.0 - t) + e * t).Normalized();
lat = Functions.Safe_Asin(v.z);
lon = Math.Atan2(v.y, v.x);
}
public override void Move(Vector3d oldp, Vector3d p, double speed)
{
var oldPosition = oldp.Normalized();
var position = p.Normalized();
var oldlat = Functions.Safe_Asin(oldPosition.z);
var oldlon = Math.Atan2(oldPosition.y, oldPosition.x);
var lat = Functions.Safe_Asin(position.z);
var lon = Math.Atan2(position.y, position.x);
base.position.X -= (lon - oldlon) * speed * Math.Max(1.0, worldPosition.Magnitude() - Radius);
base.position.Y -= (lat - oldlat) * speed * Math.Max(1.0, worldPosition.Magnitude() - Radius);
}
public override void MoveForward(double distance)
{
// NOTE : co - x; so - y; ca - z; sa - w;
var oa = CalculatelongitudeLatitudeVector(position.X, position.Y);
var po = new Vector3d(oa.x * oa.z, oa.y * oa.z, oa.w) * Radius;
var px = new Vector3d(-oa.y, oa.x, 0.0);
var py = new Vector3d(-oa.x * oa.w, -oa.y * oa.w, oa.z);
var pd = (po - px * Math.Sin(position.Phi) * distance + py * Math.Cos(position.Phi) * distance).Normalized();
position.X = Math.Atan2(pd.y, pd.x);
position.Y = Functions.Safe_Asin(pd.z);
}
public override double Interpolate(Position from, Position to, double t)
{
var s = new Vector3d(Math.Cos(from.X) * Math.Cos(from.Y), Math.Sin(from.X) * Math.Cos(from.Y), Math.Sin(from.Y));
var e = new Vector3d(Math.Cos(to.X) * Math.Cos(to.Y), Math.Sin(to.X) * Math.Cos(to.Y), Math.Sin(to.Y));
var distance = Math.Max(Functions.Safe_Acos(s.Dot(e)) * Radius, 1e-3);
t = Math.Min(t + Math.Min(0.1, 5000.0 / distance), 1.0);
var T = 0.5 * Math.Atan(4.0 * (t - 0.5)) / Math.Atan(4.0 * 0.5) + 0.5;
var W = 10.0;
InterpolateDirection(from.X, from.Y, to.X, to.Y, T, ref position.X, ref position.Y);
InterpolateDirection(from.Phi, from.Theta, to.Phi, to.Theta, T, ref position.Phi, ref position.Theta);
position.Distance = from.Distance * (1.0 - t) + to.Distance * t + distance * (Math.Exp(-W * (t - 0.5) * (t - 0.5)) - Math.Exp(-W * 0.25));
return(t);
}
public override Matrix4x4d LocalToDeformedDifferential(Vector3d localPoint, bool clamp = false)
{
if (!Functions.IsFinite(localPoint.x) || !Functions.IsFinite(localPoint.y) || !Functions.IsFinite(localPoint.z))
{
return(Matrix4x4d.identity);
}
var point = new Vector2d(localPoint);
if (clamp)
{
point.x = point.x - Math.Floor((point.x + R) / (2.0 * R)) * 2.0 * R;
point.y = point.y - Math.Floor((point.y + R) / (2.0 * R)) * 2.0 * R;
}
var r2 = R * R;
var l = point.x * point.x + point.y * point.y + r2;
var c0 = 1.0 / Math.Sqrt(l);
var c1 = c0 * R / l;
return(new Matrix4x4d((point.y * point.y + r2) * c1, -point.x * point.y * c1, point.x * c0, R * point.x * c0,
-point.x * point.y * c1, (point.x * point.x + r2) * c1, point.y * c0, R * point.y * c0,
-point.x * R * c1, -point.y * R * c1, R * c0, (r2) * c0, 0.0, 0.0, 0.0, 1.0));
}
public override void UpdateNode()
{
TerrainMaterial.renderQueue = (int)ParentBody.RenderQueue + ParentBody.RenderQueueOffset;
// NOTE : Body shape dependent...
LocalToWorld = Matrix4x4d.ToMatrix4x4d(ParentBody.transform.localToWorldMatrix) * FaceToLocal;
TangentFrameToWorld = new Matrix3x3d(LocalToWorld.m[0, 0], LocalToWorld.m[0, 1], LocalToWorld.m[0, 2],
LocalToWorld.m[1, 0], LocalToWorld.m[1, 1], LocalToWorld.m[1, 2],
LocalToWorld.m[2, 0], LocalToWorld.m[2, 1], LocalToWorld.m[2, 2]);
LocalToCamera = GodManager.Instance.View.WorldToCameraMatrix * LocalToWorld;
LocalToScreen = GodManager.Instance.View.CameraToScreenMatrix * LocalToCamera;
var invLocalToCamera = LocalToCamera.Inverse();
DeformedCameraPosition = invLocalToCamera * Vector3d.zero;
DeformedFrustumPlanes = Frustum3d.GetFrustumPlanes(LocalToScreen); // NOTE : Extract frustum planes from LocalToScreen matrix...
LocalCameraPosition = Deformation.DeformedToLocal(DeformedCameraPosition);
DeformedLocalToTangent = Deformation.DeformedToTangentFrame(GodManager.Instance.View.WorldCameraPosition) * LocalToWorld * Deformation.LocalToDeformedDifferential(LocalCameraPosition);
var m = Deformation.LocalToDeformedDifferential(LocalCameraPosition, true);
var left = DeformedFrustumPlanes[0].xyz.Normalized();
var right = DeformedFrustumPlanes[1].xyz.Normalized();
var fov = (float)Functions.Safe_Acos(-left.Dot(right));
SplitDistance = SplitFactor * Screen.width / 1024.0f * Mathf.Tan(40.0f * Mathf.Deg2Rad) / Mathf.Tan(fov / 2.0f);
DistanceFactor = (float)Math.Max(new Vector3d(m.m[0, 0], m.m[1, 0], m.m[2, 0]).Magnitude(), new Vector3d(m.m[0, 1], m.m[1, 1], m.m[2, 1]).Magnitude());
if (SplitDistance < 1.1f || SplitDistance > 128.0f || !Functions.IsFinite(SplitDistance))
{
SplitDistance = 1.1f;
}
var splitDistanceBlending = SplitDistance + 1.0f;
DistanceBlending = new Vector2(splitDistanceBlending, 2.0f * SplitDistance - splitDistanceBlending);
// Initializes data structures for horizon occlusion culling
if (UseHorizonCulling && LocalCameraPosition.z <= TerrainQuadRoot.ZMax)
{
var deformedDirection = invLocalToCamera * Vector3d.forward;
var localDirection = (Deformation.DeformedToLocal(deformedDirection) - LocalCameraPosition).Normalized();
LocalCameraDirection = new Matrix2x2d(localDirection.y, -localDirection.x, -localDirection.x, -localDirection.y);
for (var i = 0; i < HORIZON_SIZE; ++i)
{
Horizon[i] = float.NegativeInfinity;
}
}
if (ParentBody.UpdateLOD)
{
TerrainQuadRoot.UpdateLOD();
}
SetUniforms(TerrainMaterial);
}
