public void TransformToPolar(ref Vector3f p, ref GeoPolar3d delta)
{
// Figure out angle in x-y plane.
delta.Lat = Math.Atan2(p.X, p.Y);
// Then the "height" angle.
var xy = p.Y * p.Y + p.X * p.X;
var dZ = p.Z - Camera.HeightOffset;
delta.Lon = Math.Atan2(dZ, Math.Sqrt(xy));
delta.Height = Math.Sqrt(xy + dZ * dZ);
}
// Project takes some 3D coordinates and transform them
// in 2D coordinates using the transformation matrix
// It also transform the same coordinates and the normal to the vertex
// in the 3D world
public VertexProj Project(ref Vertex vertex, ref GeoPolar3d polar)
{
return(new VertexProj
{
Coordinates = new Vector3fProj(
GetXIndexFromLatRad(polar.Lat),
GetYIndexFromLonRad(polar.Lon),
(float)polar.Height),
Normal = vertex.Normal,
WorldCoordinates = vertex.Coordinates,
TextureCoordinates = vertex.TextureCoordinates
});
}
// The main method of the engine that re-compute each vertex projection
// during each frame
public static void RenderInto(RenderState state, params Mesh[] meshes)
{
Vector3f buffv = new Vector3f();
GeoPolar3d polarA = new GeoPolar3d();
GeoPolar3d polarB = new GeoPolar3d();
GeoPolar3d polarC = new GeoPolar3d();
Vector3f midAB = new Vector3f();
Vector3f midAC = new Vector3f();
Vector3f midBC = new Vector3f();
GeoPolar3d polarMidAB = new GeoPolar3d();
GeoPolar3d polarMidAC = new GeoPolar3d();
GeoPolar3d polarMidBC = new GeoPolar3d();
foreach (Mesh mesh in meshes)
{
for (int faceIndex = 0; faceIndex < mesh.Faces.Length; faceIndex++)
{
var face = mesh.Faces[faceIndex];
state.TransformToPolar(ref mesh.Vertices[face.A].Coordinates, ref polarA);
state.TransformToPolar(ref mesh.Vertices[face.B].Coordinates, ref polarB);
state.TransformToPolar(ref mesh.Vertices[face.C].Coordinates, ref polarC);
// TODO: Skip this triangle if it contains the point we are at?
// Also need to maintain the triangle topology that can be distrupted by
// discontinuities in arctan.
Vector3f.Avg(ref mesh.Vertices[face.A].Coordinates, ref mesh.Vertices[face.B].Coordinates, ref midAB);
Vector3f.Avg(ref mesh.Vertices[face.A].Coordinates, ref mesh.Vertices[face.C].Coordinates, ref midAC);
Vector3f.Avg(ref mesh.Vertices[face.B].Coordinates, ref mesh.Vertices[face.C].Coordinates, ref midBC);
state.TransformToPolar(ref midAB, ref polarMidAB);
state.TransformToPolar(ref midAC, ref polarMidAC);
state.TransformToPolar(ref midBC, ref polarMidBC);
bool abOK = CheckBetween(polarA.Lat, polarMidAB.Lat, polarB.Lat);
bool acOK = CheckBetween(polarA.Lat, polarMidAC.Lat, polarC.Lat);
bool bcOK = CheckBetween(polarB.Lat, polarMidBC.Lat, polarC.Lat);
if (!(abOK && acOK && bcOK))
{
if (abOK)
{
polarC.Lat += (polarC.Lat < polarA.Lat ? 1 : -1) * 2 * Math.PI;
}
if (acOK)
{
polarB.Lat += (polarB.Lat < polarA.Lat ? 1 : -1) * 2 * Math.PI;
}
if (bcOK)
{
polarA.Lat += (polarA.Lat < polarC.Lat ? 1 : -1) * 2 * Math.PI;
}
}
// Now check if any triangles need to be shifted by multiple of 2Pi to move into view
// First, shift neg
while (
polarA.Lat - 2 * Math.PI >= state.Camera.MinAngleRad ||
polarB.Lat - 2 * Math.PI >= state.Camera.MinAngleRad ||
polarC.Lat - 2 * Math.PI >= state.Camera.MinAngleRad)
{
polarC.Lat -= 2 * Math.PI;
polarB.Lat -= 2 * Math.PI;
polarA.Lat -= 2 * Math.PI;
}
while (
polarA.Lat <= state.Camera.MaxAngleRad ||
polarB.Lat <= state.Camera.MaxAngleRad ||
polarC.Lat <= state.Camera.MaxAngleRad)
{
var pixelA = state.Project(ref mesh.Vertices[face.A], ref polarA);
var pixelB = state.Project(ref mesh.Vertices[face.B], ref polarB);
var pixelC = state.Project(ref mesh.Vertices[face.C], ref polarC);
DrawTriangle(state, ref pixelA, ref pixelB, ref pixelC, mesh.Texture, ref buffv);
polarC.Lat += 2 * Math.PI;
polarB.Lat += 2 * Math.PI;
polarA.Lat += 2 * Math.PI;
}
}
}
}