public static Vector2 ComputeGlobalTextureCoords(LatLon latlon, Ellipsoid ellipsoid)
{
Vector3 pos = LatLonToPosition(latlon, ellipsoid);
Vector3 normal = ellipsoid.GeodeticSurfaceNormal(pos);
return(ComputeGlobalTextureCoordinate(normal));
}
// TODO may want to treat the poles as a tri-fan instead of a tri-strip, unless we do something more sophisticated to deal with the singularity at the poles.
public Mesh GenerateSector(LatLonBoundingBox bbox, Ellipsoid ellipsoid, int numberOfStackPartitions, int numberOfSlicePartitions)
{
Mesh mesh = new Mesh();
LatLonBoundingBox geometryBBox = bbox.Clamp();
float deltaLat = geometryBBox.DeltaLat / numberOfStackPartitions;
float deltaLon = geometryBBox.DeltaLon / numberOfSlicePartitions;
// Create positions
int numberOfVertices = NumberOfVertices(numberOfStackPartitions, numberOfSlicePartitions);
List <Vector3> positions = new List <Vector3>(numberOfVertices);
// Generates geometry
for (int i = 0; i <= numberOfStackPartitions; i++)
{
float lat = i * deltaLat + geometryBBox.minLat;
// To avoid singularities at the poles, don't let the latitude quite reach 90 degrees
lat = Mathf.Clamp(lat, -90 + eps, 90 - eps);
// Phi is like latitude, but ranges from [0, pi]. Add 90 degrees and convert to radians to get phi.
float phi = (lat + 90f) * Mathf.Deg2Rad;
float sinPhi = Mathf.Sin(phi);
// Generate positions on Ellipsoid following Eq. 4.4 from "3D Engine Design for Virtual Globes":
// x = a cos(theta) sin(phi)
// y = a sin(theta) sing(phi)
// z = c cos(phi)
float xSinPhi = ellipsoid.Radii.x * sinPhi;
float ySinPhi = ellipsoid.Radii.y * sinPhi;
float zCosPhi = ellipsoid.Radii.z * Mathf.Cos(phi);
for (int j = 0; j <= numberOfSlicePartitions; j++)
{
float lon = j * deltaLon + geometryBBox.minLon;
float theta = lon * Mathf.Deg2Rad;
Vector3 pos = new Vector3(Mathf.Cos(theta) * xSinPhi, Mathf.Sin(theta) * ySinPhi, zCosPhi);
positions.Add(pos);
}
}
// Compute normals & texture coordinates
List <Vector3> normals = new List <Vector3>(numberOfVertices);
List <Vector2> uvs = new List <Vector2>(numberOfVertices);
for (int i = 0; i < positions.Count; i++)
{
Vector3 normal = ellipsoid.GeodeticSurfaceNormal(positions[i]);
normals.Add(normal);
uvs.Add(GetUvFromNormal(geometryBBox, bbox, ellipsoid, normal));
}
// Compute triangle indices
List <int> indices = new List <int>(NumberOfTriangles(numberOfSlicePartitions, numberOfStackPartitions) * 3);
// Generate a triangle strip for each row
for (int i = 0; i < numberOfStackPartitions; ++i)
{
int topRowOffset = i * (numberOfSlicePartitions + 1);
int bottomRowOffset = (i + 1) * (numberOfSlicePartitions + 1);
for (int j = 0; j < numberOfSlicePartitions; ++j)
{
indices.Add(bottomRowOffset + j);
indices.Add(bottomRowOffset + j + 1);
indices.Add(topRowOffset + j + 1);
indices.Add(bottomRowOffset + j);
indices.Add(topRowOffset + j + 1);
indices.Add(topRowOffset + j);
}
}
List <Color> colors = new List <Color>();
while (colors.Count < positions.Count)
{
colors.Add(Color.white);
}
// Generate skirt geometry to help hide cracks between adjacent levels of detail
AddSkirt(positions, normals, uvs, indices, numberOfStackPartitions, numberOfSlicePartitions, ellipsoid.Radii.x * skirtHeightFactor);
// Add colors verts for the skirt so we can fade it on if needed
while (colors.Count < positions.Count)
{
colors.Add(new Color(0, 0, 0, 0));
}
mesh.SetVertices(positions);
mesh.SetColors(colors);
mesh.uv = uvs.ToArray();
mesh.SetNormals(normals);
mesh.triangles = indices.ToArray();
return(mesh);
}
/// <summary>
/// Generate geometry for an ellipsoid globe.
/// </summary>
/// <param name="ellipsoid">Ellipsoid model to use to generate geometry</param>
/// <param name="numberOfStackPartitions">Number of horizontal tessellations</param>
/// <param name="numberOfSlicePartitions">Number of vertical tessellations</param>
/// <returns></returns>
// TODO this method is mostly redundant with GenerateSector. See if we can consolidate this code
public Mesh GenerateGlobe(Ellipsoid ellipsoid, int numberOfStackPartitions, int numberOfSlicePartitions)
{
Mesh mesh = new Mesh();
// Precompute sin/cos
float[] cosTheta = new float[numberOfSlicePartitions];
float[] sinTheta = new float[numberOfSlicePartitions];
for (int i = 0; i < numberOfSlicePartitions; ++i)
{
float theta = 2 * Mathf.PI * ((float)i / numberOfSlicePartitions);
cosTheta[i] = Mathf.Cos(theta);
sinTheta[i] = Mathf.Sin(theta);
}
// Create positions
List <Vector3> positions = new List <Vector3> {
new Vector3(0, 0, ellipsoid.Radii.z)
};
// Add top vertex
// For each latitude stack...
for (int i = 1; i < numberOfStackPartitions; ++i)
{
float phi = Mathf.PI * ((float)i / numberOfStackPartitions);
float sinPhi = Mathf.Sin(phi);
float xSinPhi = ellipsoid.Radii.x * sinPhi;
float ySinPhi = ellipsoid.Radii.y * sinPhi;
float zCosPhi = ellipsoid.Radii.z * Mathf.Cos(phi);
// For each longitude slice, add a position
for (int j = 0; j < numberOfSlicePartitions; ++j)
{
positions.Add(new Vector3(cosTheta[j] * xSinPhi, sinTheta[j] * ySinPhi, zCosPhi));
}
}
// Add bottom vertex
positions.Add(new Vector3(0, 0, -ellipsoid.Radii.z));
// Compute normals and UVs
List <Vector3> normals = new List <Vector3>();
List <Vector2> uvs = new List <Vector2>();
for (int i = 0; i < positions.Count; i++)
{
Vector3 normal = ellipsoid.GeodeticSurfaceNormal(positions[i]);
normals.Add(normal);
uvs.Add(GetUvFromNormal(null, null, ellipsoid, normal));
}
// Compute triangle indices
List <int> indices = new List <int>(NumberOfTriangles(numberOfSlicePartitions, numberOfStackPartitions) * 3);
// Triangle fan top row
for (int j = 1; j < numberOfSlicePartitions; ++j)
{
indices.Add(0);
indices.Add(j);
indices.Add(j + 1);
}
indices.Add(0);
indices.Add(numberOfStackPartitions);
indices.Add(1);
// Middle rows are triangle strips
for (int i = 0; i < numberOfStackPartitions - 2; ++i)
{
int topRowOffset = i * numberOfSlicePartitions + 1;
int bottomRowOffset = (i + 1) * numberOfSlicePartitions + 1;
for (int j = 0; j < numberOfSlicePartitions - 1; ++j)
{
indices.Add(bottomRowOffset + j);
indices.Add(bottomRowOffset + j + 1);
indices.Add(topRowOffset + j + 1);
indices.Add(bottomRowOffset + j);
indices.Add(topRowOffset + j + 1);
indices.Add(topRowOffset + j);
}
indices.Add(bottomRowOffset + numberOfSlicePartitions - 1);
indices.Add(bottomRowOffset);
indices.Add(topRowOffset);
indices.Add(bottomRowOffset + numberOfSlicePartitions - 1);
indices.Add(topRowOffset);
indices.Add(topRowOffset + numberOfSlicePartitions - 1);
}
// Triangle fan bottom row
int lastPosition = positions.Count - 1;
for (int j = lastPosition - 1; j > lastPosition - numberOfSlicePartitions; --j)
{
indices.Add(lastPosition);
indices.Add(j);
indices.Add(j - 1);
}
indices.Add(lastPosition);
indices.Add(lastPosition - numberOfSlicePartitions);
indices.Add(lastPosition - 1);
mesh.SetVertices(positions);
mesh.uv = uvs.ToArray();
mesh.SetNormals(normals);
mesh.triangles = indices.ToArray();
return(mesh);
}