double vtIcoGlobe::AddSurfaceLineToMesh(vtGeomFactory *pMF, const DLine2 &line)
{
DPoint2 g1, g2;
DPoint3 p1, p2;
double scale = 1.0002;
int length = 0;
DMatrix3 rot3;
pMF->PrimStart();
int i, j, size = line.GetSize();
for (i = 0; i < size-1; i++)
{
g1 = line.GetAt(i);
g2 = line.GetAt(i+1);
// for each pair of points, determine how many more points are needed
// for a smooth arc
geo_to_xyz(1.0, g1, p1);
geo_to_xyz(1.0, g2, p2);
double angle = acos(p1.Dot(p2));
int segments = (int) (angle * 2000);
if (segments < 1)
segments = 1;
if (segments > 1)
{
// calculate the axis of rotation
DPoint3 cross = p1.Cross(p2);
cross.Normalize();
rot3.AxisAngle(cross, angle / segments);
}
// curved arc on great-circle path
for (j = 0; j < segments; j++)
{
FPoint3 fp = p1 * 1.0002;
pMF->AddVertex(fp);
length++;
if (j < segments-1)
{
rot3.Transform(p1, p2);
p1 = p2;
}
}
}
// last vertex
if (size > 1)
{
g2 = line.GetAt(size-1);
geo_to_xyz(1.0, g2, p2);
pMF->AddVertex(p2 * scale);
length++;
}
pMF->PrimEnd();
return 0.0;
}
/**
* Given a geographic coordinate (lon, lat), find the corresponding
* face, subface, and UVW coordinates on surface of the icosahedron.
*/
void DymaxIcosa::FindFaceUV(const DPoint2 &p, int &face, int &subface,
DPoint3 &uvw)
{
DPoint3 p3;
geo_to_xyz(p, p3);
FindFace(p3, face, subface);
FindUV(p3, face, uvw);
}
double vtIcoGlobe::AddSurfaceLineToMesh(vtGeomFactory *pMF, const DPoint2 &g1, const DPoint2 &g2)
{
// first determine how many points we should use for a smooth arc
DPoint3 p1, p2;
geo_to_xyz(1.0, g1, p1);
geo_to_xyz(1.0, g2, p2);
double dot = p1.Dot(p2);
double angle = acos(dot);
int points = (int) (angle * 3000);
if (points < 2)
points = 2;
pMF->PrimStart();
if (points == 2)
{
// simple case
pMF->AddVertex(p1*1.0002);
pMF->AddVertex(p2*1.0002);
}
else
{
// calculate the axis of rotation
DPoint3 cross = p1.Cross(p2);
cross.Normalize();
double angle_spacing = angle / (points-1);
DMatrix4 rot4;
rot4.AxisAngle(cross, angle_spacing);
DMatrix3 rot3;
rot3.SetByMatrix4(rot4);
// curved arc on great-circle path
for (int i = 0; i < points; i++)
{
FPoint3 fp = p1 * 1.0002;
pMF->AddVertex(fp);
rot3.Transform(p1, p2);
p1 = p2;
}
}
pMF->PrimEnd();
return angle;
}
/**
* Given a geographic coordinate (lon, lat), find the corresponding
* point on the surface of the icosahedron.
*/
void DymaxIcosa::GeoToFacePoint(const DPoint2 &p, int &face, int &subface,
DPoint3 &p_out)
{
DPoint3 p3, uvw;
geo_to_xyz(p, p3);
FindFace(p3, face, subface);
FindUV(p3, face, uvw);
p_out = m_face[face].base +
(m_face[face].vec_a * uvw.x) +
(m_face[face].vec_b * uvw.y);
}
void vtIcoGlobe::BuildSphericalPoints(GlobeLayer *glay, float fSize)
{
vtFeatureSet *feat = glay->m_pSet;
int i, j, size;
vtArray<FSphere> spheres;
size = feat->GetNumEntities();
spheres.SetSize(size);
vtFeatureSetPoint2D *pSetP2 = dynamic_cast<vtFeatureSetPoint2D*>(feat);
if (!pSetP2)
return;
DPoint2 p;
for (i = 0; i < size; i++)
{
pSetP2->GetPoint(i, p);
if (p.x == 0.0 && p.y == 0.0) // ignore some
continue;
FPoint3 loc;
geo_to_xyz(1.0, p, loc);
spheres[i].center = loc;
spheres[i].radius = fSize;
}
FPoint3 diff;
// volume of sphere, 4/3 PI r^3
// surface area of sphere, 4 PI r^2
// area of circle of sphere as seen from distance, PI r^2
int merges;
do {
merges = 0;
// Try merging overlapping points together, so that information
// is not lost in the overlap.
// To consider: do we combine the blobs based on their 2d radius,
// their 2d area, their 3d radius, or their 3d volume? See
// Tufte, http://www.edwardtufte.com/
// Implemented here: preserve 2d area
for (i = 0; i < size-1; i++)
{
for (j = i+1; j < size; j++)
{
if (spheres[i].radius == 0.0f || spheres[j].radius == 0.0f)
continue;
diff = spheres[i].center - spheres[j].center;
// if one sphere contains the center of the other
if (diff.Length() < spheres[i].radius ||
diff.Length() < spheres[j].radius)
{
// combine
float area1 = PIf * spheres[i].radius * spheres[i].radius;
float area2 = PIf * spheres[j].radius * spheres[j].radius;
float combined = (area1 + area2);
float newrad = sqrtf( combined / PIf );
// larger eats the smaller
if (area1 > area2)
{
spheres[i].radius = newrad;
spheres[j].radius = 0.0f;
}
else
{
spheres[j].radius = newrad;
spheres[i].radius = 0.0f;
}
merges++;
break;
}
}
}
}
while (merges != 0);
// Now create and place the little geometry objects to represent the
// point data.
#if 0
// create simple hemisphere mesh
int res = 6;
vtMesh *mesh = new vtMesh(osg::PrimitiveSet::TRIANGLE_STRIP, 0, res*res*2);
FPoint3 scale(1.0f, 1.0f, 1.0f);
mesh->CreateEllipsoid(scale, res, true);
#else
// create cylinder mesh instead
int res = 14;
int verts = res * 2;
vtMesh *mesh = new vtMesh(osg::PrimitiveSet::TRIANGLE_STRIP, 0, verts);
mesh->CreateCylinder(1.0f, 1.0f, res, true, false, false);
#endif
// use Area to show amount, otherwise height
bool bArea = true;
// create and place the geometries
size = spheres.GetSize();
for (i = 0; i < size; i++)
{
if (spheres[i].radius == 0.0f)
continue;
vtGeode *geode = new vtGeode;
geode->SetMaterials(m_coremats);
geode->AddMesh(mesh, m_yellow);
vtMovGeode *mgeom = new vtMovGeode(geode);
mgeom->setName("GlobeShape");
mgeom->PointTowards(spheres[i].center);
mgeom->RotateLocal(FPoint3(1,0,0), -PID2f);
mgeom->SetTrans(spheres[i].center);
if (bArea)
{
// scale just the radius of the cylinder
mgeom->Scale3(spheres[i].radius, 0.001f, spheres[i].radius);
}
else
{
// scale just the height of the cylinder
double area = PIf * spheres[i].radius * spheres[i].radius;
mgeom->Scale3(0.002f, (float)area*1000, 0.002f);
}
m_SurfaceGroup->addChild(mgeom);
glay->addChild(mgeom);
}
}
void geo_to_xyz(double radius, const DPoint2 &geo, FPoint3 &p)
{
DPoint3 dp;
geo_to_xyz(radius, geo, dp);
p = dp;
}
/**
* Given a geographic coordinate (lon, lat), find the corresponding
* dymaxion map coordinate, on the classic flattened dymaxion map.
* The output is unit-edge triangles, which means the whole output
* extents are x [0, 5.5] and y [0, 2.6].
*/
bool DymaxIcosa::GeoToDymax(const DPoint2 &geo, DPoint2 &dymax)
{
DPoint3 p3, uvw;
int face, subface;
geo_to_xyz(geo, p3);
FindFace(p3, face, subface);
FindUV(p3, face, uvw);
DPoint2 uv(uvw.x, uvw.y);
//assert(uv.x <= 1 && uv.y <= 1);
// Not exactly sure why we need to do this - apparently the UV are
// assuming a unit-radius, rather than unit-edge icosahedron
uv /= m_edge_length;
int a, b, c;
switch (face)
{
case 0:
a = 17; b = 22; c = 16; break;
case 1:
a = 17; b = 16; c = 10; break;
case 2:
a = 17; b = 10; c = 11; break;
case 3:
a = 17; b = 11; c = 18; break;
case 4:
a = 17; b = 23; c = 22; break;
case 5:
a = 21; b = 16; c = 22; break;
case 6:
a = 16; b = 15; c = 9; break;
case 7:
a = 9; b = 10; c = 16; break;
case 8:
if (subface == 4 || subface == 5)
{ a = 10; b = 1; c = 2; }
else
{ a = 10; b = 9; c = 1; }
break;
case 9:
a = 2; b = 11; c = 10; break;
case 10:
a = 11; b = 3; c = 12; break;
case 11:
a = 12; b = 18; c = 11; break;
case 12:
a = 18; b = 12; c = 19; break;
case 13:
a = 19; b = 24; c = 18; break;
case 14:
a = 25; b = 19; c = 20; break;
case 15:
if (subface == 0 || subface == 4 || subface == 5)
{ a = 13; b = 26; c = 20; }
else
{ a = 0; b = 9; c = 8; }
break;
case 16:
a = 0; b = 1; c = 9; break;
case 17:
a = 4; b = 12; c = 3; break;
case 18:
a = 13; b = 19; c = 12; break;
case 19:
a = 13; b = 20; c = 19; break;
default:
return false;
}
DPoint2 base = m_flatverts[a];
DPoint2 vec1 = m_flatverts[b] - base;
DPoint2 vec2 = m_flatverts[c] - base;
dymax = base + (vec1 * uv.x) + (vec2 * uv.y);
return true;
}
