void cone (Scene &scene, int nseg, const Trafo& P, const ColorB* color)
//
// Adds a unit cone of radius 1 in x-y-plane with base at z = 1 and
// tip at z = -1 to the scene. The mantle will be approximated by
// nseg segments. The cone can be scaled by an arbitrary
// transformation matrix P.
// Optionally a color (precisely a pointer to ColorB) can be given to set the
// color of the surface facets (defaults to NULL).
//
{
int i,j;
double theta = 0, dtheta = 2*M_PI/nseg;
Vertex& tip = scene.AddVertex( P*Vertex(0,0,-1) );
Facet& base = scene.AddFacet(nseg);
base(nseg-1) = &scene.AddVertex( P*Vertex(1,0,1) );
if (color) {
base.SetColor(*color);
base[nseg-1].SetColor(*color);
tip.SetColor(*color);
}
for (i = 0, j = nseg-1; i < nseg; j = i++) {
theta += dtheta;
if (i != nseg-1)
base(i) = &scene.AddVertex( P*Vertex(cos(theta),sin(theta),1) );
Facet& mantle = scene.AddFacet(3);
mantle(2) = base(j);
mantle(1) = base(i);
mantle(0) = &tip;
if (color) {
mantle.SetColor(*color);
base[i].SetColor(*color);
}
}
}
void MpIcosahedron (Scene &scene, const Trafo &P, const ColorB* color)
{
const short faces[20][3] = {
{1, 3, 2}, {1, 4, 3}, {1, 5, 4}, {1, 6, 5},
{1, 2, 6}, {2, 3, 7}, {3, 4, 8}, {4, 5, 9},
{5, 6, 10}, {6, 2, 11}, {7, 3, 8}, {8, 4, 9},
{9, 5, 10}, {10, 6, 11}, {11, 2, 7}, {7, 8, 12},
{8, 9, 12}, {9, 10, 12}, {10, 11, 12}, {11, 7, 12}};
const float g = 0.5*(1+sqrt(5.0)), g1 = g-1, p = 0.52573111211913360602567f;
const float edges[12][3] = {{ 0, 0, g1/p }, { 2*p, 0, p },
{ g1*p, 1, p }, { -g*p, g1, p },
{ -g*p,-g1, p }, { g1*p, -1, p },
{ g*p, g1, -p }, { -g1*p, 1, -p },
{ -2*p, 0, -p }, { -g1*p, -1, -p },
{ g*p,-g1, -p }, { 0, 0, -g1/p }};
Vertex *v[12];
int i;
for (i = 0; i < 12; i++) {
v[i] = &scene.AddVertex( P * Vertex(edges[i]) );
if (color) v[i]->SetColor(*color);
}
for (i = 0; i < 20; i++) {
Facet &f = scene.AddFacet(3);
for (int j = 0; j < 3; j++)
f(j) = v[faces[i][2-j]-1];
if (color) f.SetColor(*color);
}
}
void stellate (Scene &body, float height)
//
// Adds starlike jags to every facet of the body. The tip
// of a jag is placed in the given height over the center
// of the facet.
//
{
float nx,ny,nz,nk,nn,cx,cy,cz,h;
Vertex* tip;
Facet* f;
int i,j,n;
Scene stella;
for (f = body.TheFacets(); f; f = f->NextFacet() ) {
// calculate the normal form and the center of the facet
f->Normal(nx,ny,nz,nk);
f->Center(cx,cy,cz);
// normalization of the normal vector to unit length
nn = hypot(nx,ny,nz);
// check if facet is degenerate
if (nn == 0) continue;
// add the tip vertex of the jag
h = height / nn;
tip = &stella.AddVertex( cx+h*nx, cy+h*ny, cz+h*nz );
// add three-sided facets for each side of the jag
n = f->GetNumVertices();
for (i = 0, j = n-1; i < n; j = i++) {
Facet& s = stella.AddFacet(3);
s(0) = &stella.AddVertex( *(*f)(j) );
s(1) = &stella.AddVertex( *(*f)(i) );
s(2) = tip;
}
}
// now clear the original
body.Remove();
// and add the stellated body instead (duplicate vertices are now removed)
body.AddScene(stella,Identity);
}
void MpOctahedron (Scene &scene, const Trafo &P, const ColorB* color)
{
const short faces[8][3] = {{1, 2, 3}, {1, 3, 5}, {1, 5, 6}, {1, 6, 2},
{2, 6, 4}, {2, 4, 3}, {4, 6, 5}, {3, 4, 5}};
const float t = sqrt(2.0);
const float edges[6][3] = {{0, 0, t}, { t, 0, 0}, {0, t, 0},
{0, 0, -t}, {-t, 0, 0}, {0, -t, 0}};
Vertex *v[6];
int i;
for (i = 0; i < 6; i++) {
v[i] = &scene.AddVertex( P * Vertex(edges[i]) );
if (color) v[i]->SetColor(*color);
}
for (i = 0; i < 8; i++) {
Facet &f = scene.AddFacet(3);
for (int j = 0; j < 3; j++)
f(j) = v[faces[i][j]-1];
if (color) f.SetColor(*color);
}
}
void MpCube (Scene &scene, const Trafo &P, const ColorB* color)
{
const float edge[8][3] = {
{ 1, 1, 1},
{ 1,-1, 1},
{ 1,-1,-1},
{ 1, 1,-1},
{-1, 1, 1},
{-1,-1, 1},
{-1,-1,-1},
{-1, 1,-1}
};
const signed char face[6][4] = {
{ 0, 1, 2, 3},
{ 0, 3, 7, 4},
{ 0, 4, 5, 1},
{ 2, 6, 7, 3},
{ 1, 5, 6, 2},
{ 4, 7, 6, 5}
};
Vertex* v[8];
int i;
// create 8 new vertices in this scene transforming them using P
for (i = 0; i < 8; i++) {
v[i] = &scene.AddVertex( P * Vertex(edge[i]) );
if (color) v[i]->SetColor(*color);
}
// create 6 new facets in this scene
for (i = 0; i < 6; i++) {
// add a new 4-sided facet to this scene
Facet &f = scene.AddFacet(4);
// link the edges in this facet to the corresponding vertices
for (int j = 0; j < 4; j++)
f(j) = v[face[i][j]];
// optionally set color
if (color) f.SetColor(*color);
}
}
void Scene::Polygon (short n, float *x, float *y, float *z,
long color, short mode)
{
// check for valid range of vertices
if (n < 3 || n > MaxVertices)
Matpack.Error("Scene::Polygon: number of vertices (%d) not within 3..%d",
n,MaxVertices);
Scene scn; // local scene copying the original settings
scn.CopySettingsFrom(*this);
Facet& f = scn.AddFacet(n); // add one facet to our local scene
for (int i = 0; i < n; i++) f(i) = &scn.AddVertex(x[i],y[i],z[i]);
scn.ClipBoxScene(); // clip at box
scn.ObserveFacets(); // do observer transformation
scn.ClipViewScene(); // clip at viewport
scn.ProjectFacets(); // do perspective projection
Facet* cf; // find the clipped facet
for (cf = scn.facets; cf && cf->clipped; cf = cf->next);
if ( cf ) { // something left after clipping ?
for (int i = 0; i < n; i++) // copy projected vertices to polygon array
pix[i] = (*cf)[i].p;
Polygon(n,pix,color,mode); // draw the facet within the original scene
}
}
int MpWarpMatrixToSphere (Scene& S,
Matrix& H,
Vector& Pol, Vector& Azm,
double r,
const Trafo& T,
int facet_culling,
bool periodic,
bool south_pole_cap,
double h_south,
bool north_pole_cap,
double h_north,
const ColorMap& cmap,
double cmin, double cmax,
int PolStride, int AzmStride)
{
int a,p,ncmap = 0;
double x,y,z,pol,hr,sp,cp;
double dz,scale = 0.0;
bool usecolormap;
int p1 = H.Rlo(), p2 = H.Rhi(),
a1 = H.Clo(), a2 = H.Chi();
// check matrix and vector dimensions
if (p1 != Pol.Lo() || p2 != Pol.Hi() ||
a1 != Azm.Lo() || a2 != Azm.Hi())
return 1;
// check edge line stride values
if (PolStride <= 0 || AzmStride <= 0) return 4;
// evaluate facet culling flag
int addFront = (facet_culling == Scene::Front) || (facet_culling == false),
addBack = (facet_culling == Scene::Back) || (facet_culling == false);
// number of facets in polar and azimuthal direction
int np = p2-p1+1,
na = a2-a1+1;
// nothing that can be drawn
if (np < 2 || na < 2) return 3;
// pointer to vertices in two consecutive slices
Vertex **top,**bot=0,**act;
// allocate auxilliary storage
if ( !(top = new Vertex*[na]) || !(bot = new Vertex*[na]) )
Matpack.Error("WarpMatrixToSphere: vector allocation failure");
// check if a colormap should be used
if (cmap) {
usecolormap = true;
dz = cmax-cmin;
ncmap = cmap.Size()-1;
scale = (dz == 0.0) ? 0 : ncmap/dz;
} else
usecolormap = false;
// Precompute sines and cosines of the azimuthal angles for the
// sake of high performance
Vector s,c;
s = Sin(Azm);
c = Cos(Azm);
// loop through latitudes (polar angle)
for ( p = p1, act = top; p <= p2; p++ ) {
pol = Pol(p);
sp = sin(pol);
cp = cos(pol);
// loop through longitudes (azimuthal angle)
for ( a = a1; a <= a2; a++ ) {
// warp transformation to sphere
hr = H(p,a) + r;
x = hr * cp * s(a);
y = -hr * cp * c(a);
z = hr * sp;
// add vertices to scene storing a pointer to it
// (and apply the global transformation)
act[a-a1] = &S.AddVertex( T * Vertex((float)x,(float)z,(float)y) );
// set the vertex color
if (usecolormap) {
int cen = int((H(p,a)-cmin)*scale);
MpForceRange(cen,0,ncmap);
act[a-a1]->SetColor(cmap[cen]);
}
}
// first slice or last slice - add triangles to create pole caps
if ( (south_pole_cap && p == p1) || (north_pole_cap && p == p2) ) {
int addF = false,
addB = false;
double h = 0.0;
if (p == p1 && south_pole_cap) {
addF = addBack;
addB = addFront;
h = -(r + h_south);
} else if (p == p2 && north_pole_cap) {
addF = addFront;
addB = addBack;
h = r + h_north;
}
// add vertices to scene storing a pointer to it
// (and apply the global transformation)
Vertex* v = &S.AddVertex(T * Vertex((float)0,(float)h,(float)0) );
// set the vertex color
if (usecolormap) {
int cen = int((h-cmin)*scale);
MpForceRange(cen,0,ncmap);
v->SetColor(cmap[cen]);
}
for (a = 0; a < na-1; a++) {
// add with reverse orientation
if (addB) {
Facet &f = S.AddFacet(3);
f(0) = v;
f(1) = act[a];
f(2) = act[a+1];
SetEdgeLineVisibility(f,a,AzmStride,p-p1,PolStride,true);
// set color of facet according to colormap
if (usecolormap) {
int cen = int((H(p,a+a1)-cmin)*scale);
MpForceRange(cen,0,ncmap);
f.SetFrontColor(cmap[cen]);
f.SetBackColor(cmap[cen]);
}
}
// add with normal orientation
if (addF) {
Facet &f = S.AddFacet(3);
f(2) = act[a];
f(1) = act[a+1];
f(0) = v;
SetEdgeLineVisibility(f,a,AzmStride,p-p1,PolStride);
// set color of facet according to colormap
if (usecolormap) {
int cen = int((H(p,a+a1)-cmin)*scale);
MpForceRange(cen,0,ncmap);
f.SetFrontColor(cmap[cen]);
f.SetBackColor(cmap[cen]);
}
}
}
// close sphere periodically in azimuthal direction
if (periodic) {
// add with opposite orientation
if (addB) {
Facet &f = S.AddFacet(3);
f(0) = v;
f(1) = act[na-1];
f(2) = act[0];
SetEdgeLineVisibility(f,a,AzmStride,p-p1,PolStride,true);
// set color of facet according to colormap
if (usecolormap) {
int cen = int((H(p,a1)-cmin)*scale);
MpForceRange(cen,0,ncmap);
f.SetFrontColor(cmap[cen]);
f.SetBackColor(cmap[cen]);
}
}
// add with normal orientation
if (addF) {
Facet &f = S.AddFacet(3);
f(2) = act[na-1];
f(1) = act[0];
f(0) = v;
SetEdgeLineVisibility(f,a,AzmStride,p-p1,PolStride);
// set color of facet according to colormap
if (usecolormap) {
int cen = int((H(p,a1)-cmin)*scale);
MpForceRange(cen,0,ncmap);
f.SetFrontColor(cmap[cen]);
f.SetBackColor(cmap[cen]);
}
}
}
} // if ((south_pole_cap && p == p1) || (north_pole_cap && p == p2)) //
// normal case: add quadrilaterals with top and bottom slices
if (p != p1) {
for (a = 0; a < na-1; a++) {
// add with reverse orientation
if (addBack) {
Facet &f = S.AddFacet(4);
f(0) = top[a];
f(1) = bot[a];
f(2) = bot[a+1];
f(3) = top[a+1];
SetEdgeLineVisibility(f,a,AzmStride,p-p1,PolStride,true);
// set color of facet according to colormap
if (usecolormap) {
int cen = int((H(p,a+a1)-cmin)*scale);
MpForceRange(cen,0,ncmap);
f.SetFrontColor(cmap[cen]);
f.SetBackColor(cmap[cen]);
}
}
// add with normal orientation
if (addFront) {
Facet &f = S.AddFacet(4);
f(3) = top[a];
f(2) = bot[a];
f(1) = bot[a+1];
f(0) = top[a+1];
SetEdgeLineVisibility(f,a,AzmStride,p-p1,PolStride);
// set color of facet according to colormap
if (usecolormap) {
int cen = int((H(p,a+a1)-cmin)*scale);
MpForceRange(cen,0,ncmap);
f.SetFrontColor(cmap[cen]);
f.SetBackColor(cmap[cen]);
}
}
}
// close sphere periodically in azimuthal direction
if (periodic) {
// add with reverse orientation
if (addBack) {
Facet &f = S.AddFacet(4);
f(0) = top[na-1];
f(1) = bot[na-1];
f(2) = bot[0];
f(3) = top[0];
SetEdgeLineVisibility(f,na-1,AzmStride,p-p1,PolStride,true);
// set color of facet according to colormap
if (usecolormap) {
int cen = int((H(p,a1)-cmin)*scale);
MpForceRange(cen,0,ncmap);
f.SetFrontColor(cmap[cen]);
f.SetBackColor(cmap[cen]);
}
}
// add with normal orientation
if (addFront) {
Facet &f = S.AddFacet(4);
f(3) = top[na-1];
f(2) = bot[na-1];
f(1) = bot[0];
f(0) = top[0];
SetEdgeLineVisibility(f,na-1,AzmStride,p-p1,PolStride);
// set color of facet according to colormap
if (usecolormap) {
int cen = int((H(p,a1)-cmin)*scale);
MpForceRange(cen,0,ncmap);
f.SetFrontColor(cmap[cen]);
f.SetBackColor(cmap[cen]);
}
}
}
} // if (p == p1) //
// swap top with bot pointers
act = bot;
bot = top;
top = act;
} // for ( p = p1, ... ) //
// remove auxilliary storage
delete bot;
delete top;
// no problems occured
return 0;
}
void MpSurfaceBands (Scene& S, const Matrix& z,
int direction, double width,
const ColorMap& cmap, double cmin, double cmax)
{
Vertex *v0,*v1,*v2,*v3;
double scale = 0.0;
bool usecolormap;
// the width of the bands
MpForceRange(width,1e-3,1.0);
// 0.5 is half the mesh unit
width /= 2;
int ncmap = 0,
nx = z.Rows(),
ny = z.Cols();
// check arguments
if ( nx < 0 || ny < 0 ) return; // nothing to draw
// check if a colormap should be used
if (cmap) {
usecolormap = true;
ncmap = cmap.Size()-1;
double dz = cmax - cmin;
scale = (dz == 0.0) ? 0.0 : ncmap/dz;
} else
usecolormap = false;
switch (direction) {
case RowBandsGrid:
case RowBands:
{
for ( int y = z.Clo(); y <= z.Chi(); y++ ) {
int x = z.Rlo();
v0 = &S.AddVertex(y+width,z[x][y],x);
v1 = &S.AddVertex(y-width,z[x][y],x);
if (usecolormap) {
int c = int((z[x][y]-cmin)*scale);
if (c > ncmap)
c = ncmap;
else if (c < 0)
c = 0;
const ColorB &col = cmap[c];
v0->SetColor(col);
v1->SetColor(col);
}
for ( ; x < z.Rhi(); x++) {
// create facet
Facet &f = S.AddFacet(4);
v2 = &S.AddVertex(y-width,z[x+1][y],x+1);
v3 = &S.AddVertex(y+width,z[x+1][y],x+1);
f(0) = v0;
f(1) = v1;
f(2) = v2;
f(3) = v3;
v0 = v3;
v1 = v2;
// set edge line mask
if (direction == RowBands)
if (x == z.Rlo())
f.SetEdgeLineVisibility(Facet::Individual,0xb); // (1011=0xb)
else if (x == z.Rhi()-1)
f.SetEdgeLineVisibility(Facet::Individual,0xe); // (1110=0xe)
else
f.SetEdgeLineVisibility(Facet::Individual,0xa); // (1010=0xa)
// set color of facet according to colormap
if (usecolormap) {
float cx,cy,cz;
f.Center(cy,cz,cx);
int c = int((cz-cmin)*scale);
if (c > ncmap)
c = ncmap;
else if (c < 0)
c = 0;
const ColorB ¢er = cmap[c];
f.SetColor(center);
c = int((z[x+1][y]-cmin)*scale);
if (c > ncmap)
c = ncmap;
else if (c < 0)
c = 0;
const ColorB &col = cmap[c];
v2->SetColor(col);
v3->SetColor(col);
}
}
}
break;
}
case ColumnBandsGrid:
case ColumnBands:
{
for ( int x = z.Rlo(); x <= z.Rhi(); x++ ) {
int y = z.Clo();
v1 = &S.AddVertex(y,z[x][y],x-width);
v2 = &S.AddVertex(y,z[x][y],x+width);
if (usecolormap) {
int c = int((z[x][y]-cmin)*scale);
const ColorB &col = cmap[c];
if (c > ncmap)
c = ncmap;
else if (c < 0)
c = 0;
v1->SetColor(col);
v2->SetColor(col);
}
for ( ; y < z.Chi(); y++) {
// create facet
Facet &f = S.AddFacet(4);
v0 = &S.AddVertex(y+1,z[x][y+1],x-width);
v3 = &S.AddVertex(y+1,z[x][y+1],x+width);
f(0) = v0;
f(1) = v1;
f(2) = v2;
f(3) = v3;
v1 = v0;
v2 = v3;
// set edge line mask
if (direction == ColumnBands)
if (y == z.Clo())
f.SetEdgeLineVisibility(Facet::Individual,0x7); // (0111=0x7)
else if (y == z.Chi()-1)
f.SetEdgeLineVisibility(Facet::Individual,0xd); // (1101=0xd)
else
f.SetEdgeLineVisibility(Facet::Individual,0x5); // (0101=0x5)
// set color of facet according to colormap
if (usecolormap) {
float cx,cy,cz;
f.Center(cy,cz,cx);
int c = int((cz-cmin)*scale);
if (c > ncmap)
c = ncmap;
else if (c < 0)
c = 0;
const ColorB ¢er = cmap[c];
f.SetColor(center);
c = int((z[x][y+1]-cmin)*scale);
if (c > ncmap)
c = ncmap;
else if (c < 0)
c = 0;
const ColorB &col = cmap[c];
v0->SetColor(col);
v3->SetColor(col);
}
}
}
break;
}
default:
Matpack.Error("MpSurfaceBands: Illegal value for direction argument");
break;
}
}