void CSpline::CSplineInit(int x[], int y[], int n, int grain, float tension)
{
int i,np;
np = n;
QPoint jd[100];
QPoint *knots;
allCount = 0;
lengthList[0] = 0;
for(i=1;i<=np;i++)
{
jd[i].setX(x[i-1]);
jd[i].setY(y[i-1]);
}
jd[0].setX(x[0]);
jd[0].setY(y[0]);
jd[np+1].setX(x[np-1]);
jd[np+1].setY(y[np-1]);
np=np+2;
// for(i=0;i<=np;i++)
// {
// jd[i].setX(x[i-1]);
// jd[i].setY(y[i-1]);
// }
knots = jd;
CubicSpline(np,knots,grain,tension);
}
// [TODO] Comment/Cleanup
void CubicSpline::CalculateCubicSpline(uint32 n, Array<TransferControlPoint> &v, Array<CubicSpline> &cubic)
{
if (n) {
// From: http://graphicsrunner.blogspot.com/2009/01/volume-rendering-102-transfer-functions.html
float *gamma = new float[n + 1];
float *delta = new float[n + 1];
float *D = new float[n + 1];
// We need to solve the equation
// * taken from: http://mathworld.wolfram.com/CubicSpline.html
// [2 1 ] [D[0]] [3(v[1] - v[0]) ]
// |1 4 1 | |D[1]| |3(v[2] - v[0]) |
// | 1 4 1 | | . | = | . |
// | ..... | | . | | . |
// | 1 4 1| | . | |3(v[n] - v[n-2])|
// [ 1 2] [D[n]] [3(v[n] - v[n-1])]
// by converting the matrix to upper triangular.
// The D[i] are the derivatives at the control points.
// This builds the coefficients of the left matrix
gamma[0] = 1.0f / 2.0f;
for (uint32 i=1; i<n; i++)
gamma[i] = 1.0f / ((4 * 1.0f) - gamma[i - 1]);
gamma[n] = 1.0f / ((2 * 1.0f) - gamma[n - 1]);
delta[0] = 3 * (v[1].GetValue() - v[0].GetValue()) * gamma[0];
for (uint32 i=1; i<n; i++)
delta[i] = (3 * (v[i + 1].GetValue() - v[i - 1].GetValue()) - delta[i - 1]) * gamma[i];
delta[n] = (3 * (v[n].GetValue() - v[n - 1].GetValue()) - delta[n - 1]) * gamma[n];
D[n] = delta[n];
for (int i=n-1; i>= 0; i--)
D[i] = delta[i] - gamma[i] * D[i + 1];
// Now compute the coefficients of the cubics
cubic.Clear();
for (uint32 i=0; i<n; i++)
cubic.Add(CubicSpline(v[i].GetValue(), D[i], 3*(v[i + 1].GetValue() - v[i].GetValue()) - 2*D[i] - D[i + 1], 2*(v[i].GetValue() - v[i + 1].GetValue()) + D[i] + D[i + 1]));
delete [] gamma;
delete [] delta;
delete [] D;
}
}
RealModel::RealModel(Config cfg) {
/* Read prior power spectrum from file */
if(!cfg_has_key(cfg, "pkfile")) {
fprintf(stderr, "RealModel: must set config option 'pkfile'\n");
return;
}
const char* pkfile = cfg_get(cfg, "pkfile");
pk = CubicSpline(pkfile);
/* Determine bands */
Band b;
if(cfg_has_key(cfg, "bands")) {
/* Read bands directly */
vector<double> kvals(100);
cfg_get_array_double(cfg, "bands", 100, &kvals[0]);
if((kvals.size() % 2) != 0) {
fprintf(stderr, "RealModel: odd number of kvals\n");
kvals.pop_back();
}
for(int n = 0; n < (int)kvals.size()/2; n++) {
b.min = kvals[2*n];
b.max = kvals[2*n+1];
bands.push_back(b);
}
Nbands = bands.size();
}
else if(cfg_has_keys(cfg, "Nbands,kmin,kmax")) {
/* Use regularly spaced bands */
Nbands = cfg_get_int(cfg, "Nbands");
double kmin = cfg_get_double(cfg, "kmin");
double kmax = cfg_get_double(cfg, "kmax");
/* (Assume linearly spaced bands for now) */
for(int n = 0; n < Nbands; n++) {
b.min = kmin + n*(kmax - kmin)/Nbands;
b.max = kmin + (n+1)*(kmax - kmin)/Nbands;
bands.push_back(b);
}
}
else {
fprintf(stderr, "RealModel: k-bands not specified in configuration\n");
return;
}
}
/*
* OpenGL (GLUT) calls this routine to display the scene
*/
void display()
{
int k,i;
Point S[NMAX];
// Erase the window and the depth buffer
glClear(GL_COLOR_BUFFER_BIT);
// Enable vertex generation
glEnable(GL_MAP1_VERTEX_3);
// Draw and label points
glColor3f(1,1,1);
glPointSize(5);
glBegin(GL_POINTS);
for (k=0;k<n;k++)
glVertex2f(P[k].x,P[k].y);
glEnd();
for (k=0;k<n;k++)
{
glRasterPos2d(P[k].x,P[k].y);
Print("P%d",k);
}
// Draw curve when we have enough points
switch (mode)
{
// Continuous Bezier
case 0:
for (k=0;k<n-3;k+=3)
{
glColor3f(1,1,0);
glMap1d(GL_MAP1_VERTEX_3,0.0,1.0,3,4,(void*)(P+k));
glMapGrid1f(m,0.0,1.0);
glEvalMesh1(GL_LINE,0,m);
}
break;
// Smooth Bezier
case 1:
// First four
if (n>=4)
{
glColor3f(1,1,0);
glMap1d(GL_MAP1_VERTEX_3,0.0,1.0,3,4,(void*)P);
glMapGrid1f(m,0.0,1.0);
glEvalMesh1(GL_LINE,0,m);
}
// Subsequent triples
for (k=3;k<n-2;k+=2)
{
Point r[4];
// P0, P2 and P3 are specified points
r[0] = P[k];
r[2] = P[k+1];
r[3] = P[k+2];
// P1 is computed by reflecting P2 from previous segment
r[1].x = 2*P[k].x-P[k-1].x;
r[1].y = 2*P[k].y-P[k-1].y;
r[1].z = 2*P[k].z-P[k-1].z;
// Draw curve
glColor3f(1,1,0);
glMap1d(GL_MAP1_VERTEX_3,0.0,1.0,3,4,(void*)r);
glMapGrid1f(m,0.0,1.0);
glEvalMesh1(GL_LINE,0,m);
// Draw reflected point in red
glColor3f(1,0,0);
glBegin(GL_POINTS);
glVertex2f(r[1].x,r[1].y);
glEnd();
glRasterPos2d(r[1].x,r[1].y);Print("R%d",k-1);
}
break;
// Interpolate 4 at a time
case 2:
for (k=0;k<n-3;k+=3)
{
Point r[4];
// Transform 4 data points to 4 control points
Pmult(Mi,P+k,r);
// Draw curve
glColor3f(1,1,0);
glMap1d(GL_MAP1_VERTEX_3,0.0,1.0,3,4,(void*)r);
glMapGrid1f(m,0.0,1.0);
glEvalMesh1(GL_LINE,0,m);
// Draw control points
glColor3f(1,0,0);
glBegin(GL_POINTS);
glVertex2f(r[1].x,r[1].y);
glVertex2f(r[2].x,r[2].y);
glEnd();
glRasterPos2d(r[1].x,r[1].y);Print("R%d",k+1);
glRasterPos2d(r[2].x,r[2].y);Print("R%d",k+2);
}
break;
// B Spline 4 at a time
case 3:
for (k=0;k<n-3;k++)
{
int j;
Point r[4];
// Transform 4 data points to 4 control points (note increment is 1)
Pmult(Ms,P+k,r);
// Draw curve
glColor3f(1,1,0);
glMap1d(GL_MAP1_VERTEX_3,0.0,1.0,3,4,(void*)r);
glMapGrid1f(m,0.0,1.0);
glEvalMesh1(GL_LINE,0,m);
// Draw control points
glColor3f(1,0,0);
glBegin(GL_POINTS);
for (j=0;j<4;j++)
glVertex2f(r[j].x,r[j].y);
glEnd();
}
break;
// Cubic Natural Spline
case 4:
// Calculate (x,y,z) splines
CubicSpline((void*)P,(void*)S,0,n);
CubicSpline((void*)P,(void*)S,1,n);
CubicSpline((void*)P,(void*)S,2,n);
// Draw entire curve
glColor3f(1,1,0);
glBegin(GL_LINE_STRIP);
for (k=0;k<n-1;k++)
{
// Cardinal point
glVertex2d(P[k].x,P[k].y);
// Increment between k and k+1
for (i=1;i<m;i++)
{
double f = (double)i/m;
double g = 1-f;
double f2 = (f*f*f-f)/6;
double g2 = (g*g*g-g)/6;
double x = f*P[k+1].x + g*P[k].x + f2*S[k+1].x + g2*S[k].x;
double y = f*P[k+1].y + g*P[k].y + f2*S[k+1].y + g2*S[k].y;
double z = f*P[k+1].z + g*P[k].z + f2*S[k+1].z + g2*S[k].z;
glVertex3d(x,y,z);
}
}
// Last cardinal point
glVertex2d(P[n-1].x,P[n-1].y);
glEnd();
break;
default:
break;
}
// Display parameters
glColor3f(1,1,1);
glWindowPos2i(5,5);
Print(text[mode]);
if (n<NMAX)
Print(" Click to add point\n");
else
Print(" Click to start new curve\n");
// Render the scene and make it visible
ErrCheck("display");
glFlush();
glutSwapBuffers();
}
