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NURBSSurface.cpp
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NURBSSurface.cpp
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// This file is part of NURBS, a simple NURBS library.
// github repo: https://github.com/aijm/NURBS
// Copyright (C) 2018 Jiaming Ai <[email protected]>
#include "NURBSSurface.h"
/*input format:
_order : // _order(0):u direction; _order(1): v direction
_controlP: _controlP[i] represents u direction control point ,matrix (m+1) by 3 or 4
v
|
_controlP[n]: | P_0n P_1n ... P_mn
_controlP[i]: | ...
_controlP[1]: | P_01 P_11 ... P_m1
_controlP[0]: | P_00 P_10 ... P_m0
------------------------> u
_uknots : u_0,u_1,...,u_(m+u_order)
_vknots : v_0,v_1,...,v_(n+v_order)
_isRational: */
NURBSSurface::NURBSSurface(
VectorXi _order,
vector<MatrixXd> _controlP,
VectorXd _uknots,
VectorXd _vknots,
bool _isRational)
{
// pass and check the parameters of NURBS surface
u_order = _order(0);
v_order = _order(1);
v_num = _controlP.size() - 1;
assert(u_order >= 1 && v_order >= 1 && v_num >= 1);
u_num = _controlP[0].rows() - 1;
assert(_uknots.size() == u_num + u_order + 1 && _vknots.size() == v_num + v_order + 1);
assert(u_num >= u_order - 1 && v_num >= v_order - 1);
dimension = _controlP[0].cols(); // the dimension of control point 2 or 3 or 4(weighted)
uknots = _uknots;
vknots = _vknots;
controlPw = _controlP;
isRational = _isRational;
if (isRational) { assert(dimension == 4); }
else { assert(dimension == 3); }
}
// load
bool NURBSSurface::loadNURBS(string name){
ifstream in(name);
if(!in){
return false;
}
char sep;
dimension=3;
in>> isRational;
in>> u_num >> v_num;
in>> u_order >> v_order;
in>> dimension;
controlPw = vector<MatrixXd>(v_num+1);
for(int i=0;i<controlPw.size();i++){
controlPw[i] = MatrixXd(u_num+1,dimension);
}
for(int i=0;i<controlPw.size();i++){
for(int j=0;j<=u_num;j++){
for(int k=0;k<dimension;k++){
in>> controlPw[i](j,k);
}
in>>sep;
}
}
uknots = VectorXd(u_num+u_order+1);
vknots = VectorXd(v_num+v_order+1);
for(int i=0;i<uknots.size();i++){
in>>uknots(i);
}
for(int i=0;i<vknots.size();i++){
in>>vknots(i);
}
return true;
}
// save
bool NURBSSurface::saveNURBS(string name){
if(controlPw.size()==0){
cout<< "nothing to save!"<<endl;
return false;
}
if(isRational){
name+=".cptw";
}else{
name+=".cpt";
}
ofstream out(name);
if(!out){
return false;
}
IOFormat outputFmt(4, 0, " ", " ", "", ",");
out<< isRational<<endl;
out<< u_num << " " <<v_num<<endl;
out<< u_order << " "<< v_order<<endl;
out<< controlPw[0].cols()<<endl;
for(int i=0;i<controlPw.size();i++){
for(int j=0;j<=u_num;j++){
out<<controlPw[i].row(j).format(outputFmt);
}
out<<endl;
}
out<<uknots.transpose()<<endl;
out<<vknots.transpose();
return true;
}
// find the knot interval of t by binary searching
int NURBSSurface::find_ind(double t, int k, int n, const VectorXd& knots)
{
if (t == knots(n + 1)) return n;
int low = 0;
int high = n + k;
assert(t >= knots(low) && t < knots(high));
int mid = (low + high) / 2;
while (t < knots(mid) || t >= knots(mid + 1))
{
if (t < knots(mid)) high = mid;
else low = mid;
mid = (low + high) / 2;
}
return mid;
}
// calculate coordinate of curve point with parameter u & v
MatrixXd NURBSSurface::eval(double u, double v)
{
//Calculating the Control Points of U-direction Isoparametric Line
MatrixXd v_controlP(v_num + 1, dimension);
for (int i = 0; i <= v_num; i++)
{
v_controlP.row(i) = eval(u, controlPw[i], uknots);
}
return eval(v, v_controlP, vknots); // Calculating the coordinate of parameter v
}
MatrixXd NURBSSurface::eval(
double t,
const MatrixXd &_controlP,
const VectorXd &knots)
{
int n = _controlP.rows() - 1;
int k = knots.size() - _controlP.rows();
/*if (t<knots(k - 1) || t>knots(n + 1)) {*/
//cout << "t: " << t << ", left: " << knots(k - 1) << ", right: " << knots(n + 1) << endl;
/*}*/
assert(t>=knots(k-1) && t<=knots(n+1));
// find the knot interval of t by binary searching
int L = find_ind(t, k, n, knots); //[t_L,t_(L+1)]
// P_(L-k+1),..,P_L control the interval [t_L,t_(L+1)]
MatrixXd temp = _controlP.block(L - k + 1, 0, k, _controlP.cols());
for (int r = 1; r <= k - 1; r++)
for (int i = L - k + 1 + r; i <= L; i++)
{
double factor = (t - knots(i)) / (knots(i + k - r) - knots(i));
int start = i - (L - k + 1 + r);
temp.row(start) = (1.0 - factor)*temp.row(start) + factor*temp.row(start + 1);
}
MatrixXd curvePoint = temp.row(0);
return curvePoint;
}
// knot insertion
bool NURBSSurface::insert(double s, char dir){
assert(dir=='u' || dir=='v');
if(dir=='u'){
for(int i=0;i<controlPw.size();i++){
NURBSCurve nurbs(u_num,u_order,controlPw[i],uknots,isRational);
nurbs.insert(s);
controlPw[i]=nurbs.controlPw;
if (i == controlPw.size() - 1) {
uknots = nurbs.knots;
u_num = nurbs.n;
}
}
return true;
}else if(dir=='v'){
vector<MatrixXd> new_controlPw(controlPw.size()+1);
for (int i = 0; i < new_controlPw.size(); i++) {
new_controlPw[i] = MatrixXd(u_num + 1, controlPw[0].cols());
}
MatrixXd v_controlPw(v_num+1,controlPw[0].cols());
for(int i=0;i<=u_num;i++){
for(int j=0;j<=v_num;j++){
v_controlPw.row(j) = controlPw[j].row(i);
}
NURBSCurve nurbs(v_num,v_order,v_controlPw,vknots,isRational);
nurbs.insert(s);
for(int k=0;k<new_controlPw.size();k++){
new_controlPw[k].row(i) = nurbs.controlPw.row(k);
}
if (i == u_num) {
vknots = nurbs.knots;
v_num = nurbs.n;
}
}
controlPw = new_controlPw;
return true;
}else{
cout<< "please input dir as u or v!"<<endl;
return false;
}
}
// kont insertion
bool NURBSSurface::insert(double s, double t){
if(insert(s,'u') && insert(t,'v')){
return true;
}
return false;
}
// draw controlpolygon
void NURBSSurface::drawControlPolygon(igl::opengl::glfw::Viewer &viewer){
//plot control points and control polygon
//plot control points
for (int i = 0; i < controlP.size(); i++)
{
viewer.data().add_points(
controlP[i],
Eigen::RowVector3d(1, 1, 1));
}
// plot control polygon
for (int j = 0; j <= v_num; j++)
for (int i = 0; i <= u_num; i++)
{
if (i != u_num) {
viewer.data().add_edges(
controlP[j].row(i),
controlP[j].row(i + 1),
Eigen::RowVector3d(1, 1, 1));
}
if (j != v_num) {
viewer.data().add_edges(
controlP[j].row(i),
controlP[j + 1].row(i),
Eigen::RowVector3d(1, 1, 1));
}
}
}
// draw NURBS surface
void NURBSSurface::drawSurface(igl::opengl::glfw::Viewer &viewer, double resolution){
// cut apart the parameter domain
double u_low = uknots(u_order - 1);
double u_high = uknots(u_num + 1);
const int uspan = (u_high - u_low) / resolution;
double u_resolution = (u_high - u_low) / uspan;
double v_low = vknots(v_order - 1);
double v_high = vknots(v_num + 1);
const int vspan = (v_high - v_low) / resolution;
double v_resolution = (v_high - v_low) / vspan;
mesh_V = MatrixXd((uspan + 1)*(vspan + 1), 3);
mesh_F = MatrixXi(2 * uspan*vspan, 3);
// discretize NURBS Surface into triangular mesh(V,F) in libigl mesh structure
// calculate mesh_V
for (int j = 0; j <= vspan; j++)
for (int i = 0; i <= uspan; i++)
{
RowVectorXd curvePoint = eval(u_low + i*u_resolution, v_low + j*v_resolution).row(0);
//cout << "curvepoint: " << curvePoint << endl;
if (isRational) { mesh_V.row(j*(uspan + 1) + i) = curvePoint.hnormalized(); }
else { mesh_V.row(j*(uspan + 1) + i) = curvePoint; }
}
for (int j = 0; j<vspan; j++)
for (int i = 0; i < uspan; i++)
{
int V_index = j*(uspan + 1) + i;
int F_index = 2 * j*uspan + 2 * i;
mesh_F.row(F_index) << V_index, V_index + 1, V_index + uspan + 1;
mesh_F.row(F_index + 1) << V_index + uspan + 1, V_index + 1, V_index + uspan + 2;
}
viewer.data().set_mesh(mesh_V, mesh_F);
}
void NURBSSurface::draw(
igl::opengl::glfw::Viewer &viewer,
bool showpolygon,bool showsurface,
double resolution){
if(controlP.size()!=controlPw.size()){
controlP = vector<MatrixXd>(controlPw.size());
}
if(isRational){
for(int i=0;i<controlP.size();i++){
controlP[i] = controlPw[i].rowwise().hnormalized();
}
}else{
controlP = controlPw;
}
if(showpolygon){
drawControlPolygon(viewer);
viewer.core.align_camera_center(controlP[controlP.size()/2]);
}
if(showsurface){
drawSurface(viewer,resolution);
viewer.core.align_camera_center(mesh_V,mesh_F);
}
}
// surface skinning: order is the same for every curves
void NURBSSurface::skinning(const vector<NURBSCurve> &curves,igl::opengl::glfw::Viewer &viewer){
assert(curves.size()>1);
isRational = curves[0].isRational;
// count knots of every curve
vector<map<double,int>> curve_knots(curves.size());
for(int i=0;i<curves.size();i++){
for(int j=0;j<curves[i].knots.size();j++){
if(curve_knots[i].find(curves[i].knots(j))==curve_knots[i].end()){
curve_knots[i][curves[i].knots(j)] = 1;
}else{
curve_knots[i][curves[i].knots(j)] += 1;
}
}
}
// compute merge knots
map<double, int> merge_knots;
for (int i = 0; i < curve_knots.size(); i++) {
for (auto it = curve_knots[i].begin(); it != curve_knots[i].end(); it++) {
if (merge_knots.find(it->first) == merge_knots.end()) {
merge_knots[it->first] = it->second;
}
else if (merge_knots[it->first] < it->second) {
merge_knots[it->first] = it->second;
}
}
}
cout << "merge_knots:\n" << endl;
for (auto it = merge_knots.begin(); it != merge_knots.end(); it++) {
cout << it->first << ", " << it->second << endl;
}
// change every curve to 3D and rational
vector<NURBSCurve> new_curves = curves;
// for every curve, insert knots to make curve knots compatible
for (int i = 0; i < curve_knots.size(); i++) {
for (auto it = merge_knots.begin(); it != merge_knots.end(); it++) {
int insert_num = 0;
if (curve_knots[i].find(it->first) == curve_knots[i].end()) {
insert_num = it->second;
}
else {
insert_num = it->second - curve_knots[i][it->first];
}
// insert
for (int j = 0; j < insert_num; j++) {
new_curves[i].insert(it->first);
}
}
}
for (int i = 0; i < new_curves.size(); i++) {
cout << "curve " << i << ": " << new_curves[i].knots.transpose() << endl;
new_curves[i].draw(viewer);
}
vknots = new_curves[0].knots;
//cout << "after insert knots: " << vknots.transpose() << endl;
// compute u-direction knot vector
VectorXd curves_param = VectorXd::Zero(new_curves.size());
v_num = new_curves[0].n;
v_order = new_curves[0].k;
dimension = new_curves[0].controlPw.cols();
//u_num = new_curves.size() - 1;
u_order = 4;
int curve_num = curves.size() - 1;
u_num = curve_num + 2;
for (int i = 0; i <= v_num; i++) {
MatrixXd u_cpts(curve_num + 1, dimension);
for (int j = 0; j <= curve_num; j++) {
u_cpts.row(j) = new_curves[j].controlPw.row(i);
}
curves_param += NURBSCurve::parameterize(u_cpts);
}
curves_param /= (v_num + 1);
uknots = VectorXd::Zero(curve_num + 7); // u_0,u_0,u_0, u_0,...,u_K, u_K,u_K,u_K
uknots.block(3, 0, curve_num + 1, 1) = curves_param;
uknots(curve_num + 6) = 1.0; uknots(curve_num + 5) = 1.0; uknots(curve_num + 4) = 1.0;
//uknots << 0, 0, 0, 0, 2.0/12, 4.0/12, 5.0/12, 7.0/12, 8.0/12, 11.0/12, 1, 1, 1, 1;
cout << "uknots: " << uknots.transpose() << endl;
// interpolate points to get the NURBS skinning surface control points
controlPw = vector<MatrixXd>(v_num + 1);
for (int i = 0; i < controlPw.size(); i++) {
controlPw[i] = MatrixXd(u_num + 1, dimension);
}
for (int i = 0; i <= v_num; i++) {
MatrixXd u_ctps = MatrixXd::Zero(curve_num + 1, dimension);
for (int j = 0; j <= curve_num; j++) {
u_ctps.row(j) = new_curves[j].controlPw.row(i);
}
//viewer.data().add_points(u_ctps, RowVector3d(0, 1, 0));
NURBSCurve nurbs;
nurbs.interpolate(u_ctps, uknots);
//nurbs.interpolate(u_ctps);
nurbs.draw(viewer, false, true);
controlPw[i] = nurbs.controlPw;
}
cout << "skinning finished!" << endl;
}