cylinder.h
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#ifndef STIM_CYLINDER_H
#define STIM_CYLINDER_H
#include <iostream>
#include <stim/math/circle.h>
#include <stim/biomodels/centerline.h>
#include <stim/visualization/obj.h>
namespace stim
{
template<typename T>
class cylinder : public centerline<T> {
protected:
std::vector< stim::vec3<T> > U; //stores the array of U vectors defining the Frenet frame
std::vector< std::vector<T> > M; //stores a list of magnitudes for each point in the centerline (assuming mags[0] is the radius)
using stim::centerline<T>::findIdx;
//calculates the U values for each point to initialize the frenet frame
// this function assumes that the centerline has already been set
void init() {
U.resize(size()); //allocate space for the frenet frame vectors
stim::circle<T> c; //create a circle
stim::vec3<T> d0, d1;
for (size_t i = 0; i < size() - 1; i++) { //for each line segment in the centerline
c.rotate(d(i)); //rotate the circle to match that normal
U[i] = c.U; //save the U vector from the circle
}
U[size() - 1] = c.U; //for the last point, duplicate the final frenet frame vector
}
public:
using stim::centerline<T>::size;
using stim::centerline<T>::at;
cylinder() : centerline(){}
cylinder(centerline& c) : centerline(c) {
init();
}
cylinder(centerline& c, T r) : centerline(c) {
init();
add_mag(r);
}
//initialize a cylinder with a list of points and magnitude values
cylinder(centerline& c, std::vector<T> r) : centerline(c){
init();
add_mag(r);
}
///Returns magnitude i at the given length into the fiber (based on the pvalue).
///Interpolates the position along the line.
///@param l: the location of the in the cylinder.
///@param idx: integer location of the point closest to l but prior to it.
T m(T l, int idx, size_t i) {
T a = (l - L[idx]) / (L[idx + 1] - L[idx]);
T v2 = (M[idx][i] + (M[idx + 1][i] - M[idx][i])*a);
return v2;
}
///Returns the ith magnitude at the given p-value (p value ranges from 0 to 1).
///interpolates the radius along the line.
///@param pvalue: the location of the in the cylinder, from 0 (beginning to 1).
T m(T pvalue, unsigned i = 0) {
if (pvalue <= 0.0) return M[0][i];
if (pvalue >= 1.0) return M[size() - 1][i];
T l = pvalue*L[L.size() - 1];
int idx = findIdx(l);
return m(l, idx, i);
}
/// Returns the magnitude at the given index
/// @param i is the index of the desired point
/// @param m is the index of the magnitude value
T m(unsigned i, unsigned m) {
return M[i][m];
}
///adds a magnitude to each point in the cylinder
void add_mag(T val = 0) {
if (M.size() == 0) M.resize(size()); //if the magnitude vector isn't initialized, resize it to match the centerline
for (size_t i = 0; i < size(); i++) //for each point
M[i].push_back(val); //add this value to the magnitude vector at each point
}
//adds a magnitude based on a list of magnitudes for each point
void add_mag(std::vector<T> val) {
if (M.size() == 0) M.resize(size()); //if the magnitude vector isn't initialized, resize it to match the centerline
for (size_t i = 0; i < size(); i++) //for each point
M[i].push_back(val[i]); //add this value to the magnitude vector at each point
}
//sets the value of magnitude m at point i
void set_mag(size_t m, size_t i, T v) {
M[i][m] = v;
}
size_t nmags() {
if (M.size() == 0) return 0;
else return M[0].size();
}
///Returns a circle representing the cylinder cross section at point i
stim::circle<T> circ(size_t i, size_t m = 0) {
return stim::circle<T>(at(i), M[i][m], d(i), U[i]);
}
///Returns an OBJ object representing the cylinder with a radial tesselation value of N using magnitude m
stim::obj<T> OBJ(size_t N, size_t m = 0) {
stim::obj<T> out; //create an OBJ object
stim::circle<T> c0, c1;
std::vector< stim::vec3<T> > p0, p1; //allocate space for the point sets representing the circles bounding each cylinder segment
T u0, u1, v0, v1; //allocate variables to store running texture coordinates
for (size_t i = 1; i < size(); i++) { //for each line segment in the cylinder
c0 = circ(i - 1); //get the two circles bounding the line segment
c1 = circ(i);
p0 = c0.points(N); //get t points for each of the end caps
p1 = c1.points(N);
u0 = L[i - 1] / length(); //calculate the texture coordinate (u, v) where u runs along the cylinder length
u1 = L[i] / length();
for (size_t n = 1; n < N; n++) { //for each point in the circle
v0 = (double)(n-1) / (double)(N - 1); //v texture coordinate runs around the cylinder
v1 = (double)(n) / (double)(N - 1);
out.Begin(OBJ_FACE); //start a face (quad)
out.TexCoord(u0, v0);
out.Vertex(p0[n - 1][0], p0[n - 1][1], p0[n - 1][2]); //output the points composing a strip of quads wrapping the cylinder segment
out.TexCoord(u1, v0);
out.Vertex(p1[n - 1][0], p1[n - 1][1], p1[n - 1][2]);
out.TexCoord(u0, v1);
out.Vertex(p1[n][0], p1[n][1], p1[n][2]);
out.TexCoord(u1, v1);
out.Vertex(p0[n][0], p0[n][1], p0[n][2]);
out.End();
}
v0 = (double)(N - 2) / (double)(N - 1); //v texture coordinate runs around the cylinder
v1 = 1.0;
out.Begin(OBJ_FACE);
out.TexCoord(u0, v0);
out.Vertex(p0[N - 1][0], p0[N - 1][1], p0[N - 1][2]); //output the points composing a strip of quads wrapping the cylinder segment
out.TexCoord(u1, v0);
out.Vertex(p1[N - 1][0], p1[N - 1][1], p1[N - 1][2]);
out.TexCoord(u0, v1);
out.Vertex(p1[0][0], p1[0][1], p1[0][2]);
out.TexCoord(u1, v1);
out.Vertex(p0[0][0], p0[0][1], p0[0][2]);
out.End();
}
return out;
}
std::string str() {
std::stringstream ss;
size_t N = std::vector< stim::vec3<T> >::size();
ss << "---------[" << N << "]---------" << std::endl;
for (size_t i = 0; i < N; i++)
ss << std::vector< stim::vec3<T> >::at(i) << " r = " << M[i][0] << " u = " << U[i] << std::endl;
ss << "--------------------" << std::endl;
return ss.str();
}
/// Integrates a magnitude value along the cylinder.
/// @param m is the magnitude value to be integrated (this is usually the radius)
T integrate(size_t m = 0) {
T sum = 0; //initialize the integral to zero
T m0, m1; //allocate space for both magnitudes in a single segment
m0 = M[0][m]; //initialize the first point and magnitude to the first point in the cylinder
T len = L[1]; //allocate space for the segment length
for (unsigned p = 1; p < size(); p++) { //for every consecutive point in the cylinder
m1 = M[p][m];
if (p > 1) len = (L[p] - L[p - 1]); //calculate the segment length using the L array
sum += (m0 + m1) / (T)2.0 * len; //add the average magnitude, weighted by the segment length
m0 = m1; //move to the next segment by shifting points
}
return sum; //return the integral
}
/// Resamples the cylinder to provide a maximum distance of "spacing" between centerline points. All current
/// centerline points are guaranteed to exist in the new cylinder
/// @param spacing is the maximum spacing allowed between sample points
cylinder<T> resample(T spacing) {
cylinder<T> c = stim::centerline<T>::resample(spacing); //resample the centerline and use it to create a new cylinder
size_t nm = nmags(); //get the number of magnitude values in the current cylinder
if (nm > 0) { //if there are magnitude values
std::vector<T> magvec(nm, 0); //create a magnitude vector for a single point
c.M.resize(c.size(), magvec); //allocate space for a magnitude vector at each point of the new cylinder
}
T l, t;
for (size_t i = 0; i < c.size(); i++) { //for each point in the new cylinder
l = c.L[i]; //get the length along the new cylinder
t = l / length(); //calculate the parameter value along the new cylinder
for (size_t mag = 0; mag < nm; mag++) { //for each magnitude value
c.M[i][mag] = m(t, mag); //retrieve the interpolated magnitude from the current cylinder and store it in the new one
}
}
return c;
}
std::vector< stim::cylinder<T> > split(unsigned int idx){
unsigned N = size();
std::vector< stim::centerline<T> > LL;
LL.resize(2);
LL = (*this).centerline<T>::split(idx);
std::vector< stim::cylinder<T> > C(LL.size());
unsigned i = 0;
C[0] = LL[0];
C[0].M.resize(idx);
for( ; i < idx; i++){
//for(unsigned d = 0; d < 3; d++)
//C[0][i][d] = LL[0].c[i][d];
C[0].M[i] = M[i];
C[0].M[i].resize(1);
}
if(C.size() == 2){
C[1] = LL[1];
C[1].M.resize(N - idx);
for( ; i < N; i++){
//for(unsigned d = 0; d < 3; d++)
//C[1][i - idx][d] = LL[1].c[i - idx][d];
C[1].M[i - idx] = M[i];
C[1].M[i - idx].resize(1);
}
}
return C;
}
/*
///inits the cylinder from a list of points (std::vector of stim::vec3 --inP) and magnitudes (inM)
void
init(centerline inP, std::vector< std::vector<T> > inM) {
M = inM; //the magnitude vector can be copied directly
(*this) = inP; //the centerline can be copied to this class directly
stim::vec3<float> v1;
stim::vec3<float> v2;
e.resize(inP.size());
norms.resize(inP.size());
Us.resize(inP.size());
if(inP.size() < 2)
return;
//calculate each L.
L.resize(inP.size()); //the number of precomputed lengths will equal the number of points
T temp = (T)0; //length up to that point
L[0] = temp;
for(size_t i = 1; i < L.size(); i++)
{
temp += (inP[i-1] - inP[i]).len();
L[i] = temp;
}
stim::vec3<T> dr = (inP[1] - inP[0]).norm();
s = stim::circle<T>(inP[0], inM[0][0], dr, stim::vec3<T>(1,0,0));
norms[0] = s.N;
e[0] = s;
Us[0] = e[0].U;
for(size_t i = 1; i < inP.size()-1; i++)
{
s.center(inP[i]);
v1 = (inP[i] - inP[i-1]).norm();
v2 = (inP[i+1] - inP[i]).norm();
dr = (v1+v2).norm();
s.normal(dr);
norms[i] = s.N;
s.scale(inM[i][0]/inM[i-1][0]);
e[i] = s;
Us[i] = e[i].U;
}
int j = inP.size()-1;
s.center(inP[j]);
dr = (inP[j] - inP[j-1]).norm();
s.normal(dr);
norms[j] = s.N;
s.scale(inM[j][0]/inM[j-1][0]);
e[j] = s;
Us[j] = e[j].U;
}
///returns the direction vector at point idx.
stim::vec3<T>
d(int idx)
{
if(idx == 0)
{
stim::vec3<T> temp(
c[idx+1][0]-c[idx][0],
c[idx+1][1]-c[idx][1],
c[idx+1][2]-c[idx][2]
);
// return (e[idx+1].P - e[idx].P).norm();
return (temp.norm());
}
else if(idx == N-1)
{
stim::vec3<T> temp(
c[idx][0]-c[idx+1][0],
c[idx][1]-c[idx+1][1],
c[idx][2]-c[idx+1][2]
);
// return (e[idx].P - e[idx-1].P).norm();
return (temp.norm());
}
else
{
// return (e[idx+1].P - e[idx].P).norm();
// stim::vec3<float> v1 = (e[idx].P-e[idx-1].P).norm();
stim::vec3<T> v1(
c[idx][0]-c[idx-1][0],
c[idx][1]-c[idx-1][1],
c[idx][2]-c[idx-1][2]
);
// stim::vec3<float> v2 = (e[idx+1].P-e[idx].P).norm();
stim::vec3<T> v2(
c[idx+1][0]-c[idx][0],
c[idx+1][1]-c[idx][1],
c[idx+1][2]-c[idx][2]
);
return (v1.norm()+v2.norm()).norm();
}
// return e[idx].N;
}
stim::vec3<T>
d(T l, int idx)
{
if(idx == 0 || idx == N-1)
{
return norms[idx];
// return e[idx].N;
}
else
{
T rat = (l-L[idx])/(L[idx+1]-L[idx]);
return( norms[idx] + (norms[idx+1] - norms[idx])*rat);
// return( e[idx].N + (e[idx+1].N - e[idx].N)*rat);
}
}
///finds the index of the point closest to the length l on the lower bound.
///binary search.
int
findIdx(T l)
{
unsigned int i = L.size()/2;
unsigned int max = L.size()-1;
unsigned int min = 0;
while(i > 0 && i < L.size()-1)
{
// std::cerr << "Trying " << i << std::endl;
// std::cerr << "l is " << l << ", L[" << i << "]" << L[i] << std::endl;
if(l < L[i])
{
max = i;
i = min+(max-min)/2;
}
else if(L[i] <= l && L[i+1] >= l)
{
break;
}
else
{
min = i;
i = min+(max-min)/2;
}
}
return i;
}
public:
///default constructor
cylinder()
// : centerline<T>()
{
}
///constructor to create a cylinder from a set of points, radii, and the number of sides for the cylinder.
///@param inP: Vector of stim vec3 composing the points of the centerline.
///@param inM: Vector of stim vecs composing the radii of the centerline.
cylinder(std::vector<stim::vec3<T> > inP, std::vector<stim::vec<T> > inM)
: centerline<T>(inP)
{
init(inP, inM);
}
///constructor to create a cylinder from a set of points, radii, and the number of sides for the cylinder.
///@param inP: Vector of stim vec3 composing the points of the centerline.
///@param inM: Vector of stim vecs composing the radii of the centerline.
cylinder(std::vector<stim::vec3<T> > inP, std::vector< T > inM)
: centerline<T>(inP)
{
std::vector<stim::vec<T> > temp;
stim::vec<T> zero(0.0,0.0);
temp.resize(inM.size(), zero);
for(int i = 0; i < inM.size(); i++)
temp[i][0] = inM[i];
init(inP, temp);
}
///Constructor defines a cylinder with centerline inP and magnitudes of zero
///@param inP: Vector of stim vec3 composing the points of the centerline
cylinder(std::vector< stim::vec3<T> > inP)
: centerline<T>(inP)
{
std::vector< stim::vec<T> > inM; //create an array of arbitrary magnitudes
stim::vec<T> zero;
zero.push_back(0);
inM.resize(inP.size(), zero); //initialize the magnitude values to zero
init(inP, inM);
}
//assignment operator creates a cylinder from a centerline (default radius is zero)
cylinder& operator=(stim::centerline<T> c) {
init(c);
}
///Returns the number of points on the cylinder centerline
unsigned int size(){
return N;
}
///Returns a position vector at the given p-value (p value ranges from 0 to 1).
///interpolates the position along the line.
///@param pvalue: the location of the in the cylinder, from 0 (beginning to 1).
stim::vec3<T>
p(T pvalue)
{
if(pvalue < 0.0 || pvalue > 1.0)
{
return stim::vec3<float>(-1,-1,-1);
}
T l = pvalue*L[L.size()-1];
int idx = findIdx(l);
return (p(l,idx));
}
///Returns a position vector at the given length into the fiber (based on the pvalue).
///Interpolates the radius along the line.
///@param l: the location of the in the cylinder.
///@param idx: integer location of the point closest to l but prior to it.
stim::vec3<T>
p(T l, int idx)
{
T rat = (l-L[idx])/(L[idx+1]-L[idx]);
stim::vec3<T> v1(
c[idx][0],
c[idx][1],
c[idx][2]
);
stim::vec3<T> v2(
c[idx+1][0],
c[idx+1][1],
c[idx+1][2]
);
// return( e[idx].P + (e[idx+1].P-e[idx].P)*rat);
return( v1 + (v2-v1)*rat);
// return(
// return (pos[idx] + (pos[idx+1]-pos[idx])*((l-L[idx])/(L[idx+1]- L[idx])));
}
///Returns a radius at the given p-value (p value ranges from 0 to 1).
///interpolates the radius along the line.
///@param pvalue: the location of the in the cylinder, from 0 (beginning to 1).
T
r(T pvalue)
{
if(pvalue < 0.0 || pvalue > 1.0){
std::cerr<<"Error, value "<<pvalue<<" is outside of [0 1]."<<std::endl;
exit(1);
}
T l = pvalue*L[L.size()-1];
int idx = findIdx(l);
return (r(l,idx));
}
///Returns a radius at the given length into the fiber (based on the pvalue).
///Interpolates the position along the line.
///@param l: the location of the in the cylinder.
///@param idx: integer location of the point closest to l but prior to it.
T
r(T l, int idx)
{
T rat = (l-L[idx])/(L[idx+1]-L[idx]);
T v1 = (e[idx].U.len() + (e[idx+1].U.len() - e[idx].U.len())*rat);
T v3 = (Us[idx].len() + (Us[idx+1].len() - Us[idx].len())*rat);
T v2 = (mags[idx][0] + (mags[idx+1][0]-mags[idx][0])*rat);
// std::cout << (float)v1 = (float) v2 << std::endl;
if(abs(v3 - v1) >= 10e-6)
{
std::cout << "-------------------------" << std::endl;
std::cout << e[idx].str() << std::endl << std::endl;
std::cout << Us[idx].str() << std::endl;
std::cout << (float)v1 - (float) v2 << std::endl;
std::cout << "failed" << std::endl;
}
// std::cout << e[idx].U.len() << " " << mags[idx][0] << std::endl;
// std::cout << v2 << std::endl;
return(v2);
// return (mags[idx][0] + (mags[idx+1][0]-mags[idx][0])*rat);
// (
}
/// Returns the magnitude at the given index
/// @param i is the index of the desired point
/// @param m is the index of the magnitude value
T ri(unsigned i, unsigned m = 0){
return mags[i][m];
}
/// Adds a new magnitude value to all points
/// @param m is the starting value for the new magnitude
void add_mag(T m = 0){
for(unsigned int p = 0; p < N; p++)
mags[p].push_back(m);
}
/// Sets a magnitude value
/// @param val is the new value for the magnitude
/// @param p is the point index for the magnitude to be set
/// @param m is the index for the magnitude
void set_mag(T val, unsigned p, unsigned m = 0){
mags[p][m] = val;
}
/// Returns the number of magnitude values at each point
unsigned nmags(){
return mags[0].size();
}
///returns the position of the point with a given pvalue and theta on the surface
///in x, y, z coordinates. Theta is in degrees from 0 to 360.
///@param pvalue: the location of the in the cylinder, from 0 (beginning to 1).
///@param theta: the angle to the point of a circle.
stim::vec3<T>
surf(T pvalue, T theta)
{
if(pvalue < 0.0 || pvalue > 1.0)
{
return stim::vec3<float>(-1,-1,-1);
} else {
T l = pvalue*L[L.size()-1];
int idx = findIdx(l);
stim::vec3<T> ps = p(l, idx);
T m = r(l, idx);
s = e[idx];
s.center(ps);
s.normal(d(l, idx));
s.scale(m/e[idx].U.len());
return(s.p(theta));
}
}
///returns a vector of points necessary to create a circle at every position in the fiber.
///@param sides: the number of sides of each circle.
std::vector<std::vector<vec3<T> > >
getPoints(int sides)
{
std::vector<std::vector <vec3<T> > > points;
points.resize(N);
for(int i = 0; i < N; i++)
{
points[i] = e[i].getPoints(sides);
}
return points;
}
///returns the total length of the line at index j.
T
getl(int j)
{
return (L[j]);
}
/// Allows a point on the centerline to be accessed using bracket notation
vec3<T> operator[](unsigned int i){
return e[i].P;
}
/// Returns the total length of the cylinder centerline
T length(){
return L.back();
}
/// Integrates a magnitude value along the cylinder.
/// @param m is the magnitude value to be integrated (this is usually the radius)
T integrate(unsigned m = 0){
T M = 0; //initialize the integral to zero
T m0, m1; //allocate space for both magnitudes in a single segment
//vec3<T> p0, p1; //allocate space for both points in a single segment
m0 = mags[0][m]; //initialize the first point and magnitude to the first point in the cylinder
//p0 = pos[0];
T len = L[0]; //allocate space for the segment length
//for every consecutive point in the cylinder
for(unsigned p = 1; p < N; p++){
//p1 = pos[p]; //get the position and magnitude for the next point
m1 = mags[p][m];
if(p > 1) len = (L[p-1] - L[p-2]); //calculate the segment length using the L array
//add the average magnitude, weighted by the segment length
M += (m0 + m1)/(T)2.0 * len;
m0 = m1; //move to the next segment by shifting points
}
return M; //return the integral
}
/// Averages a magnitude value across the cylinder
/// @param m is the magnitude value to be averaged (this is usually the radius)
T average(unsigned m = 0){
//return the average magnitude
return integrate(m) / L.back();
}
/// Resamples the cylinder to provide a maximum distance of "spacing" between centerline points. All current
/// centerline points are guaranteed to exist in the new cylinder
/// @param spacing is the maximum spacing allowed between sample points
cylinder<T> resample(T spacing){
std::vector< vec3<T> > result;
vec3<T> p0 = e[0].P; //initialize p0 to the first point on the centerline
vec3<T> p1;
unsigned N = size(); //number of points in the current centerline
//for each line segment on the centerline
for(unsigned int i = 1; i < N; i++){
p1 = e[i].P; //get the second point in the line segment
vec3<T> v = p1 - p0; //calculate the vector between these two points
T d = v.len(); //calculate the distance between these two points (length of the line segment)
size_t nsteps = (size_t)std::ceil(d / spacing); //calculate the number of steps to take along the segment to meet the spacing criteria
T stepsize = (T)1.0 / nsteps; //calculate the parametric step size between new centerline points
//for each step along the line segment
for(unsigned s = 0; s < nsteps; s++){
T alpha = stepsize * s; //calculate the fraction of the distance along the line segment covered
result.push_back(p0 + alpha * v); //push the point at alpha position along the line segment
}
p0 = p1; //shift the points to move to the next line segment
}
result.push_back(e[size() - 1].P); //push the last point in the centerline
return cylinder<T>(result);
}*/
};
}
#endif