ce6381d7
 David Mayerich
updating to TIRA
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#ifndef STIM_SPH_HARMONICS
#define STIM_SPH_HARMONICS
#include <complex>
#include <boost/math/special_functions/spherical_harmonic.hpp>
#include <stim/math/constants.h>
#include <stim/math/random.h>
#include <vector>
#define WIRE_SCALE 1.001
namespace stim {
template<class T>
class spharmonics {
public:
std::vector<T> C; //list of SH coefficients
protected:
unsigned int mcN; //number of Monte-Carlo samples
unsigned int coeff_1d(unsigned int l, int m) { //convert (l,m) to i (1D coefficient index)
return pow(l + 1, 2) - (l - m) - 1;
}
void coeff_2d(size_t c, unsigned int& l, int& m) { //convert a 1D coefficient index into (l, m)
l = (unsigned int)ceil(sqrt((double)c + 1)) - 1; //the major index is equal to sqrt(c) - 1
m = (int)(c - (size_t)(l * l)) - (int)l; //the minor index is calculated by finding the difference
}
public:
spharmonics() {
mcN = 0;
}
spharmonics(size_t c) : spharmonics() {
resize(c);
}
void push(T c) {
C.push_back(c);
}
void resize(unsigned int n) {
C.resize(n);
}
void setc(unsigned int l, int m, T value) {
u44nsigned int c = coeff_1d(l, m);
C[c] = value;
}
T getc(unsigned int l, int m) {
unsigned int c = coeff_1d(l, m);
return C[c];
}
void setc(unsigned int c, T value) {
C[c] = value;
}
unsigned int getSize() const {
return C.size();
}
std::vector<T> getC() const {
return C;
}
//calculate the value of the SH basis function (l, m) at (theta, phi)
//here, theta = [0, PI], phi = [0, 2*PI]
T SH(unsigned int l, int m, T theta, T phi) {
//std::complex<T> result = boost::math::spherical_harmonic(l, m, phi, theta);
//return result.imag() + result.real();
//this calculation is based on calculating the real spherical harmonics:
// https://en.wikipedia.org/wiki/Spherical_harmonics#Addition_theorem
if (m < 0) {
return sqrt(2.0) * pow(-1, m) * boost::math::spherical_harmonic(l, abs(m), phi, theta).imag();
}
else if (m == 0) {
return boost::math::spherical_harmonic(l, m, phi, theta).real();
}
else {
return sqrt(2.0) * pow(-1, m) * boost::math::spherical_harmonic(l, m, phi, theta).real();
}
}
/// Calculate the spherical harmonic result given a 1D coefficient index
T SH(size_t c, T theta, T phi) {
unsigned int l;
int m;
coeff_2d(c, l, m);
return SH(l, m, theta, phi);
}
/// Initialize Monte-Carlo sampling of a function using N spherical harmonics coefficients
/// @param N is the number of spherical harmonics coefficients used to represent the user function
void mcBegin(unsigned int coefficients) {
C.resize(coefficients, 0);
mcN = 0;
}
void mcBegin(unsigned int l, int m) {
unsigned int c = pow(l + 1, 2) - (l - m);
mcBegin(c);
}
void mcSample(T theta, T phi, T val) {
int l, m;
T sh;
l = m = 0;
for (unsigned int i = 0; i < C.size(); i++) {
sh = SH(l, m, theta, phi);
C[i] += sh * val;
m++; //increment m
//if we're in a new tier, increment l and set m = -l
if (m > l) {
l++;
m = -l;
}
} //end for all coefficients
//increment the number of samples
mcN++;
} //end mcSample()
void mcEnd() {
//divide all coefficients by the number of samples
for (unsigned int i = 0; i < C.size(); i++)
C[i] /= mcN;
}
/// Generates a PDF describing the probability distribution of points on a spherical surface
/// @param sph_pts is a list of points in spherical coordinates (theta, phi) where theta = [0, 2pi] and phi = [0, pi]
/// @param l is the maximum degree of the spherical harmonic function
/// @param m is the maximum order
void pdf(std::vector<stim::vec3<T> > sph_pts, unsigned int l, int m) {
mcBegin(l, m); //begin spherical harmonic sampling
unsigned int nP = sph_pts.size();
for (unsigned int p = 0; p < nP; p++) {
mcSample(sph_pts[p][1], sph_pts[p][2], 1.0);
}
mcEnd();
}
void pdf(std::vector<stim::vec3<T> > sph_pts, size_t c) {
unsigned int l;
int m;
coeff_2d(c, l, m);
pdf(sph_pts, l, m);
}
/// Project a set of samples onto a spherical harmonic basis
void project(std::vector<stim::vec3<T> > sph_pts, unsigned int l, int m) {
mcBegin(l, m); //begin spherical harmonic sampling
unsigned int nP = sph_pts.size();
for (unsigned int p = 0; p < nP; p++) {
mcSample(sph_pts[p][1], sph_pts[p][2], sph_pts[p][0]);
}
mcEnd();
}
void project(std::vector<stim::vec3<T> > sph_pts, size_t c) {
unsigned int l;
int m;
coeff_2d(c, l, m);
project(sph_pts, l, m);
}
/// Generates a PDF describing the density distribution of points on a sphere
/// @param sph_pts is a list of points in cartesian coordinates
/// @param l is the maximum degree of the spherical harmonic function
/// @param m is the maximum order
/// @param c is the centroid of the points in sph_pts. DEFAULT 0,0,0
/// @param n is the number of points of the surface of the sphere used to create the PDF. DEFAULT 1000
/// @param norm, a boolean that sets where the output vectors will be normalized between 0 and 1.
/// @param
void pdf(std::vector<stim::vec3<T> > sph_pts, unsigned int l, int m, stim::vec3<T> c = stim::vec3<T>(0, 0, 0), unsigned int n = 1000, bool norm = true, std::vector<T> w = std::vector<T>(), int normfactor = 1)
{
std::vector<double> weights; ///the weight at each point on the surface of the sphere.
// weights.resize(n);
unsigned int nP = sph_pts.size(); ///sph_pts is the vectors we want to fit a spehrical harmonic to.
std::vector<stim::vec3<T> > sphere = stim::Random<T>::sample_sphere(n, 1.0, stim::TAU); ///randomsample a sphere of radius 1 and return the sampled vectors.
if (w.size() < nP)
w = std::vector<T>(nP, 1.0); //1 weight per each m.
for (int i = 0; i < n; i++) //for each weight
{
T val = 0;
for (int j = 0; j < nP; j++) //for each vector
{
stim::vec3<T> temp = sph_pts[j] - c;
if (temp.dot(sphere[i]) > 0)
val += pow(temp.dot(sphere[i]), normfactor)*w[j];
}
weights.push_back(val);
}
mcBegin(l, m); //begin spherical harmonic sampling
if (norm)
{
T min = *std::min_element(weights.begin(), weights.end());
T max = *std::max_element(weights.begin(), weights.end());
for (unsigned int i = 0; i < n; i++)
{
stim::vec3<T> sph = sphere[i].cart2sph();
mcSample(sph[1], sph[2], (weights[i] - min) / (max - min));
}
}
else {
for (unsigned int i = 0; i < n; i++)
{
stim::vec3<T> sph = sphere[i].cart2sph();
mcSample(sph[1], sph[2], weights[i]);
}
}
mcEnd();
}
std::string str() {
std::stringstream ss;
int l, m;
l = m = 0;
for (unsigned int i = 0; i < C.size(); i++) {
ss << C[i] << '\t';
m++; //increment m
//if we're in a new tier, increment l and set m = -l
if (m > l) {
l++;
m = -l;
ss << std::endl;
}
}
return ss.str();
}
/// Returns the value of the function at coordinate (theta, phi)
T p(T theta, T phi) {
T fx = 0;
int l = 0;
int m = 0;
for (unsigned int i = 0; i < C.size(); i++) {
fx += C[i] * SH(l, m, theta, phi);
m++;
if (m > l) {
l++;
m = -l;
}
}
return fx;
}
/// Returns the derivative of the spherical function with respect to theta
/// return value is in cartesian coordinates
vec3<T> dtheta(T theta, T phi, T d = 0.01) {
T r = p(theta, phi); //calculate the value of the spherical function at three points
T rt = p(theta + d, phi);
//double rp = p(theta, phi + d);
vec3<T> s(r, theta, phi); //get the spherical coordinate position for all three points
vec3<T> st(rt, theta + d, phi);
//vec3<double> sp(rp, theta, phi + d);
vec3<T> c = s.sph2cart();
vec3<T> ct = st.sph2cart();
//vec3<double> cp = sp.sph2cart();
vec3<T> dt = (ct - c)/d; //calculate the derivative
return dt;
}
/// Returns the derivative of the spherical function with respect to phi
/// return value is in cartesian coordinates
vec3<T> dphi(T theta, T phi, T d = 0.01) {
T r = p(theta, phi); //calculate the value of the spherical function at three points
//double rt = p(theta + d, phi);
T rp = p(theta, phi + d);
vec3<T> s(r, theta, phi); //get the spherical coordinate position for all three points
//vec3<double> st(rt, theta + d, phi);
vec3<T> sp(rp, theta, phi + d);
vec3<T> c = s.sph2cart();
//vec3<double> ct = st.sph2cart();
vec3<T> cp = sp.sph2cart();
vec3<T> dp = (cp - c) / d; //calculate the derivative
return dp;
}
/// Returns the value of the function at the coordinate (theta, phi)
/// @param theta = [0, 2pi]
/// @param phi = [0, pi]
T operator()(T theta, T phi) {
return p(theta, phi);
}
//overload arithmetic operations
spharmonics<T> operator*(T rhs) const {
spharmonics<T> result(C.size()); //create a new spherical harmonics object
for (size_t c = 0; c < C.size(); c++) //for each coefficient
result.C[c] = C[c] * rhs; //calculate the factor and store the result in the new spharmonics object
return result;
}
spharmonics<T> operator+(spharmonics<T> rhs) {
size_t low = std::min(C.size(), rhs.C.size()); //store the number of coefficients in the lowest object
size_t high = std::max(C.size(), rhs.C.size()); //store the number of coefficients in the result
bool rhs_lowest = false; //true if rhs has the lowest number of coefficients
if (rhs.C.size() < C.size()) rhs_lowest = true; //if rhs has a lower number of coefficients, set the flag
spharmonics<T> result(high); //create a new object
size_t c;
for (c = 0; c < low; c++) //perform the first batch of additions
result.C[c] = C[c] + rhs.C[c]; //perform the addition
for (c = low; c < high; c++) {
if (rhs_lowest)
result.C[c] = C[c];
else
result.C[c] = rhs.C[c];
}
return result;
}
spharmonics<T> operator-(spharmonics<T> rhs) {
return (*this) + (rhs * (T)(-1));
}
/// Fill an NxN grid with the spherical function for theta = [0 2pi] and phi = [0 pi]
void get_func(T* data, size_t X, size_t Y) {
T dt = stim::TAU / (T)X; //calculate the step size in each direction
T dp = stim::PI / (T)(Y - 1);
for (size_t ti = 0; ti < X; ti++) {
for (size_t pi = 0; pi < Y; pi++) {
data[pi * X + ti] = (*this)((T)ti * dt, (T)pi * dp);
}
}
}
/// Project a spherical function onto the basis using C coefficients
/// @param data is a pointer to the function values in (theta, phi) coordinates
/// @param N is the number of samples along each axis, where theta = [0 2pi), phi = [0 pi]
void project(T* data, size_t x, size_t y, size_t nc) {
stim::cpu2image(data, "test.ppm", x, y, stim::cmBrewer);
C.resize(nc, 0); //resize the coefficient array to store the necessary coefficients
T dtheta = stim::TAU / (T)(x - 1); //calculate the grid spacing along theta
T dphi = stim::PI / (T)y; //calculate the grid spacing along phi
T theta, phi;
for (size_t c = 0; c < nc; c++) { //for each coefficient
for (size_t theta_i = 0; theta_i < x; theta_i++) { //for each coordinate in the provided array
theta = theta_i * dtheta; //calculate theta
for (size_t phi_i = 0; phi_i < y; phi_i++) {
phi = phi_i * dphi; //calculate phi
C[c] += data[phi_i * x + theta_i] * SH(c, theta, phi) * dtheta * dphi * sin(phi);
}
}
}
}
///imperpolates a spherical harmonic linearly from itself to the spherical harmonic passed as an input.
///@param target, spharmonic class to which we are interpolating.
///@param dist float value representing the distance we are interpolating [0,1]
stim::spharmonics<T>
interp(stim::spharmonics<T> target, float dist)
{
stim::spharmonics<T> ret(std::max(target.C.size(), C.size()));
for(int i = 0; i < target.C.size(); i++)
{
if(i < C.size())
{
T slope = target.C[i] - C[i];
ret.C[i] = C[i] + dist * slope;
}
else
{
T slope = target.C[i];
ret.C[i] = dist * slope;
}
}
return ret;
}
/// Generate spherical harmonic coefficients based on a set of N samples
/*void fit(std::vector<stim::vec3<T> > sph_pts, unsigned int L, bool norm = true)
{
//std::vector<T> coeffs;
//generate a matrix for fitting
int B = L*(L+2)+1; //calculate the matrix size
stim::matrix<T> mat(B, B); //allocate space for the matrix
std::vector<T> sums;
//int B = l*(l+2)+1;
coeffs.resize(B);
sums.resize(B);
//stim::matrix<T> mat(B, B);
for(int i = 0; i < sph_pts.size(); i++)
{
mcBegin(l,m);
mcSample(sph_pts[i][1], sph_pts[i][2], 1.0);
for(int j = 0; j < B; j++)
{
sums[j] += C[j];
// sums[j] += C[j]*sums[j];
}
mcEnd();
}
for(int i = 0; i < B; i++)
{
for(int j = 0; j < B; j++)
{
mat(i,j) = sums[i]*sums[j];
}
}
if(mat.det() == 0)
{
std::cerr << " matrix not solvable " << std::endl;
}
else
{
//for(int i = 0; i <
}
}*/
}; //end class sph_harmonics
}
#endif
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