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#ifndef SEEN_SBASIS_2D_H
#define SEEN_SBASIS_2D_H
#include <vector>
#include <cassert>
#include <algorithm>
#include "d2.h"
#include "sbasis.h"
#include <iostream>
namespace Geom{
class Linear2d{
public:
/*
u 0,1
v 0,2
*/
double a[4];
Linear2d() {}
Linear2d(double aa) {
for(unsigned i = 0 ; i < 4; i ++)
a[i] = aa;
}
Linear2d(double a00, double a01, double a10, double a11)
{
a[0] = a00;
a[1] = a01;
a[2] = a10;
a[3] = a11;
}
double operator[](const int i) const {
assert(i >= 0);
assert(i < 4);
return a[i];
}
double& operator[](const int i) {
assert(i >= 0);
assert(i < 4);
return a[i];
}
double apply(double u, double v) {
return (a[0]*(1-u)*(1-v) +
a[1]*u*(1-v) +
a[2]*(1-u)*v +
a[3]*u*v);
}
};
inline Linear extract_u(Linear2d const &a, double u) {
return Linear(a[0]*(1-u) +
a[1]*u,
a[2]*(1-u) +
a[3]*u);
}
inline Linear extract_v(Linear2d const &a, double v) {
return Linear(a[0]*(1-v) +
a[2]*v,
a[1]*(1-v) +
a[3]*v);
}
inline Linear2d operator-(Linear2d const &a) {
return Linear2d(-a.a[0], -a.a[1],
-a.a[2], -a.a[3]);
}
inline Linear2d operator+(Linear2d const & a, Linear2d const & b) {
return Linear2d(a[0] + b[0],
a[1] + b[1],
a[2] + b[2],
a[3] + b[3]);
}
inline Linear2d operator-(Linear2d const & a, Linear2d const & b) {
return Linear2d(a[0] - b[0],
a[1] - b[1],
a[2] - b[2],
a[3] - b[3]);
}
inline Linear2d& operator+=(Linear2d & a, Linear2d const & b) {
for(unsigned i = 0; i < 4; i++)
a[i] += b[i];
return a;
}
inline Linear2d& operator-=(Linear2d & a, Linear2d const & b) {
for(unsigned i = 0; i < 4; i++)
a[i] -= b[i];
return a;
}
inline Linear2d& operator*=(Linear2d & a, double b) {
for(unsigned i = 0; i < 4; i++)
a[i] *= b;
return a;
}
inline bool operator==(Linear2d const & a, Linear2d const & b) {
for(unsigned i = 0; i < 4; i++)
if(a[i] != b[i])
return false;
return true;
}
inline bool operator!=(Linear2d const & a, Linear2d const & b) {
for(unsigned i = 0; i < 4; i++)
if(a[i] == b[i])
return false;
return true;
}
inline Linear2d operator*(double const a, Linear2d const & b) {
return Linear2d(a*b[0], a*b[1],
a*b[2], a*b[3]);
}
class SBasis2d : public std::vector<Linear2d>{
public:
// vector in u,v
unsigned us, vs; // number of u terms, v terms
SBasis2d() {}
SBasis2d(Linear2d const & bo)
: us(1), vs(1) {
push_back(bo);
}
SBasis2d(SBasis2d const & a)
: std::vector<Linear2d>(a), us(a.us), vs(a.vs) {}
Linear2d& index(unsigned ui, unsigned vi) {
assert(ui < us);
assert(vi < vs);
return (*this)[ui + vi*us];
}
Linear2d index(unsigned ui, unsigned vi) const {
if(ui >= us)
return Linear2d(0);
if(vi >= vs)
return Linear2d(0);
return (*this)[ui + vi*us];
}
double apply(double u, double v) const {
double s = u*(1-u);
double t = v*(1-v);
Linear2d p;
double tk = 1;
// XXX rewrite as horner
for(unsigned vi = 0; vi < vs; vi++) {
double sk = 1;
for(unsigned ui = 0; ui < us; ui++) {
p += (sk*tk)*index(ui, vi);
sk *= s;
}
tk *= t;
}
return p.apply(u,v);
}
void clear() {
fill(begin(), end(), Linear2d(0));
}
void normalize(); // remove extra zeros
double tail_error(unsigned tail) const;
void truncate(unsigned k);
};
inline SBasis2d operator-(const SBasis2d& p) {
SBasis2d result;
result.reserve(p.size());
for(unsigned i = 0; i < p.size(); i++) {
result.push_back(-p[i]);
}
return result;
}
inline SBasis2d operator+(const SBasis2d& a, const SBasis2d& b) {
SBasis2d result;
result.us = std::max(a.us, b.us);
result.vs = std::max(a.vs, b.vs);
const unsigned out_size = result.us*result.vs;
result.resize(out_size);
for(unsigned vi = 0; vi < result.vs; vi++) {
for(unsigned ui = 0; ui < result.us; ui++) {
Linear2d bo;
if(ui < a.us && vi < a.vs)
bo += a.index(ui, vi);
if(ui < b.us && vi < b.vs)
bo += b.index(ui, vi);
result.index(ui, vi) = bo;
}
}
return result;
}
inline SBasis2d operator-(const SBasis2d& a, const SBasis2d& b) {
SBasis2d result;
result.us = std::max(a.us, b.us);
result.vs = std::max(a.vs, b.vs);
const unsigned out_size = result.us*result.vs;
result.resize(out_size);
for(unsigned vi = 0; vi < result.vs; vi++) {
for(unsigned ui = 0; ui < result.us; ui++) {
Linear2d bo;
if(ui < a.us && vi < a.vs)
bo += a.index(ui, vi);
if(ui < b.us && vi < b.vs)
bo -= b.index(ui, vi);
result.index(ui, vi) = bo;
}
}
return result;
}
inline SBasis2d& operator+=(SBasis2d& a, const Linear2d& b) {
if(a.size() < 1)
a.push_back(b);
else
a[0] += b;
return a;
}
inline SBasis2d& operator-=(SBasis2d& a, const Linear2d& b) {
if(a.size() < 1)
a.push_back(-b);
else
a[0] -= b;
return a;
}
inline SBasis2d& operator+=(SBasis2d& a, double b) {
if(a.size() < 1)
a.push_back(Linear2d(b));
else {
for(unsigned i = 0; i < 4; i++)
a[0] += double(b);
}
return a;
}
inline SBasis2d& operator-=(SBasis2d& a, double b) {
if(a.size() < 1)
a.push_back(Linear2d(-b));
else {
a[0] -= b;
}
return a;
}
inline SBasis2d& operator*=(SBasis2d& a, double b) {
for(unsigned i = 0; i < a.size(); i++)
a[i] *= b;
return a;
}
inline SBasis2d& operator/=(SBasis2d& a, double b) {
for(unsigned i = 0; i < a.size(); i++)
a[i] *= (1./b);
return a;
}
SBasis2d operator*(double k, SBasis2d const &a);
SBasis2d operator*(SBasis2d const &a, SBasis2d const &b);
SBasis2d shift(SBasis2d const &a, int sh);
SBasis2d shift(Linear2d const &a, int sh);
SBasis2d truncate(SBasis2d const &a, unsigned terms);
SBasis2d multiply(SBasis2d const &a, SBasis2d const &b);
SBasis2d integral(SBasis2d const &c);
SBasis2d derivative(SBasis2d const &a);
SBasis2d sqrt(SBasis2d const &a, int k);
// return a kth order approx to 1/a)
SBasis2d reciprocal(Linear2d const &a, int k);
SBasis2d divide(SBasis2d const &a, SBasis2d const &b, int k);
// a(b(t))
SBasis2d compose(SBasis2d const &a, SBasis2d const &b);
SBasis2d compose(SBasis2d const &a, SBasis2d const &b, unsigned k);
SBasis2d inverse(SBasis2d const &a, int k);
// these two should probably be replaced with compose
SBasis extract_u(SBasis2d const &a, double u);
SBasis extract_v(SBasis2d const &a, double v);
SBasis compose(Linear2d const &a, D2<SBasis> const &p);
SBasis compose(SBasis2d const &fg, D2<SBasis> const &p);
D2<SBasis> compose_each(D2<SBasis2d> const &fg, D2<SBasis> const &p);
inline std::ostream &operator<< (std::ostream &out_file, const Linear2d &bo) {
out_file << "{" << bo[0] << ", " << bo[1] << "}, ";
out_file << "{" << bo[2] << ", " << bo[3] << "}";
return out_file;
}
inline std::ostream &operator<< (std::ostream &out_file, const SBasis2d & p) {
for(unsigned i = 0; i < p.size(); i++) {
out_file << p[i] << "s^" << i << " + ";
}
return out_file;
}
};
/*
Local Variables:
mode:c++
c-file-style:"stroustrup"
c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
indent-tabs-mode:nil
fill-column:99
End:
*/
// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:encoding=utf-8:textwidth=99 :
#endif
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