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// Copyright (C) 1999-2018
// Smithsonian Astrophysical Observatory, Cambridge, MA, USA
// For conditions of distribution and use, see copyright notice in "copyright"
#ifndef __vector3d_h__
#define __vector3d_h__
#include <math.h>
#include <float.h>
#include <iostream>
using namespace std;
class Vector;
class Matrix;
class Matrix3d;
class Vector3d {
public:
double v[4];
public:
Vector3d()
{v[0]=0;v[1]=0;v[2]=0;v[3]=1;}
Vector3d(double* f)
{v[0]=f[0]; v[1]=f[1]; v[2]=f[2]; v[3]=1;}
Vector3d(double x, double y)
{v[0]=x;v[1]=y;v[2]=0;v[3]=1;}
Vector3d(double x, double y, double z)
{v[0]=x;v[1]=y;v[2]=z;v[3]=1;}
Vector3d(const Vector&);
Vector3d(const Vector&, double);
Vector3d& operator=(const Vector&);
Vector3d(const Vector3d& a)
{v[0]=a.v[0];v[1]=a.v[1];v[2]=a.v[2];v[3]=a.v[3];}
Vector3d& operator=(const Vector3d& a)
{v[0]=a.v[0];v[1]=a.v[1];v[2]=a.v[2];v[3]=a.v[3]; return *this;}
const double& operator[](int i) const {return v[i];} // return element
double& operator[](int i) {return v[i];} // return element
double* vv() {return v;} // return vector
Vector3d& operator+=(const Vector3d& a) // addition
{v[0]+=a.v[0]; v[1]+=a.v[1]; v[2]+=a.v[2]; return *this;}
Vector3d& operator-=(const Vector3d& a) // subtraction
{v[0]-=a.v[0]; v[1]-=a.v[1]; v[2]-=a.v[2]; return *this;}
Vector3d& operator*=(double f) // scalar multiply
{v[0]*=f; v[1]*=f; v[2]*=f; return *this;}
Vector3d& operator/=(double f) // scalar division
{v[0]/=f; v[1]/=f; v[2]/=f; return *this;}
Vector3d& operator*=(const Matrix3d&); // vector multiply
Vector3d abs()
{return Vector3d(fabs(v[0]),fabs(v[1]),fabs(v[2]));}
double angleX()
{return atan2(v[2],v[1]);}
double angleY()
{return atan2(v[0],v[2]);}
double angleZ()
{return atan2(v[1],v[0]);}
Vector3d ceil()
{return Vector3d(::ceil(v[0]),::ceil(v[1]),::ceil(v[2]));}
Vector3d floor()
{return Vector3d(::floor(v[0]),::floor(v[1]),::floor(v[2]));}
Vector3d invert()
{return Vector3d(1/v[0],1/v[1],1/v[2]);}
double length()
{return sqrt(v[0]*v[0]+v[1]*v[1]+v[2]*v[2]);}
Vector3d round()
{return Vector3d((int)(v[0]+.5),(int)(v[1]+.5),(int)(v[2]+.5));}
Vector3d normalize()
{double d = sqrt(v[0]*v[0]+v[1]*v[1]+v[2]*v[2]);
return d ? Vector3d(v[0]/d,v[1]/d,v[2]/d) : Vector3d();}
Vector3d project()
{return (v[3]!=1) ? Vector3d(v[0]/v[3],v[1]/v[3],v[2]/v[3]) : *this;}
};
ostream& operator<<(ostream&, const Vector3d&);
istream& operator>>(istream&, Vector3d&);
inline Vector3d operator-(const Vector3d& a)
{return Vector3d(-a.v[0],-a.v[1],-a.v[2]);}
inline Vector3d operator+(const Vector3d& a, const Vector3d& b)
{return Vector3d(a) +=b;}
inline Vector3d operator-(const Vector3d& a, const Vector3d& b)
{return Vector3d(a) -=b;}
inline Vector3d operator*(const Vector3d& a, double b)
{return Vector3d(a) *=b;}
inline Vector3d operator/(const Vector3d& a, double b)
{return Vector3d(a) /=b;}
inline Vector3d operator*(const Vector3d& v, const Matrix3d& m)
{return Vector3d(v) *=m;}
inline double operator*(const Vector3d& a, const Vector3d& b) // dot product
{double r=0; r+=a.v[0]*b.v[0]; r+=a.v[1]*b.v[1]; r+=a.v[2]*b.v[2]; return r;}
inline Vector3d cross(Vector3d& a, Vector3d& b) // cross product
{return Vector3d(a[1]*b[2]-b[1]*a[2],a[2]*b[0]-b[2]*a[0],a[0]*b[1]-b[0]*a[1]);}
class Vertex3d {
public:
Vector3d vector;
private:
Vertex3d* next_;
Vertex3d* previous_;
public:
Vertex3d()
{next_=NULL; previous_=NULL;}
Vertex3d(double x, double y, double z)
{vector=Vector3d(x,y,z); next_=NULL; previous_=NULL;}
Vertex3d(const Vector3d& a)
{vector=a; next_=NULL; previous_=NULL;}
Vertex3d(const Vertex3d& a)
{vector=a.vector; next_=a.next_; previous_=a.previous_;}
Vertex3d& operator=(const Vertex3d& a)
{vector=a.vector; next_=a.next_; previous_=a.previous_; return *this;}
Vertex3d* next()
{return next_;}
Vertex3d* previous()
{return previous_;}
void setNext(Vertex3d* v)
{next_ = v;}
void setPrevious(Vertex3d* v)
{previous_ = v;}
};
ostream& operator<<(ostream&, const Vertex3d&);
class Matrix3d {
public:
double m[4][4];
public:
Matrix3d()
{ m[0][0]=1; m[0][1]=0; m[0][2]=0; m[0][3]=0;
m[1][0]=0; m[1][1]=1; m[1][2]=0; m[1][3]=0;
m[2][0]=0; m[2][1]=0; m[2][2]=1; m[2][3]=0;
m[3][0]=0; m[3][1]=0; m[3][2]=0; m[3][3]=1; }
Matrix3d(double a, double b, double c,
double d, double e, double f,
double g, double h, double i,
double j, double k, double l)
{ m[0][0]=a; m[0][1]=b; m[0][2]=c; m[0][3]=0;
m[1][0]=d; m[1][1]=e; m[1][2]=f; m[1][3]=0;
m[2][0]=g; m[2][1]=h; m[2][2]=i; m[2][3]=0;
m[3][0]=j; m[3][1]=k; m[3][2]=l; m[3][3]=1; }
Matrix3d(Vector3d& x, Vector3d& y, Vector3d& z)
{ m[0][0]=x[0]; m[0][1]=y[0]; m[0][2]=z[0]; m[0][3]=0;
m[1][0]=x[1]; m[1][1]=y[1]; m[1][2]=z[1]; m[1][3]=0;
m[2][0]=x[2]; m[2][1]=y[2]; m[2][2]=z[2]; m[2][3]=0;
m[3][0]=0; m[3][1]=0; m[3][2]=0; m[3][3]=1; }
Matrix3d(const Matrix3d& a)
{ m[0][0]=a.m[0][0];m[0][1]=a.m[0][1];m[0][2]=a.m[0][2];m[0][3]=a.m[0][3];
m[1][0]=a.m[1][0];m[1][1]=a.m[1][1];m[1][2]=a.m[1][2];m[1][3]=a.m[1][3];
m[2][0]=a.m[2][0];m[2][1]=a.m[2][1];m[2][2]=a.m[2][2];m[2][3]=a.m[2][3];
m[3][0]=a.m[3][0];m[3][1]=a.m[3][1];m[3][2]=a.m[3][2];m[3][3]=a.m[3][3]; }
Matrix3d& operator=(const Matrix3d& a)
{ m[0][0]=a.m[0][0];m[0][1]=a.m[0][1];m[0][2]=a.m[0][2];m[0][3]=a.m[0][3];
m[1][0]=a.m[1][0];m[1][1]=a.m[1][1];m[1][2]=a.m[1][2];m[1][3]=a.m[1][3];
m[2][0]=a.m[2][0];m[2][1]=a.m[2][1];m[2][2]=a.m[2][2];m[2][3]=a.m[2][3];
m[3][0]=a.m[3][0];m[3][1]=a.m[3][1];m[3][2]=a.m[3][2];m[3][3]=a.m[3][3];
return *this;}
Matrix3d(const Matrix& a);
double matrix(int i, int j)
{return m[i][j];} // return element
Vector3d operator[](int i)
{return Vector3d(m[i]);} // return row
double* mm()
{return (double*)m;} // return matrix
Matrix3d& identity()
{ m[0][0]=1; m[0][1]=0; m[0][2]=0; m[0][3]=0;
m[1][0]=0; m[1][1]=1; m[1][2]=0; m[1][3]=0;
m[2][0]=0; m[2][1]=0; m[2][2]=1; m[2][3]=0;
m[3][0]=0; m[3][1]=0; m[3][2]=0; m[3][3]=1; return *this;}
Matrix3d& operator*=(const Matrix3d&); // matrix multiply
Matrix3d invert();
Matrix3d cofactor();
Matrix3d adjoint();
double det();
double det2d(double& a, double& b, double& c,
double& d, double& e, double& f,
double& g, double& h, double& i)
{return a*(e*i-f*h) - b*(d*i-f*g) + c*(d*h-e*g);}
void dump();
};
ostream& operator<<(ostream&, const Matrix3d&);
istream& operator>>(istream&, Matrix3d&);
inline Matrix3d operator*(const Matrix3d& a, const Matrix3d& b)
{return Matrix3d(a) *= b;}
inline Vector3d& Vector3d::operator*=(const Matrix3d& m)
{
double vv[4];
double* mm = (double*)(m.m);
vv[0] = v[0]*mm[0] + v[1]*mm[4] + v[2]*mm[8] + v[3]*mm[12];
vv[1] = v[0]*mm[1] + v[1]*mm[5] + v[2]*mm[9] + v[3]*mm[13];
vv[2] = v[0]*mm[2] + v[1]*mm[6] + v[2]*mm[10] + v[3]*mm[14];
vv[3] = v[0]*mm[3] + v[1]*mm[7] + v[2]*mm[11] + v[3]*mm[15];
v[0] = vv[0];
v[1] = vv[1];
v[2] = vv[2];
v[3] = vv[3];
return *this;
}
class Translate3d : public Matrix3d {
public:
Translate3d() {};
Translate3d(double x, double y, double z)
{m[3][0]=x; m[3][1]=y; m[3][2]=z;}
Translate3d(const Vector3d& v)
{m[3][0]=v.v[0]; m[3][1]=v.v[1]; m[3][2]=v.v[2];}
Translate3d(const Vector& v);
Translate3d(const Vector& v, double z);
Translate3d(const Matrix3d& a)
{m[3][0] = a.m[3][0]; m[3][1] = a.m[3][1]; m[3][2] = a.m[3][2];}
};
ostream& operator<<(ostream&, const Translate3d&);
istream& operator>>(istream&, Translate3d&);
class Scale3d : public Matrix3d {
public:
Scale3d() {};
Scale3d(double a)
{m[0][0]=a; m[1][1]=a; m[2][2]=a;}
Scale3d(double a, double b)
{m[0][0]=a; m[1][1]=a; m[2][2]=b;}
Scale3d(double a, double b, double c)
{m[0][0]=a; m[1][1]=b; m[2][2]=c;}
Scale3d(const Vector& v);
Scale3d(const Vector& v, double c);
Scale3d(const Vector3d& v)
{m[0][0]=v.v[0]; m[1][1]=v.v[1]; m[2][2]=v.v[2];}
Scale3d(const Matrix3d& a)
{m[0][0] = a.m[0][0]; m[1][1] = a.m[1][1]; m[2][2] = a.m[2][2];}
};
ostream& operator<<(ostream&, const Scale3d&);
istream& operator>>(istream&, Scale3d&);
class FlipX3d : public Matrix3d {
public:
FlipX3d()
{m[0][0] = -1;}
};
class FlipY3d : public Matrix3d {
public:
FlipY3d()
{m[1][1] = -1;}
};
class FlipZ3d : public Matrix3d {
public:
FlipZ3d()
{m[2][2] = -1;}
};
class FlipXY3d : public Matrix3d {
public:
FlipXY3d()
{m[0][0] = -1; m[1][1] = -1;}
};
class FlipXYZ3d : public Matrix3d {
public:
FlipXYZ3d()
{m[0][0] = -1; m[1][1] = -1; m[2][2] = -1;}
};
class RotateX3d : public Matrix3d {
public:
RotateX3d()
{};
RotateX3d(double);
RotateX3d(double a, double b, double c, double d)
{m[1][1] = a; m[1][2] = b; m[2][1] = c; m[2][2] = d;}
};
ostream& operator<<(ostream&, const RotateX3d&);
istream& operator>>(istream&, RotateX3d&);
class RotateY3d : public Matrix3d {
public:
RotateY3d()
{};
RotateY3d(double);
RotateY3d(double a, double b, double c, double d)
{m[0][0] = a; m[0][2] = b; m[2][0] = c; m[2][2] = d;}
};
ostream& operator<<(ostream&, const RotateY3d&);
istream& operator>>(istream&, RotateY3d&);
class RotateZ3d : public Matrix3d {
public:
RotateZ3d()
{};
RotateZ3d(double);
RotateZ3d(double a, double b, double c, double d)
{m[0][0] = a; m[0][1] = b; m[1][0] = c; m[1][1] = d;}
};
ostream& operator<<(ostream&, const RotateZ3d&);
istream& operator>>(istream&, RotateZ3d&);
class Shear3d : public Matrix3d {
public:
Shear3d(double x, double y, double dist)
{m[2][0] = -x/dist; m[2][1] = -y/dist;}
};
class Perspective3d : public Matrix3d {
public:
Perspective3d(double front, double back, double dist)
{ m[2][2] = back/(back-front); m[2][3] = 1;
m[3][2] = -front*back/(dist*(back-front)); m[3][3] = 0;}
};
class BBox3d {
public:
Vector3d ll;
Vector3d ur;
public:
BBox3d()
{}
BBox3d(double w, double h, double d)
{ll.v[0]=0; ll.v[1]=0; ll.v[2]=0; ur.v[0]=w; ur.v[1]=h; ur.v[2]=d;}
BBox3d(const Vector3d& v)
{ll=v; ur=v;}
BBox3d(double, double, double, double, double, double);
BBox3d(const Vector3d&, const Vector3d&);
BBox3d(const BBox3d& a)
{ll=a.ll; ur=a.ur;}
BBox3d& operator=(const BBox3d& a)
{ll=a.ll; ur=a.ur; return *this;}
BBox3d& operator+=(const Vector3d& v) // addition
{ll+=v; ur+=v; return *this;}
BBox3d& operator-=(const Vector3d& a) // subtraction
{ll-=a; ur-=a; return *this;}
BBox3d& operator*=(const Matrix3d& m) // multiplication
{ll*=m; ur*=m; return *this;}
double volume();
Vector3d center()
{return (ur-ll)/2 + ll;}
Vector3d size()
{return ur - ll;}
int isEmpty() const
{Vector3d v = ur-ll; return (v[0]==0 && v[1]==0 && v[2]==0);}
int isIn(const Vector3d&) const;
BBox3d& expand(double a)
{ll-=Vector3d(a,a,a); ur+=Vector3d(a,a,a); return *this;}
BBox3d& expand(const Vector3d& v)
{ll-=v; ur+=v; return *this;}
BBox3d& shrink(double a)
{ll+=Vector3d(a,a,a); ur-=Vector3d(a,a,a); return *this;}
BBox3d& shrink(const Vector3d& v)
{ll+=v; ur-=v; return *this;}
// expand bbox3d to include vector3d
BBox3d& bound(const Vector3d&);
};
ostream& operator<<(ostream&, const BBox3d&);
inline BBox3d operator+(const BBox3d& b, const Vector3d& v)
{return BBox3d(b) += v;}
inline BBox3d operator-(const BBox3d& b, const Vector3d& v)
{return BBox3d(b) -= v;}
inline BBox3d operator*(const BBox3d& b, const Matrix3d& m)
{return BBox3d(b) *= m;}
// WorldToView
Matrix3d WorldToView3d(const Vector3d& cop,
const Vector3d& vpn,
const Vector3d& vup);
Matrix3d WorldToView3d(const Vector3d& cop,
double head, double pitch, double bank);
Matrix3d WorldToView3d(const Vector3d& cop, const Vector3d& vpn, double bank);
#endif
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