//  vector.c
//
//  This file supports three-dimensional vector and matrix operations.
//
//  by John D. de Boer

//  For all procedures in this file, two or more parameters of the same type may
//  safely have repeated arguments.


//  Vector functions

typedef struct { real x,y,z; } vector;

void zerovector(vector *V);
void setvector(vector *V, real X, real Y, real Z);
void scalevector(vector *V, real M);
real lengthsquared(const vector *V);
real vectorlength(const vector *V);
void vectorsum(const vector *A, const vector *B, vector *Sum);
void vectordifference(const vector *A, const vector *B, vector *Diff);
real differencesquared(const vector *A, const vector *B);
void vectorincr(vector *A, const vector *B);
void vectordecr(vector *A, const vector *B);
void vectorincrement(vector *A, real F, const vector *B);
void vectormean(const vector *A, const vector *B, vector *M);
void vectorcomb(const vector *A, real F, const vector *B, vector *M);
real dotproduct(const vector *A, const vector *B);
void crossproduct(const vector *A, const vector *B, vector *C);
void normalise(vector *V);


//  Polar vectors

typedef struct {
real r,      //  radius
     theta,  //  polar angle
     phi;    //  azimuthal angle
} polar;

void vectortopolar(const vector *V, polar *R);
void polartovector(const polar *R, vector *V);

void cartesiantopolar(const vector *V, real *Rad, real *Theta, real *Phi);
void polartocartesian(real Rad, real Theta, real Phi, vector *V);
void unitvector(real Theta, real Phi, vector *U);


//  Simple rotations

void rotx090(vector *V);
void rotx180(vector *V);
void rotx270(vector *V);
void roty090(vector *V);
void roty180(vector *V);
void roty270(vector *V);
void rotz090(vector *V);
void rotz180(vector *V);
void rotz270(vector *V);
void rotx(vector *V, real Theta);
void roty(vector *V, real Theta);
void rotz(vector *V, real Theta);


//  Bounds

typedef struct { real x1,x2,y1,y2,z1,z2; } cuboid;

void initcuboid(cuboid *C, const vector *V);
void stretchcuboid(cuboid *C, const vector *V);
void unioncuboid(cuboid *C, const cuboid *D);


//  Matrix functions

typedef struct { real xx,xy,xz,yx,yy,yz,zx,zy,zz; } matrix;

void identitymatrix(matrix *T);
void transposematrix(matrix *T);
void product(const matrix *R, const vector *A, vector *B);
void matrixproduct(const matrix *R2, const matrix *R1, matrix *R);


//  Rotation matrices

void xrotation(real Theta, matrix *R);
void yrotation(real Theta, matrix *R);
void zrotation(real Theta, matrix *R);
void eulermatrix(real Precession, real Nutation, real Body, matrix *R);
void invertrotation(matrix *R);
void rotationinverse(const matrix *R, matrix *R1);
void rotatevector(const matrix *R, vector *V);
void unrotatevector(const matrix *R, vector *V);
void rotatematrix(const matrix *R, matrix *T);
void unrotatematrix(const matrix *R, matrix *T);