#ifndef r2_H
#define r2_H

/* Operations on points and vectors of R^2 */
/* Last edited on 2005-01-16 15:19:56 by stolfi */
/* Copyright © 2005 Jorge Stolfi, UNICAMP. See note at end of file. */

#include <stdio.h>

typedef struct { double c[2]; } r2_t;

void r2_zero (r2_t *r);
  /* Sets {r} to the zero vector. */
  
void r2_all (double x, r2_t *r);
  /* Sets all coordinates of {r} to the value {x}. */
  
void r2_axis (int i, r2_t *r);
  /* Sets {r} to the {i}th vector of the canonical basis. */

void r2_add (r2_t *a, r2_t *b, r2_t *r);
  /* Sets {r = a + b}. */

void r2_sub (r2_t *a, r2_t *b, r2_t *r);
  /* Sets {r = a - b}. */

void r2_neg (r2_t *a, r2_t *r);
  /* Sets {r} to {-a}. */

void r2_scale (double s, r2_t *a, r2_t *r);
  /* Sets {r := s * a}. */

void r2_mix (double s, r2_t *a, double t, r2_t *b, r2_t *r);
  /* Sets {r := s * a + t * b}. */

void r2_mix_in (double s, r2_t *a, r2_t *r);
  /* Sets {r := r + s * a}. */

void r2_weigh (r2_t *a, r2_t *w, r2_t *r);
  /* Sets {r[i] := a[i] * w[i]}. */

double r2_norm (r2_t *a);
  /* Returns the Euclidean length of {a}. */

double r2_norm_sqr (r2_t *a);
  /* Returns the square of the Euclidean length of {a}. */

double r2_L_inf_norm (r2_t *a);
  /* Returns the L-infinity norm of {a} (max absolute coordinate). */

double r2_dist (r2_t *a, r2_t *b);
  /* Returns the Euclidean distance between {a} and {b}. */

double r2_dist_sqr (r2_t *a, r2_t *b);
  /* Returns the square of the Euclidean distance between {a} and {b}. */

double r2_L_inf_dist (r2_t *a, r2_t *b);
  /* Returns the L-infinity distance between {a} and {b} 
    (max absolute diff). */

double r2_dir (r2_t *a, r2_t *r); 
  /* Sets {r} to {a} normalized to unit Euclidean length; 
    returns the original length. */
  
double r2_L_inf_dir (r2_t *a, r2_t *r); 
  /* Sets {r} to the vector {a/r2_L_inf_norm(a)}; 
    returns the original norm. */

double r2_dot (r2_t *a, r2_t *b);
  /* Dot product of vectors {a} and {b}. */

double r2_cos (r2_t *a, r2_t *b);
  /* Cosine of angle between vectors {a} and {b}. */

double r2_sin (r2_t *a, r2_t *b);
  /* Absolute sine of angle between vectors {a} and {b}. */

void r2_cross (r2_t *a, r2_t *r);
  /* Sets {r} to the `cross product' of the vector {a}, namely 
    {a} rotated 90 degrees counterclockwise. */
  
double r2_det (r2_t *a, r2_t *b);
  /* Returns the determinant of the 2 x 2 matrix whose rows
    are {a} and {b}. */

double r2_decomp (r2_t *a, r2_t *u, r2_t *para, r2_t *perp);
  /* Sets {para} and {perp} (when not NULL) to the components of 
    {a} that are parallel and perpendicular to to {u}, respectively.
    Namely, {para = c*u} and {perp = a - c*u}, where 
    {c = r2_dot(a,u)/r2_dot(u,u)}. Also returns {c}. */

void r2_throw_cube (r2_t *r);
  /* Sets {r} to a uniformly random point of the 2-cube {[-1 .. +1]^2}. */
  
void r2_throw_ball (r2_t *r);
  /* Sets {r} to a uniformly random point of the unit N-ball. */

void r2_throw_normal (r2_t *r);
  /* Sets each coordinate {r[i]} to an independent Gaussian random
    number with zero mean and unit standard deviation. */

void r2_print (FILE *f, r2_t *a);
  /* Prints {a} on file {f}, with some default format. */

void r2_gen_print (FILE *f, r2_t *a, char *fmt, char *lp, char *sep, char *rp);
  /* Prints {a} on file {f}, formatting each coordinate with {fmt}. 
    The strings {lp}, {sep}, and {rp} are printed respectively before,
    between, and after all the coordinates of {a}.  When NULL, they default 
    to "%16.8e", "(", " ", and ")", respectively. */

#endif
/* COPYRIGHT AND AUTHORSHIP NOTICE

  Copyright © 2005 Jorge Stolfi, Universidade Estadual de Campinas (UNICAMP).
  Created by Jorge Stolfi in 1992--2005.
  
  This source file can be freely distributed, used, and modified,
  provided that this copyright and authorship notice is preserved in
  all copies, and that any modified versions of this file are clearly
  marked as such.
  
  This software has NO WARRANTY of correctness or applicability for
  any purpose. Neither the author nor his employers shall be held
  responsible for any losses or damages that may result from its use.

  END OF NOTICE */