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A* -------------------------------------------------------------------
B* This file contains source code for the PyMOL computer program
C* copyright 1998-2000 by Warren Lyford Delano of DeLano Scientific. 
D* -------------------------------------------------------------------
E* It is unlawful to modify or remove this copyright notice.
F* -------------------------------------------------------------------
G* Please see the accompanying LICENSE file for further information. 
H* -------------------------------------------------------------------
I* Additional authors of this source file include:
Z* -------------------------------------------------------------------
#ifndef _H_Vector
#define _H_Vector


/* NOTE: Matrices are assumed to be row-major (C-like not
 * OpenGL-like) unless explictly labeled as per the following
 * conventions:
 * row-major:    33f, 33d, 44f, 44d, R33f, R33d, R44f, R44d
 * column-major: C33f, C33d, C44f, C44d

#define cPI            3.14159265358979323846  /* pi */

typedef float Vector3f[3]; /* for local vars only - use float* for parameters */
typedef int Vector3i[3];
typedef float Matrix33f[3][3]; 
typedef double Matrix33d[3][3]; 
typedef float Matrix53f[5][3];
typedef double Matrix53d[5][3];

unsigned int optimizer_workaround1u(unsigned int value);

float get_random0to1f(void);

float deg_to_rad(float angle);
float rad_to_deg(float angle);

double slow_sqrt1f(float f);
double slow_sqrt1d(double d);

void slow_normalize3f( float *v1 );
void normalize23f( float *v1 , float *v2);
void normalize3d( double *v1 );

void clamp3f(float *v1);
void get_divergent3f(float *src,float *dst);
void get_random3f(float *x);
void scatter3f(float *v,float weight);
void wiggle3f(float *v,float *p,float *s);
void extrapolate3f(float *v1, float *unit, float *result);

void mix3f(float *v1,float *v2,float fxn,float *v3);
void mix3d(double *v1,double *v2,double fxn,double *v3);

void get_system3f(float *x,float *y,float *z); /* make random system */
void get_system1f3f(float *x,float *y,float *z); /* make system in direction of x */
void get_system2f3f(float *x,float *y,float *z); /* make system in direction of x, perp to x,y */

double dot_product3d ( double *v1, double *v2 );
float slow_project3f ( float *v1, float *v2, float *proj );
void slow_remove_component3f ( float *v1, float *unit, float *result);
void remove_component3d ( double *v1, double *unit, double *result);
void cross_product3d ( double *v1, double *v2, double *cross );
void scale3d ( double *v1, double v0, double *v2);
void add3d ( double *v1, double *v0, double *v2);

double distance_line2point3f(float *base,float *normal,float *point,float *alongNormalSq);
double distance_halfline2point3f(float *base,float *normal,float *point,float *alongNormalSq);

double slow_diffsq3f ( float *v1, float *v2 );
double slow_diff3f ( float *v1, float *v2 );
int slow_within3f(float *v1,float *v2,float dist);
int slow_within3fsq(float *v1,float *v2,float dist,float dist2);
int slow_within3fret(float *v1,float *v2,float cutoff, float cutoff2, float *diff, float *dist);

int equal3f(float *v1,float *v2);

int pymol_roundf(float f);

float get_angle3f( float *v1, float *v2 );
float get_dihedral3f( float *v0, float *v1, float *v2, float *v3 );
double length3d ( double *v1 );

void min3f ( float *v1, float *v2, float *v3 );
void max3f ( float *v1, float *v2, float *v3 );

void dump3i( int *v, char *prefix );
void dump3f( float *v, char *prefix );
void dump3d( double *v, char *prefix );
void dump4f( float *v, char *prefix );
void dump33f( float *m, char *prefix );
void dump33d( double *m, char *prefix );
void dump44f( float *m, char *prefix );
void dump44d( double *m, char *prefix );

void copy44f( float *src,float *dst);
void copy44d ( double *src, double *dst );

void identity33f ( float *m1 );
void identity33d( double *m);
void identity44f ( float *m1 );
void identity44d ( double *m1 );

void copy44f44f ( float *src, float *dst );
void copy44d44f ( double *src, float *dst );
void copy44f44d ( float *src, double *dst );

void copy44d33f ( double *src, float *dst );
void copy44f33f ( float *src, float *dst );
void copy33f44d ( float *src, double *dst );
void copy33f44f ( float *src, float *dst );
void copy3d3f ( double *v1,float *v2);
void copy3f3d ( float *v1,double *v2);

/* in the following matrix multiplies and transformations:
   the last two matrices can be the same matrix! */

void transpose33f33f ( float  *m1, float  *m2);
void transpose44f44f ( float  *m1, float  *m2);
void transpose44d44d ( double  *m1, double  *m2);

void transform33f3f ( float  *m1, float  *m2,  float  *m3 );
void transform33Tf3f ( float  *m1, float  *m2,  float  *m3 ); /* uses transpose */

void transform44f3f ( float  *m1, float  *m2,  float  *m3 );
void transform44f4f ( float  *m1, float  *m2,  float  *m3 );

void transform44d3f ( double  *m1, float  *m2,  float  *m3 );
void transform44d3d (double *m1, double *m2, double *m3);
void inverse_transformC44f3f (float *m1, float *m2, float *m3);
void inverse_transform44f3f (float *m1, float *m2, float *m3);
void inverse_transform44d3f (double *m1, float *m2, float *m3);
void inverse_transform44d3d (double *m1, double *m2, double *m3);
void transform44f3fas33f3f (float *m1, float *m2, float *m3);
void transform44d3fas33d3f (double *m1, float *m2, float *m3);

void multiply33f33f ( float  *m1, float  *m2,  float  *m3 );
void multiply33d33d ( double *m1, double *m2, double  *m3 );

/* as matrix types */

void matrix_transform33f3f ( Matrix33f m1,float *v1,float *v2);
void matrix_inverse_transform33f3f ( Matrix33f m1,float *v1,float *v2);

void rotation_to_matrix33f (float *axis, float angle, Matrix33f mat);
void matrix_multiply33f33f ( Matrix33f m1,Matrix33f m2,Matrix33f m3);
void matrix_multiply33d33d ( Matrix33d m1,Matrix33d m2,Matrix33d m3);

/* A 4x4 TTT matrix is really a 3x3 rotation matrix with two translation vectors:
   (1) a pre-translation stored in forth row, first three columns.
   (2) and a post-translation stored in forth column, first three rows.
   There are certain cases where this representation is more convenient.
void combineTTT44f44f( float *m1, float *m2, float *m3);
void transformTTT44f3f ( float *m1, float *m2, float *m3 );
void transform_normalTTT44f3f ( float *m1, float *m2, float *m3 );
void initializeTTT44f ( float *m );

void multiply44d44d44d( double *left, double *right, double *product);
void left_multiply44d44d( double *left, double *right);
void right_multiply44d44d( double *left, double *right);

void multiply44f44f44f( float *left, float *right, float *product);
void left_multiply44f44f( float *left, float *right);
void right_multiply44f44f( float *left, float *right);

void reorient44d(double *matrix);

void recondition33d(double *matrix);
void recondition44d(double *matrix);
/* invert a 4x4 homogenous that contains just rotation & tranlation
  (e.g. no scaling & fourth row is 0,0,0,1) */
void invert_special44d44d( double *original, double *inv);
void invert_special44f44f( float *original, float *inv);

void invert_rotation_only44d44d( double *original, double *inv);

void convertTTTfR44d( float *ttt, double *homo);
void convertTTTfR44f( float *ttt, float *homo);
void convertR44dTTTf( double *homo, float *ttt);
void convert44d44f(double *dbl, float *flt);
void convert44f44d(float *flt, double *dbl);

void get_rotation_about3f3fTTTf(float angle, float *dir, float *origin, float *ttt);

/* end revised matrix routines */


void rotation_matrix3f( float angle, float x, float y, float z,float *m );

typedef float *oMatrix5f[5]; /* PHASE THESE OUT! - THEY CAUSE PROBLEMS! */

typedef float *oMatrix3f[3];

typedef float *oMatrix3d[3];

double matdiffsq ( float *v1, oMatrix5f m, float *v2 );

/*void matcopy ( oMatrix5f to, oMatrix5f from );
  void mattran ( oMatrix5f nm, oMatrix5f om, int axis, float dist );
  void matrot ( oMatrix5f nm, oMatrix5f om, int axis, float angle );*/

void matrix_to_rotation(Matrix53f rot,float *axis, float *angle);
void rotation_to_matrix(Matrix53f rot,float *axis, float angle);

void transform3d3f ( oMatrix3d m1,float *v1,float *v2);
void transform33d3f ( Matrix33d m1,float *v1,float *v2);
void transform5f3f ( oMatrix5f m, float *v1, float *v2 );

/* macros */



float dot_product3f ( float *v1, float *v2 );
void  invert3f ( float *v );
void  invert3f3f (float *v1, float *v2);
void  scale3f ( float *v1, float v0, float *v2);
void  copy3f( float *src , float *dst);
void  copy3d( double *src , double *dst);
void  copy4f( float *src , float *dst);
void  add3f ( float *v1, float *v2, float *sum );
void  subtract3f ( float *v1, float *v2, float *v3 );
double lengthsq3f ( float *v1 );
double length3f ( float *v1 );
void  cross_product3f ( float *v1, float *v2, float *cross );
void  average3f ( float *v1, float *v2, float *avg );
void  zero3f ( float *v1 )
void  ones3f ( float *v1);
void  set3f ( float *v1,float x,float y,float z );
void  swap1f (float *f, float *g);


#define set3f(v1,x,y,z) { (v1)[0]=(x);(v1)[1]=(y);(v1)[2]=(z); }
#define zero3f(v1) { (v1)[0]=0.0;(v1)[1]=0.0;(v1)[2]=0.0; }
#define ones3f(v1) { (v1)[0]=1.0F;(v1)[1]=1.0F;(v1)[2]=1.0F; }
#define dot_product3f(v1,v2) ((v1)[0]*(v2)[0] + (v1)[1]*(v2)[1] + (v1)[2]*(v2)[2])
#define invert3f(v) {(v)[0]=-(v)[0]; (v)[1]=-(v)[1]; (v)[2]=-(v)[2];}
#define invert3f3f(v1,v2) {(v2)[0]=-(v1)[0]; (v2)[1]=-(v1)[1]; (v2)[2]=-(v1)[2];}
#define scale3f(v1,v0,v2) {(v2)[0]=(v1)[0]*(v0); (v2)[1]=(v1)[1]*(v0); (v2)[2]=(v1)[2]*(v0);}
#define copy3f(v1,v2) {(v2)[0]=(v1)[0]; (v2)[1]=(v1)[1]; (v2)[2]=(v1)[2];}
#define copy3d(v1,v2) {(v2)[0]=(v1)[0]; (v2)[1]=(v1)[1]; (v2)[2]=(v1)[2];}
#define copy4f(v1,v2) {(v2)[0]=(v1)[0]; (v2)[1]=(v1)[1]; (v2)[2]=(v1)[2]; (v2)[3]=(v1)[3];}
#define add3f(v1,v2,v3) {(v3)[0]=(v1)[0]+(v2)[0]; (v3)[1]=(v1)[1]+(v2)[1]; (v3)[2]=(v1)[2]+(v2)[2];}
#define subtract3f(v1,v2,v3) {(v3)[0]=(v1)[0]-(v2)[0]; (v3)[1]=(v1)[1]-(v2)[1]; (v3)[2]=(v1)[2]-(v2)[2];}
#define lengthsq3f(v1) (((v1)[0]*(v1)[0]) + ((v1)[1]*(v1)[1]) + ((v1)[2]*(v1)[2]))
#define length3f(v1) (sqrt1f(((v1)[0]*(v1)[0]) + ((v1)[1]*(v1)[1]) + ((v1)[2]*(v1)[2])))
#define average3f(v1,v2,avg) { \
  (avg)[0] = ((v1)[0]+(v2)[0])/2; \
  (avg)[1] = ((v1)[1]+(v2)[1])/2; \
  (avg)[2] = ((v1)[2]+(v2)[2])/2; \
#define cross_product3f(v1,v2,cross) { \
  (cross)[0] = ((v1)[1]*(v2)[2]) - ((v1)[2]*(v2)[1]); \
  (cross)[1] = ((v1)[2]*(v2)[0]) - ((v1)[0]*(v2)[2]); \
  (cross)[2] = ((v1)[0]*(v2)[1]) - ((v1)[1]*(v2)[0]); \
#define swap1f(f,g) { float h;h=*(f);*(f)=*(g);*(g)=h; }


static const float _0f_inline = 0.0F;
static const double _0d_inline = 0.0;
static const float _1f_inline = 1.0F;
static const double _1d_inline = 1.0;
static const float R_SMALL_inline = 0.000000001F;
static const double R_SMALLd_inline = 0.000000001;

#define normalize3f inline_normalize3f
#define sqrt1f inline_sqrt1f
#define sqrt1d inline_sqrt1d
#define diff3f inline_diff3f
#define diffsq3f inline_diffsq3f
#define within3f inline_within3f
#define within3fsq inline_within3fsq
#define within3fret inline_within3fret
#define remove_component3f inline_remove_component3f
#define project3f inline_project3f

__inline__ static double inline_sqrt1f(float f) { /* no good as a macro because f is used twice */

__inline__ static double inline_sqrt1d(double f) { /* no good as a macro because f is used twice */

__inline__ static void inline_normalize3f( float *v1 )
   register double vlen = length3f(v1);
      if(vlen > R_SMALLd_inline)
            register float    inV   = (float)(_1d_inline / vlen);
            v1[0] *= inV;
            v1[1] *= inV;
            v1[2] *= inV;

__inline__ static double inline_diff3f ( float *v1, float *v2 )
  register float dx,dy,dz;
  dx = (v1[0]-v2[0]);
  dy = (v1[1]-v2[1]);
  dz = (v1[2]-v2[2]);
  return(sqrt1d(dx*dx + dy*dy + dz*dz));

__inline__ static double inline_diffsq3f ( float *v1, float *v2 )
  register double dx,dy,dz;
  dx = (v1[0]-v2[0]);
  dy = (v1[1]-v2[1]);
  dx = dx * dx;
  dz = (v1[2]-v2[2]);
  dy = dy*dy;
  return( dz*dz + (dx + dy) );

__inline__ static int inline_within3f(float *v1,float *v2,float dist)
  register float dx,dy,dz,dist2;
  dx = (float)fabs(v1[0]-v2[0]);
  dy = (float)fabs(v1[1]-v2[1]);
  if(dx>dist) return(0);
  dz = (float)fabs(v1[2]-v2[2]);
  dx = dx * dx;
  if(dy>dist) return(0);
  dy = dy * dy;
  dist2 = dist*dist;
  if(dz>dist) return(0);
  return(((dx + dy) + dz*dz)<=dist2);

__inline__ static int inline_within3fsq(float *v1,float *v2,float dist,float dist2)
  /* manually optimized to take advantage of parallel execution units */
  register float dx,dy,dz;
  dx = v1[0]-v2[0];
  dy = v1[1]-v2[1];
  dx = (float)fabs(dx);
  dy = (float)fabs(dy);
  if(dx>dist) return(0);
  dz = v1[2]-v2[2];
  dx = dx * dx;
  if(dy>dist) return(0);
  dz = (float)fabs(dz);
  dy = dy * dy;
  if(dz>dist) return(0);
  dx = dx + dy;
  dz = dz * dz;
  if(dx>dist2) return(0);
  return((dx + dz)<=(dist2));

__inline__ static int inline_within3fret(float *v1,float *v2,float cutoff, float cutoff2, float *diff, float *dist)
  register float dx,dy,dz,dist2;
  dx = (float)fabs( (diff[0] = v1[0]-v2[0]) );
  dy = (float)fabs( (diff[1] = v1[1]-v2[1]) );
  if(dx>cutoff) return 0;
  dz = (float)fabs( (diff[2] = v1[2]-v2[2]) );
  dx = dx * dx;
  if(dy>cutoff) return 0;
  dy = dy * dy;
  if(dz>cutoff) return 0;
  if((dist2 = ((dx + dy) + dz*dz))>cutoff2) 
    return 0;
  *dist = (float)sqrt1f(dist2);
  return 1;

__inline__ static void inline_remove_component3f ( float *v1, float *unit, float *result)
  register float dot;

  dot = v1[0]*unit[0] + v1[1]*unit[1] + v1[2]*unit[2];

__inline__ static float inline_project3f ( float *v1, float *v2, float *proj )
  register float dot;

      dot = v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2];
      proj[0] = v2[0] * dot;
      proj[1] = v2[1] * dot;
      proj[2] = v2[2] * dot;


#define normalize3f slow_normalize3f
#define sqrt1f slow_sqrt1f
#define sqrt1d slow_sqrt1d
#define diff3f slow_diff3f
#define diffsq3f slow_diffsq3f
#define within3f slow_within3f
#define within3fsq slow_within3fsq
#define within3fret slow_within3fret
#define project3f slow_project3f
#define remove_component3f slow_remove_component3f



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