Geometric functions. More...

#include "geometry.h"
#include <cassert>

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Functions
void	min_max3 (double a1, double a2, double a3, double &min, double &max)
	Find minimum and maximum of 3 numbers. More...

void	min_max4 (double a1, double a2, double a3, double a4, double &min, double &max)
	Find minimum and maximum of 4 numbers. More...

void	min_max6 (double a1, double a2, double a3, double a4, double a5, double a6, double &min, double &max)
	Find minimum and maximum of 6 numbers. More...

void	min_max12 (double a1, double a2, double a3, double a4, double a5, double a6, double a7, double a8, double a9, double a10, double a11, double a12, double &min, double &max)
	Find minimum and maximum of 12 numbers. More...

double	angle (Vector_3< double > v1, Vector_3< double > v2)
	Compute the angle between two vectors. More...

double	f_angle (Vector_3< double > v1, Vector_3< double >v2)
	Compute the angle between two faces. More...

void	printv (const Vector_3< double > &v)
	Print a vector. More...

void	unit_normal (const Vector_3< double > &v1, const Vector_3< double > &v2, Vector_3< double > &v3)
	Compute the unit vector normal to two input vectors. More...

double	edge_length (const Vector_3< double > &v)
	Compute the edge length of a vector. More...

double	tri_area (const Vector_3< double > &v1, const Vector_3< double > &v2, const Vector_3< double > &v3)
	Compute the area of a triangle defined by its three sides as vectors. More...

double	tet_vol (const Vector_3< double > &a, const Vector_3< double > &b, const Vector_3< double > &c)
	Compute the volume of a tetrahedron given three edges from a point as vectors. More...

Detailed Description

Geometric functions.

Implementation of geometric helper functions used by 2D and 3D geometric mesh quality measures.

Definition in file geometry.C.

Function Documentation

double angle	(	Vector_3< double >	v1,
		Vector_3< double >	v2
	)

Compute the angle between two vectors.

Definition at line 61 of file geometry.C.

References cimg_library::acos(), angle(), dot_product(), dotP(), nvc::norm2(), and sqrt().

Referenced by angle(), Geo_Metric_Base_2::compute_angles(), Geo_Metric_Base_3::compute_angles(), Rocmop::compute_medial_quadric(), FaceOffset_3::compute_quadrics(), CImg< uintT >::cone3d(), CFacet::contains_point(), CImg< uintT >::cylinder3d(), CImg< uintT >::draw_arrow(), f_angle(), and CImg< uintT >::FFT().

                                  {
   double dot_product, norm1, norm2, angle;
   dot_product = dotP(v1,v2);
   norm1 = sqrt(dotP(v1,v1)); norm2 = sqrt(dotP(v2,v2));
   angle = acos(dot_product/(norm1*norm2));
   assert(dot_product/(norm1*norm2) <=1 && dot_product/(norm1*norm2)>= -1);
   angle *= (double)180; angle  = angle/M_PI;
   return angle;
 }

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double edge_length ( const Vector_3< double > & v )

Compute the edge length of a vector.

Definition at line 89 of file geometry.C.

References sqrt().

Referenced by Geo_Metric_Base_2::compute_aspects(), Geo_Metric_Base_3::compute_aspects(), and tri_area().

                                               {
   return sqrt(v[0]*v[0] + v[1]*v[1] + v[2]*v[2]);
 }

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double f_angle	(	Vector_3< double >	v1,
		Vector_3< double >	v2
	)

Compute the angle between two faces.

Definition at line 72 of file geometry.C.

References angle().

Referenced by Geo_Metric_Base_3::compute_angles().

                                                        {
   return double(180) - angle(v1,v2);
 }

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void min_max12	(	double	a1,
		double	a2,
		double	a3,
		double	a4,
		double	a5,
		double	a6,
		double	a7,
		double	a8,
		double	a9,
		double	a10,
		double	a11,
		double	a12,
		double &	min,
		double &	max
	)

Find minimum and maximum of 12 numbers.

Definition at line 53 of file geometry.C.

References min_max6().

Referenced by Geo_Metric_Base_3::compute_angles().

                                                                                       {
   double min2, max2;
   min_max6(a1,a2,a3,a4,a5,a6,min,max); min_max6(a7,a8,a9,a10,a11,a12,min2,max2);
   min = (min < min2)? min : min2;      max = (max > max2)? max : max2;
 }

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void min_max3	(	double	a1,
		double	a2,
		double	a3,
		double &	min,
		double &	max
	)

Find minimum and maximum of 3 numbers.

Definition at line 36 of file geometry.C.

Referenced by Geo_Metric_Base_2::compute_angles(), min_max4(), and min_max6().

                                                                         {
 min = ( a1 < a2 )? a1 : a2;    max = ( a1 > a2 )? a1 : a2;
 min = ( min < a3 ) ? min : a3; max = ( max > a3 ) ? max : a3;
 }

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void min_max4	(	double	a1,
		double	a2,
		double	a3,
		double	a4,
		double &	min,
		double &	max
	)

Find minimum and maximum of 4 numbers.

Definition at line 41 of file geometry.C.

References min_max3().

Referenced by Geo_Metric_Base_2::compute_angles().

                                                                                    {
   min_max3(a1,a2,a3,min,max);
   min = (min < a4)? min : a4; max = (max > a4)? max : a4;
 }

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void min_max6	(	double	a1,
		double	a2,
		double	a3,
		double	a4,
		double	a5,
		double	a6,
		double &	min,
		double &	max
	)

Find minimum and maximum of 6 numbers.

Definition at line 46 of file geometry.C.

References min_max3().

Referenced by Geo_Metric_Base_3::compute_angles(), and min_max12().

                                                              {
   double min2, max2;
   min_max3(a1,a2,a3,min,max);     min_max3(a4,a5,a6,min2,max2);
   min = (min < min2)? min : min2; max = (max > max2)? max : max2;
 }

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void printv ( const Vector_3< double > & v )

Print a vector.

Definition at line 76 of file geometry.C.

                                        {
   cout << v[0] <<"  " << v[1] << "  " << v[2] << endl;
 }

double tet_vol	(	const Vector_3< double > &	a,
		const Vector_3< double > &	b,
		const Vector_3< double > &	c
	)

Compute the volume of a tetrahedron given three edges from a point as vectors.

Definition at line 103 of file geometry.C.

References NTS::abs(), crossP(), and dotP().

Referenced by Geo_Metric_Base_3::compute_aspects().

                                           {
   Vector_3<double> temp;
   crossP(b,c,temp);
   return  (1/(double)6) * abs (dotP(a,temp)  ) ;
 }

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double tri_area	(	const Vector_3< double > &	v1,
		const Vector_3< double > &	v2,
		const Vector_3< double > &	v3
	)

Compute the area of a triangle defined by its three sides as vectors.

Definition at line 93 of file geometry.C.

References edge_length(), s, and sqrt().

Referenced by Geo_Metric_Base_3::compute_aspects().

                                             {
   double a = edge_length(v1);
   double b = edge_length(v2);
   double c = edge_length(v3);
   double s = .5 * (a+b+c);
   return sqrt( s * (s-a) * (s-b) * (s-c) ); 
 }

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void unit_normal	(	const Vector_3< double > &	v1,
		const Vector_3< double > &	v2,
		Vector_3< double > &	v3
	)

Compute the unit vector normal to two input vectors.

Definition at line 80 of file geometry.C.

References crossP(), dotP(), and sqrt().

Referenced by Geo_Metric_Base_3::compute_angles().

                                       {
   crossP(v1,v2,v3);
   double normalizer = sqrt( dotP (v3,v3) );
   if (normalizer == 0) return;
   v3[0] = v3[0]/normalizer; v3[1] = v3[1]/normalizer; v3[2] = v3[2]/normalizer;
 } 

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Functions

Detailed Description

Function Documentation