src/math/Vector.hpp

/*
 * Copyright (C) 2000-2004  Object Oriented Parallel Simulation Engine (OOPSE) project
 * 
 * Contact: oopse@oopse.org
 * 
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public License
 * as published by the Free Software Foundation; either version 2.1
 * of the License, or (at your option) any later version.
 * All we ask is that proper credit is given for our work, which includes
 * - but is not limited to - adding the above copyright notice to the beginning
 * of your source code files, and to any copyright notice that you may distribute
 * with programs based on this work.
 * 
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Lesser General Public License for more details.
 * 
 * You should have received a copy of the GNU Lesser General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.
 *
 */

/**
 * @file Vector.hpp
 * @author Teng Lin
 * @date 09/14/2004
 * @version 1.0
 */
 
#ifndef MATH_VECTOR_HPP
#define MATH_VECTOR_HPP

#include <cassert>
#include <cmath>
#include <iostream>

namespace oopse {

    const double epsilon = 0.000001;

    template<typename T>
    inline bool equal(T e1, T e2) {
        return e1 == e2;
    }

    template<>
    inline bool equal(float e1, float e2) {
        return fabs(e1 - e2) < epsilon;
    }

    template<>
    inline bool equal(double e1, double e2) {
        return fabs(e1 - e2) < epsilon;
    }
    
    /**
     * @class Vector Vector.hpp "math/Vector.hpp"
     * @brief Fix length vector class
     */
    template<typename Real, unsigned int Dim>
    class Vector{
        public:

            /** default constructor */
            inline Vector(){
                for (unsigned int i = 0; i < Dim; i++)
                    data_[i] = 0.0;
            }

            /** Constructs and initializes a Vector from a vector */
            inline Vector(const Vector<Real, Dim>& v) {
                *this  = v;
            }

            /** copy assignment operator */
            inline Vector<Real, Dim>& operator=(const Vector<Real, Dim>& v) {
                if (this == &v)
                    return *this;
                
                for (unsigned int i = 0; i < Dim; i++)            
                    data_[i] = v[i];
                
                return *this;
            }

            template<typename T>
            inline Vector(const T& s){
                for (unsigned int i = 0; i < Dim; i++)
                    data_[i] = s;
            }
            
            /** Constructs and initializes a Vector from an array */            
            inline Vector( double* v) {
                for (unsigned int i = 0; i < Dim; i++)
                    data_[i] = v[i];
            }

            /** 
             * Returns reference of ith element.
             * @return reference of ith element
             * @param i index
             */
            inline double& operator[](unsigned int  i) {
                assert( i < Dim);
                return data_[i];
            }

            /** 
             * Returns reference of ith element.
             * @return reference of ith element
             * @param i index
             */
            inline double& operator()(unsigned int  i) {
                assert( i < Dim);
                return data_[i];
            }

            /** 
             * Returns constant reference of ith element.
             * @return reference of ith element
             * @param i index
             */
            inline  const double& operator[](unsigned int i) const {
                assert( i < Dim);
                return data_[i];
            }

            /** 
             * Returns constant reference of ith element.
             * @return reference of ith element
             * @param i index
             */
            inline  const double& operator()(unsigned int i) const {
                assert( i < Dim);
                return data_[i];
            }

            /**
             * Tests if this vetor is equal to other vector
             * @return true if equal, otherwise return false
             * @param v vector to be compared
             */
             inline bool operator ==(const Vector<Real, Dim>& v) {

                for (unsigned int i = 0; i < Dim; i ++) {
                    if (!equal(data_[i], v[i])) {
                        return false;
                    }
                }
                
                return true;
            }

            /**
             * Tests if this vetor is not equal to other vector
             * @return true if equal, otherwise return false
             * @param v vector to be compared
             */
            inline bool operator !=(const Vector<Real, Dim>& v) {
                return !(*this == v);
            }
             
            /** Negates the value of this vector in place. */           
            inline void negate() {
                for (unsigned int i = 0; i < Dim; i++)
                    data_[i] = -data_[i];
            }

            /**
            * Sets the value of this vector to the negation of vector v1.
            * @param v1 the source vector
            */
            inline void negate(const Vector<Real, Dim>& v1) {
                for (unsigned int i = 0; i < Dim; i++)
                    data_[i] = -v1.data_[i];

            }
            
            /**
            * Sets the value of this vector to the sum of itself and v1 (*this += v1).
            * @param v1 the other vector
            */
            inline void add( const Vector<Real, Dim>& v1 ) {
            for (unsigned int i = 0; i < Dim; i++)
                data_[i] += v1.data_[i];
                }

            /**
            * Sets the value of this vector to the sum of v1 and v2 (*this = v1 + v2).
            * @param v1 the first vector
            * @param v2 the second vector
            */
            inline void add( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
                for (unsigned int i = 0; i < Dim; i++)
                    data_[i] = v1.data_[i] + v2.data_[i];
            }

            /**
            * Sets the value of this vector to the difference  of itself and v1 (*this -= v1).
            * @param v1 the other vector
            */
            inline void sub( const Vector<Real, Dim>& v1 ) {
                for (unsigned int i = 0; i < Dim; i++)
                    data_[i] -= v1.data_[i];
            }

            /**
            * Sets the value of this vector to the difference of vector v1 and v2 (*this = v1 - v2).
            * @param v1 the first vector
            * @param v2 the second vector
            */
            inline void sub( const Vector<Real, Dim>& v1, const Vector  &v2 ){
                for (unsigned int i = 0; i < Dim; i++)
                    data_[i] = v1.data_[i] - v2.data_[i];
            }

            /**
            * Sets the value of this vector to the scalar multiplication of itself (*this *= s).
            * @param s the scalar value
            */
            inline void mul( double s ) {
                for (unsigned int i = 0; i < Dim; i++)
                   data_[i] *= s;
            }

            /**
            * Sets the value of this vector to the scalar multiplication of vector v1  
            * (*this = s * v1).
            * @param v1 the vector            
            * @param s the scalar value
            */
            inline void mul( const Vector<Real, Dim>& v1, double s) {
                for (unsigned int i = 0; i < Dim; i++)
                    data_[i] = s * v1.data_[i];
            }

            /**
            * Sets the value of this vector to the scalar division of itself  (*this /= s ).
            * @param s the scalar value
            */             
            inline void div( double s) {
                for (unsigned int i = 0; i < Dim; i++)            
                    data_[i] /= s;
            }

            /**
            * Sets the value of this vector to the scalar division of vector v1  (*this = v1 / s ).
            * @param v1 the source vector
            * @param s the scalar value
            */                         
            inline void div( const Vector<Real, Dim>& v1, double s ) {
                for (unsigned int i = 0; i < Dim; i++)
                    data_[i] = v1.data_[i] / s;
            }

            /** @see #add */
            inline Vector<Real, Dim>& operator +=( const Vector<Real, Dim>& v1 ) {
                add(v1);
                return *this;
            }

            /** @see #sub */
            inline Vector<Real, Dim>& operator -=( const Vector<Real, Dim>& v1 ) {
                sub(v1);
                return *this;
            }

            /** @see #mul */
            inline Vector<Real, Dim>& operator *=( double s) {
                mul(s);
                return *this;
            }

            /** @see #div */
            inline Vector<Real, Dim>& operator /=( double s ) {
                div(s);
                return *this;
            }

            /**
             * Returns the length of this vector.
             * @return the length of this vector
             */
             inline double length() {
                return sqrt(lengthSquare());  
            }
            
            /**
             * Returns the squared length of this vector.
             * @return the squared length of this vector
             */
             inline double lengthSquare() {
                return dot(*this, *this);
            }
            
            /** Normalizes this vector in place */
            inline void normalize() {
                double len;

                len = length();
                
                //if (len < oopse:epsilon)
                //  throw();
                
                *this /= len;
            }

            /**
             * Tests if this vector is normalized
             * @return true if this vector is normalized, otherwise return false
             */
            inline bool isNormalized() {
                return equal(lengthSquare(), 1.0);
            }           
            
        protected:
            double data_[Dim];
        
    };

    /** unary minus*/
    template<typename Real, unsigned int Dim>    
    inline Vector<Real, Dim> operator -(const Vector<Real, Dim>& v1){
        Vector<Real, Dim> tmp(v1);
        tmp.negate();
        return tmp;
    }

    /**
     * Return the sum of two vectors  (v1 - v2). 
     * @return the sum of two vectors
     * @param v1 the first vector
     * @param v2 the second vector
     */   
    template<typename Real, unsigned int Dim>    
    inline Vector<Real, Dim> operator +(const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2) {
        Vector<Real, Dim> result;
        
        result.add(v1, v2);
        return result;        
    }

    /**
     * Return the difference of two vectors  (v1 - v2). 
     * @return the difference of two vectors
     * @param v1 the first vector
     * @param v2 the second vector
     */  
    template<typename Real, unsigned int Dim>    
    Vector<Real, Dim> operator -(const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2) {
        Vector<Real, Dim> result;
        result.sub(v1, v2);
        return result;        
    }
    
    /**
     * Returns the vaule of scalar multiplication of this vector v1 (v1 * r). 
     * @return  the vaule of scalar multiplication of this vector
     * @param v1 the source vector
     * @param s the scalar value
     */ 
    template<typename Real, unsigned int Dim>                 
    Vector<Real, Dim> operator * ( const Vector<Real, Dim>& v1, double s) {       
        Vector<Real, Dim> result;
        result.mul(v1,s);
        return result;           
    }
    
    /**
     * Returns the vaule of scalar multiplication of this vector v1 (v1 * r). 
     * @return  the vaule of scalar multiplication of this vector
     * @param s the scalar value
     * @param v1 the source vector
     */  
    template<typename Real, unsigned int Dim>
    Vector<Real, Dim> operator * ( double s, const Vector<Real, Dim>& v1 ) {
        Vector<Real, Dim> result;
        result.mul(v1, s);
        return result;           
    }

    /**
     * Returns the  value of division of a vector by a scalar. 
     * @return  the vaule of scalar division of this vector
     * @param v1 the source vector
     * @param s the scalar value
     */
    template<typename Real, unsigned int Dim>    
    Vector<Real, Dim> operator / ( const Vector<Real, Dim>& v1, double s) {       
        Vector<Real, Dim> result;
        result.div( v1,s);
        return result;           
    }
    
    /**
     * Returns the dot product of two Vectors
     * @param v1 first vector
     * @param v2 second vector
     * @return the dot product of v1 and v2
     */
    template<typename Real, unsigned int Dim>    
    inline Real dot( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
        Real tmp;
        tmp = 0;

        for (unsigned int i = 0; i < Dim; i++)
            tmp += v1[i] + v2[i];

        return tmp;
    }

    /**
     * Returns the distance between  two Vectors
     * @param v1 first vector
     * @param v2 second vector
     * @return the distance between v1 and v2
     */ 
    template<typename Real, unsigned int Dim>    
    inline Real distance( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
        Vector<Real, Dim> tempVector = v1 - v2;
        return tempVector.length();
    }

    /**
     * Returns the squared distance between  two Vectors
     * @param v1 first vector
     * @param v2 second vector
     * @return the squared distance between v1 and v2
     */
    template<typename Real, unsigned int Dim>
    inline Real distanceSquare( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
        Vector<Real, Dim> tempVector = v1 - v2;
        return tempVector.lengthSquare();
    }

    /**
     * Write to an output stream
     */
    template<typename Real, unsigned int Dim>
    std::ostream &operator<< ( std::ostream& o, const Vector<Real, Dim>& v) {

        o << "[" << v[0] << ", " << v[1] << ", " << v[2] << "]" << endl;
        return o;        
    }
    
}
#endif
Revision:	104
Committed:	Tue Oct 19 04:34:35 2004 UTC (21 years ago) by tim
File size:	14570 byte(s)
Log Message:	more bugs are fixed in Vector class
#	User	Rev	Content
1	tim	70	/*
2			* Copyright (C) 2000-2004 Object Oriented Parallel Simulation Engine (OOPSE) project
3			*
4			* Contact: oopse@oopse.org
5			*
6			* This program is free software; you can redistribute it and/or
7			* modify it under the terms of the GNU Lesser General Public License
8			* as published by the Free Software Foundation; either version 2.1
9			* of the License, or (at your option) any later version.
10			* All we ask is that proper credit is given for our work, which includes
11			* - but is not limited to - adding the above copyright notice to the beginning
12			* of your source code files, and to any copyright notice that you may distribute
13			* with programs based on this work.
14			*
15			* This program is distributed in the hope that it will be useful,
16			* but WITHOUT ANY WARRANTY; without even the implied warranty of
17			* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
18			* GNU Lesser General Public License for more details.
19			*
20			* You should have received a copy of the GNU Lesser General Public License
21			* along with this program; if not, write to the Free Software
22			* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
23			*
24			*/
25
26			/**
27			* @file Vector.hpp
28			* @author Teng Lin
29			* @date 09/14/2004
30			* @version 1.0
31			*/
32
33			#ifndef MATH_VECTOR_HPP
34			#define MATH_VECTOR_HPP
35
36			#include <cassert>
37			#include <cmath>
38	tim	71	#include <iostream>
39	tim	70
40			namespace oopse {
41
42	tim	76	const double epsilon = 0.000001;
43
44			template<typename T>
45			inline bool equal(T e1, T e2) {
46			return e1 == e2;
47			}
48
49			template<>
50			inline bool equal(float e1, float e2) {
51			return fabs(e1 - e2) < epsilon;
52			}
53
54			template<>
55			inline bool equal(double e1, double e2) {
56			return fabs(e1 - e2) < epsilon;
57			}
58
59	tim	70	/**
60			* @class Vector Vector.hpp "math/Vector.hpp"
61			* @brief Fix length vector class
62			*/
63	tim	71	template<typename Real, unsigned int Dim>
64	tim	70	class Vector{
65			public:
66
67			/** default constructor */
68			inline Vector(){
69			for (unsigned int i = 0; i < Dim; i++)
70			data_[i] = 0.0;
71			}
72
73			/** Constructs and initializes a Vector from a vector */
74			inline Vector(const Vector<Real, Dim>& v) {
75			*this = v;
76			}
77
78			/** copy assignment operator */
79			inline Vector<Real, Dim>& operator=(const Vector<Real, Dim>& v) {
80			if (this == &v)
81			return *this;
82
83			for (unsigned int i = 0; i < Dim; i++)
84			data_[i] = v[i];
85
86			return *this;
87			}
88	tim	101
89			template<typename T>
90			inline Vector(const T& s){
91			for (unsigned int i = 0; i < Dim; i++)
92			data_[i] = s;
93			}
94	tim	70
95			/** Constructs and initializes a Vector from an array */
96			inline Vector( double* v) {
97	tim	93	for (unsigned int i = 0; i < Dim; i++)
98			data_[i] = v[i];
99	tim	70	}
100
101			/**
102			* Returns reference of ith element.
103			* @return reference of ith element
104			* @param i index
105			*/
106			inline double& operator[](unsigned int i) {
107			assert( i < Dim);
108			return data_[i];
109			}
110
111			/**
112			* Returns reference of ith element.
113			* @return reference of ith element
114			* @param i index
115			*/
116			inline double& operator()(unsigned int i) {
117			assert( i < Dim);
118			return data_[i];
119			}
120
121			/**
122			* Returns constant reference of ith element.
123			* @return reference of ith element
124			* @param i index
125			*/
126			inline const double& operator[](unsigned int i) const {
127			assert( i < Dim);
128			return data_[i];
129			}
130
131			/**
132			* Returns constant reference of ith element.
133			* @return reference of ith element
134			* @param i index
135			*/
136			inline const double& operator()(unsigned int i) const {
137			assert( i < Dim);
138			return data_[i];
139			}
140
141	tim	76	/**
142			* Tests if this vetor is equal to other vector
143			* @return true if equal, otherwise return false
144			* @param v vector to be compared
145			*/
146			inline bool operator ==(const Vector<Real, Dim>& v) {
147
148			for (unsigned int i = 0; i < Dim; i ++) {
149			if (!equal(data_[i], v[i])) {
150			return false;
151			}
152			}
153
154			return true;
155			}
156
157			/**
158			* Tests if this vetor is not equal to other vector
159			* @return true if equal, otherwise return false
160			* @param v vector to be compared
161			*/
162			inline bool operator !=(const Vector<Real, Dim>& v) {
163			return !(*this == v);
164			}
165
166	tim	70	/** Negates the value of this vector in place. */
167			inline void negate() {
168	tim	101	for (unsigned int i = 0; i < Dim; i++)
169			data_[i] = -data_[i];
170	tim	70	}
171
172			/**
173			* Sets the value of this vector to the negation of vector v1.
174			* @param v1 the source vector
175			*/
176			inline void negate(const Vector<Real, Dim>& v1) {
177			for (unsigned int i = 0; i < Dim; i++)
178			data_[i] = -v1.data_[i];
179
180			}
181
182			/**
183			* Sets the value of this vector to the sum of itself and v1 (*this += v1).
184			* @param v1 the other vector
185			*/
186			inline void add( const Vector<Real, Dim>& v1 ) {
187	tim	93	for (unsigned int i = 0; i < Dim; i++)
188			data_[i] += v1.data_[i];
189	tim	70	}
190
191			/**
192			* Sets the value of this vector to the sum of v1 and v2 (*this = v1 + v2).
193			* @param v1 the first vector
194			* @param v2 the second vector
195			*/
196			inline void add( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
197	tim	93	for (unsigned int i = 0; i < Dim; i++)
198			data_[i] = v1.data_[i] + v2.data_[i];
199	tim	70	}
200
201			/**
202			* Sets the value of this vector to the difference of itself and v1 (*this -= v1).
203			* @param v1 the other vector
204			*/
205			inline void sub( const Vector<Real, Dim>& v1 ) {
206			for (unsigned int i = 0; i < Dim; i++)
207			data_[i] -= v1.data_[i];
208			}
209
210			/**
211			* Sets the value of this vector to the difference of vector v1 and v2 (*this = v1 - v2).
212			* @param v1 the first vector
213			* @param v2 the second vector
214			*/
215			inline void sub( const Vector<Real, Dim>& v1, const Vector &v2 ){
216			for (unsigned int i = 0; i < Dim; i++)
217			data_[i] = v1.data_[i] - v2.data_[i];
218			}
219
220			/**
221			* Sets the value of this vector to the scalar multiplication of itself (this = s).
222			* @param s the scalar value
223			*/
224			inline void mul( double s ) {
225	tim	93	for (unsigned int i = 0; i < Dim; i++)
226	tim	70	data_[i] *= s;
227			}
228
229			/**
230			* Sets the value of this vector to the scalar multiplication of vector v1
231			* (this = s v1).
232	tim	101	* @param v1 the vector
233	tim	70	* @param s the scalar value
234			*/
235	tim	101	inline void mul( const Vector<Real, Dim>& v1, double s) {
236	tim	93	for (unsigned int i = 0; i < Dim; i++)
237	tim	70	data_[i] = s * v1.data_[i];
238			}
239
240			/**
241			* Sets the value of this vector to the scalar division of itself (*this /= s ).
242			* @param s the scalar value
243			*/
244			inline void div( double s) {
245	tim	93	for (unsigned int i = 0; i < Dim; i++)
246	tim	70	data_[i] /= s;
247			}
248
249			/**
250			* Sets the value of this vector to the scalar division of vector v1 (*this = v1 / s ).
251			* @param v1 the source vector
252			* @param s the scalar value
253			*/
254			inline void div( const Vector<Real, Dim>& v1, double s ) {
255	tim	93	for (unsigned int i = 0; i < Dim; i++)
256	tim	70	data_[i] = v1.data_[i] / s;
257			}
258
259			/** @see #add */
260	tim	71	inline Vector<Real, Dim>& operator +=( const Vector<Real, Dim>& v1 ) {
261	tim	70	add(v1);
262			return *this;
263			}
264
265			/** @see #sub */
266	tim	71	inline Vector<Real, Dim>& operator -=( const Vector<Real, Dim>& v1 ) {
267	tim	70	sub(v1);
268			return *this;
269			}
270
271			/** @see #mul */
272	tim	71	inline Vector<Real, Dim>& operator *=( double s) {
273	tim	70	mul(s);
274			return *this;
275			}
276
277			/** @see #div */
278	tim	71	inline Vector<Real, Dim>& operator /=( double s ) {
279	tim	70	div(s);
280			return *this;
281			}
282
283			/**
284			* Returns the length of this vector.
285			* @return the length of this vector
286			*/
287			inline double length() {
288	tim	104	return sqrt(lengthSquare());
289	tim	70	}
290
291			/**
292			* Returns the squared length of this vector.
293			* @return the squared length of this vector
294			*/
295	tim	93	inline double lengthSquare() {
296	tim	70	return dot(this, this);
297			}
298
299			/** Normalizes this vector in place */
300			inline void normalize() {
301			double len;
302
303			len = length();
304	tim	102
305			//if (len < oopse:epsilon)
306			// throw();
307
308	tim	70	*this /= len;
309			}
310	tim	93
311			/**
312			* Tests if this vector is normalized
313			* @return true if this vector is normalized, otherwise return false
314			*/
315	tim	104	inline bool isNormalized() {
316			return equal(lengthSquare(), 1.0);
317	tim	93	}
318	tim	70
319			protected:
320	tim	101	double data_[Dim];
321	tim	70
322			};
323
324			/** unary minus*/
325	tim	71	template<typename Real, unsigned int Dim>
326	tim	70	inline Vector<Real, Dim> operator -(const Vector<Real, Dim>& v1){
327	tim	101	Vector<Real, Dim> tmp(v1);
328			tmp.negate();
329			return tmp;
330	tim	70	}
331
332			/**
333			* Return the sum of two vectors (v1 - v2).
334			* @return the sum of two vectors
335			* @param v1 the first vector
336			* @param v2 the second vector
337			*/
338	tim	71	template<typename Real, unsigned int Dim>
339	tim	70	inline Vector<Real, Dim> operator +(const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2) {
340			Vector<Real, Dim> result;
341
342			result.add(v1, v2);
343			return result;
344			}
345
346			/**
347			* Return the difference of two vectors (v1 - v2).
348			* @return the difference of two vectors
349			* @param v1 the first vector
350			* @param v2 the second vector
351			*/
352	tim	71	template<typename Real, unsigned int Dim>
353	tim	70	Vector<Real, Dim> operator -(const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2) {
354			Vector<Real, Dim> result;
355			result.sub(v1, v2);
356			return result;
357			}
358
359			/**
360			* Returns the vaule of scalar multiplication of this vector v1 (v1 * r).
361			* @return the vaule of scalar multiplication of this vector
362			* @param v1 the source vector
363			* @param s the scalar value
364			*/
365	tim	71	template<typename Real, unsigned int Dim>
366	tim	70	Vector<Real, Dim> operator * ( const Vector<Real, Dim>& v1, double s) {
367			Vector<Real, Dim> result;
368	tim	101	result.mul(v1,s);
369	tim	70	return result;
370			}
371
372			/**
373			* Returns the vaule of scalar multiplication of this vector v1 (v1 * r).
374			* @return the vaule of scalar multiplication of this vector
375			* @param s the scalar value
376			* @param v1 the source vector
377			*/
378	tim	71	template<typename Real, unsigned int Dim>
379	tim	70	Vector<Real, Dim> operator * ( double s, const Vector<Real, Dim>& v1 ) {
380			Vector<Real, Dim> result;
381	tim	101	result.mul(v1, s);
382	tim	70	return result;
383			}
384
385			/**
386			* Returns the value of division of a vector by a scalar.
387			* @return the vaule of scalar division of this vector
388			* @param v1 the source vector
389			* @param s the scalar value
390			*/
391	tim	71	template<typename Real, unsigned int Dim>
392	tim	70	Vector<Real, Dim> operator / ( const Vector<Real, Dim>& v1, double s) {
393			Vector<Real, Dim> result;
394			result.div( v1,s);
395			return result;
396			}
397
398			/**
399			* Returns the dot product of two Vectors
400			* @param v1 first vector
401			* @param v2 second vector
402			* @return the dot product of v1 and v2
403			*/
404	tim	71	template<typename Real, unsigned int Dim>
405	tim	70	inline Real dot( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
406	tim	93	Real tmp;
407			tmp = 0;
408	tim	70
409	tim	93	for (unsigned int i = 0; i < Dim; i++)
410			tmp += v1[i] + v2[i];
411
412			return tmp;
413	tim	70	}
414
415			/**
416			* Returns the distance between two Vectors
417			* @param v1 first vector
418			* @param v2 second vector
419			* @return the distance between v1 and v2
420			*/
421	tim	71	template<typename Real, unsigned int Dim>
422	tim	70	inline Real distance( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
423			Vector<Real, Dim> tempVector = v1 - v2;
424			return tempVector.length();
425			}
426
427			/**
428			* Returns the squared distance between two Vectors
429			* @param v1 first vector
430			* @param v2 second vector
431			* @return the squared distance between v1 and v2
432			*/
433	tim	71	template<typename Real, unsigned int Dim>
434	tim	70	inline Real distanceSquare( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
435			Vector<Real, Dim> tempVector = v1 - v2;
436			return tempVector.lengthSquare();
437			}
438
439			/**
440			* Write to an output stream
441			*/
442	tim	71	template<typename Real, unsigned int Dim>
443	tim	93	std::ostream &operator<< ( std::ostream& o, const Vector<Real, Dim>& v) {
444
445			o << "[" << v[0] << ", " << v[1] << ", " << v[2] << "]" << endl;
446	tim	70	return o;
447			}
448
449			}
450			#endif