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:

            typedef Real ElemType;
            typedef Real* ElemPoinerType;

            /** 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( Real* 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 Real& operator[](unsigned int  i) {
                assert( i < Dim);
                return data_[i];
            }

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

            /** Returns the pointer of internal array */
            Real* getArrayPointer() {
                return data_;
            }
            
            /**
             * 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( Real 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, Real 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( Real 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, Real 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 *=( Real s) {
                mul(s);
                return *this;
            }

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

            /**
             * Returns the length of this vector.
             * @return the length of this vector
             */
             inline Real length() {
                return sqrt(lengthSquare());  
            }
            
            /**
             * Returns the squared length of this vector.
             * @return the squared length of this vector
             */
             inline Real lengthSquare() {
                return dot(*this, *this);
            }
            
            /** Normalizes this vector in place */
            inline void normalize() {
                Real 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:
            Real 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, Real 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 * ( Real 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, Real 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 << "[ ";
        
        for (unsigned int i = 0 ; i< Dim; i++) {
            o << v[i];

            if (i  != Dim -1) {
                o<< ", ";
            }
        }

        o << " ]";
        return o;        
    }
    
}
#endif
Revision:	1630
Committed:	Thu Oct 21 21:31:39 2004 UTC (19 years, 8 months ago) by tim
Original Path:	*trunk/OOPSE-3.0/src/math/Vector.hpp*
File size:	14899 byte(s)
Log Message:	Snapshot and SnapshotManager in progress
#	User	Rev	Content
1	tim	1563	/*
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	1564	#include <iostream>
39	tim	1563
40			namespace oopse {
41
42	tim	1569	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	tim	1603
59	tim	1569
60	tim	1563	/**
61			* @class Vector Vector.hpp "math/Vector.hpp"
62			* @brief Fix length vector class
63			*/
64	tim	1564	template<typename Real, unsigned int Dim>
65	tim	1563	class Vector{
66			public:
67
68	tim	1630	typedef Real ElemType;
69			typedef Real* ElemPoinerType;
70
71	tim	1563	/** default constructor */
72			inline Vector(){
73			for (unsigned int i = 0; i < Dim; i++)
74			data_[i] = 0.0;
75			}
76
77			/** Constructs and initializes a Vector from a vector */
78			inline Vector(const Vector<Real, Dim>& v) {
79			*this = v;
80			}
81
82			/** copy assignment operator */
83			inline Vector<Real, Dim>& operator=(const Vector<Real, Dim>& v) {
84			if (this == &v)
85			return *this;
86
87			for (unsigned int i = 0; i < Dim; i++)
88			data_[i] = v[i];
89
90			return *this;
91			}
92	tim	1594
93			template<typename T>
94			inline Vector(const T& s){
95			for (unsigned int i = 0; i < Dim; i++)
96			data_[i] = s;
97			}
98	tim	1563
99			/** Constructs and initializes a Vector from an array */
100	tim	1603	inline Vector( Real* v) {
101	tim	1586	for (unsigned int i = 0; i < Dim; i++)
102			data_[i] = v[i];
103	tim	1563	}
104
105			/**
106			* Returns reference of ith element.
107			* @return reference of ith element
108			* @param i index
109			*/
110	tim	1603	inline Real& operator[](unsigned int i) {
111	tim	1563	assert( i < Dim);
112			return data_[i];
113			}
114
115			/**
116			* Returns reference of ith element.
117			* @return reference of ith element
118			* @param i index
119			*/
120	tim	1603	inline Real& operator()(unsigned int i) {
121	tim	1563	assert( i < Dim);
122			return data_[i];
123			}
124
125			/**
126			* Returns constant reference of ith element.
127			* @return reference of ith element
128			* @param i index
129			*/
130	tim	1603	inline const Real& operator[](unsigned int i) const {
131	tim	1563	assert( i < Dim);
132			return data_[i];
133			}
134
135			/**
136			* Returns constant reference of ith element.
137			* @return reference of ith element
138			* @param i index
139			*/
140	tim	1603	inline const Real& operator()(unsigned int i) const {
141	tim	1563	assert( i < Dim);
142			return data_[i];
143			}
144
145	tim	1630	/** Returns the pointer of internal array */
146			Real* getArrayPointer() {
147			return data_;
148			}
149
150	tim	1569	/**
151			* Tests if this vetor is equal to other vector
152			* @return true if equal, otherwise return false
153			* @param v vector to be compared
154			*/
155			inline bool operator ==(const Vector<Real, Dim>& v) {
156
157			for (unsigned int i = 0; i < Dim; i ++) {
158			if (!equal(data_[i], v[i])) {
159			return false;
160			}
161			}
162
163			return true;
164			}
165
166			/**
167			* Tests if this vetor is not equal to other vector
168			* @return true if equal, otherwise return false
169			* @param v vector to be compared
170			*/
171			inline bool operator !=(const Vector<Real, Dim>& v) {
172			return !(*this == v);
173			}
174
175	tim	1563	/** Negates the value of this vector in place. */
176			inline void negate() {
177	tim	1594	for (unsigned int i = 0; i < Dim; i++)
178			data_[i] = -data_[i];
179	tim	1563	}
180
181			/**
182			* Sets the value of this vector to the negation of vector v1.
183			* @param v1 the source vector
184			*/
185			inline void negate(const Vector<Real, Dim>& v1) {
186			for (unsigned int i = 0; i < Dim; i++)
187			data_[i] = -v1.data_[i];
188
189			}
190
191			/**
192			* Sets the value of this vector to the sum of itself and v1 (*this += v1).
193			* @param v1 the other vector
194			*/
195			inline void add( const Vector<Real, Dim>& v1 ) {
196	tim	1603	for (unsigned int i = 0; i < Dim; i++)
197			data_[i] += v1.data_[i];
198			}
199	tim	1563
200			/**
201			* Sets the value of this vector to the sum of v1 and v2 (*this = v1 + v2).
202			* @param v1 the first vector
203			* @param v2 the second vector
204			*/
205			inline void add( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
206	tim	1586	for (unsigned int i = 0; i < Dim; i++)
207			data_[i] = v1.data_[i] + v2.data_[i];
208	tim	1563	}
209
210			/**
211			* Sets the value of this vector to the difference of itself and v1 (*this -= v1).
212			* @param v1 the other vector
213			*/
214			inline void sub( const Vector<Real, Dim>& v1 ) {
215			for (unsigned int i = 0; i < Dim; i++)
216			data_[i] -= v1.data_[i];
217			}
218
219			/**
220			* Sets the value of this vector to the difference of vector v1 and v2 (*this = v1 - v2).
221			* @param v1 the first vector
222			* @param v2 the second vector
223			*/
224			inline void sub( const Vector<Real, Dim>& v1, const Vector &v2 ){
225			for (unsigned int i = 0; i < Dim; i++)
226			data_[i] = v1.data_[i] - v2.data_[i];
227			}
228
229			/**
230			* Sets the value of this vector to the scalar multiplication of itself (this = s).
231			* @param s the scalar value
232			*/
233	tim	1603	inline void mul( Real s ) {
234	tim	1586	for (unsigned int i = 0; i < Dim; i++)
235	tim	1563	data_[i] *= s;
236			}
237
238			/**
239			* Sets the value of this vector to the scalar multiplication of vector v1
240			* (this = s v1).
241	tim	1594	* @param v1 the vector
242	tim	1563	* @param s the scalar value
243			*/
244	tim	1603	inline void mul( const Vector<Real, Dim>& v1, Real s) {
245	tim	1586	for (unsigned int i = 0; i < Dim; i++)
246	tim	1563	data_[i] = s * v1.data_[i];
247			}
248
249			/**
250			* Sets the value of this vector to the scalar division of itself (*this /= s ).
251			* @param s the scalar value
252			*/
253	tim	1603	inline void div( Real s) {
254	tim	1586	for (unsigned int i = 0; i < Dim; i++)
255	tim	1563	data_[i] /= s;
256			}
257
258			/**
259			* Sets the value of this vector to the scalar division of vector v1 (*this = v1 / s ).
260			* @param v1 the source vector
261			* @param s the scalar value
262			*/
263	tim	1603	inline void div( const Vector<Real, Dim>& v1, Real s ) {
264	tim	1586	for (unsigned int i = 0; i < Dim; i++)
265	tim	1563	data_[i] = v1.data_[i] / s;
266			}
267
268			/** @see #add */
269	tim	1564	inline Vector<Real, Dim>& operator +=( const Vector<Real, Dim>& v1 ) {
270	tim	1563	add(v1);
271			return *this;
272			}
273
274			/** @see #sub */
275	tim	1564	inline Vector<Real, Dim>& operator -=( const Vector<Real, Dim>& v1 ) {
276	tim	1563	sub(v1);
277			return *this;
278			}
279
280			/** @see #mul */
281	tim	1603	inline Vector<Real, Dim>& operator *=( Real s) {
282	tim	1563	mul(s);
283			return *this;
284			}
285
286			/** @see #div */
287	tim	1603	inline Vector<Real, Dim>& operator /=( Real s ) {
288	tim	1563	div(s);
289			return *this;
290			}
291
292			/**
293			* Returns the length of this vector.
294			* @return the length of this vector
295			*/
296	tim	1603	inline Real length() {
297	tim	1597	return sqrt(lengthSquare());
298	tim	1563	}
299
300			/**
301			* Returns the squared length of this vector.
302			* @return the squared length of this vector
303			*/
304	tim	1603	inline Real lengthSquare() {
305	tim	1563	return dot(this, this);
306			}
307
308			/** Normalizes this vector in place */
309			inline void normalize() {
310	tim	1603	Real len;
311	tim	1563
312			len = length();
313	tim	1595
314			//if (len < oopse:epsilon)
315			// throw();
316
317	tim	1563	*this /= len;
318			}
319	tim	1586
320			/**
321			* Tests if this vector is normalized
322			* @return true if this vector is normalized, otherwise return false
323			*/
324	tim	1597	inline bool isNormalized() {
325			return equal(lengthSquare(), 1.0);
326	tim	1586	}
327	tim	1563
328			protected:
329	tim	1603	Real data_[Dim];
330	tim	1563
331			};
332
333			/** unary minus*/
334	tim	1564	template<typename Real, unsigned int Dim>
335	tim	1563	inline Vector<Real, Dim> operator -(const Vector<Real, Dim>& v1){
336	tim	1594	Vector<Real, Dim> tmp(v1);
337			tmp.negate();
338			return tmp;
339	tim	1563	}
340
341			/**
342			* Return the sum of two vectors (v1 - v2).
343			* @return the sum of two vectors
344			* @param v1 the first vector
345			* @param v2 the second vector
346			*/
347	tim	1564	template<typename Real, unsigned int Dim>
348	tim	1563	inline Vector<Real, Dim> operator +(const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2) {
349			Vector<Real, Dim> result;
350
351			result.add(v1, v2);
352			return result;
353			}
354
355			/**
356			* Return the difference of two vectors (v1 - v2).
357			* @return the difference of two vectors
358			* @param v1 the first vector
359			* @param v2 the second vector
360			*/
361	tim	1564	template<typename Real, unsigned int Dim>
362	tim	1563	Vector<Real, Dim> operator -(const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2) {
363			Vector<Real, Dim> result;
364			result.sub(v1, v2);
365			return result;
366			}
367
368			/**
369			* Returns the vaule of scalar multiplication of this vector v1 (v1 * r).
370			* @return the vaule of scalar multiplication of this vector
371			* @param v1 the source vector
372			* @param s the scalar value
373			*/
374	tim	1564	template<typename Real, unsigned int Dim>
375	tim	1603	Vector<Real, Dim> operator * ( const Vector<Real, Dim>& v1, Real s) {
376	tim	1563	Vector<Real, Dim> result;
377	tim	1594	result.mul(v1,s);
378	tim	1563	return result;
379			}
380
381			/**
382			* Returns the vaule of scalar multiplication of this vector v1 (v1 * r).
383			* @return the vaule of scalar multiplication of this vector
384			* @param s the scalar value
385			* @param v1 the source vector
386			*/
387	tim	1564	template<typename Real, unsigned int Dim>
388	tim	1603	Vector<Real, Dim> operator * ( Real s, const Vector<Real, Dim>& v1 ) {
389	tim	1563	Vector<Real, Dim> result;
390	tim	1594	result.mul(v1, s);
391	tim	1563	return result;
392			}
393
394			/**
395			* Returns the value of division of a vector by a scalar.
396			* @return the vaule of scalar division of this vector
397			* @param v1 the source vector
398			* @param s the scalar value
399			*/
400	tim	1564	template<typename Real, unsigned int Dim>
401	tim	1603	Vector<Real, Dim> operator / ( const Vector<Real, Dim>& v1, Real s) {
402	tim	1563	Vector<Real, Dim> result;
403			result.div( v1,s);
404			return result;
405			}
406
407			/**
408			* Returns the dot product of two Vectors
409			* @param v1 first vector
410			* @param v2 second vector
411			* @return the dot product of v1 and v2
412			*/
413	tim	1564	template<typename Real, unsigned int Dim>
414	tim	1563	inline Real dot( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
415	tim	1586	Real tmp;
416			tmp = 0;
417	tim	1563
418	tim	1586	for (unsigned int i = 0; i < Dim; i++)
419	tim	1603	tmp += v1[i] * v2[i];
420	tim	1586
421			return tmp;
422	tim	1563	}
423
424			/**
425			* Returns the distance between two Vectors
426			* @param v1 first vector
427			* @param v2 second vector
428			* @return the distance between v1 and v2
429			*/
430	tim	1564	template<typename Real, unsigned int Dim>
431	tim	1563	inline Real distance( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
432			Vector<Real, Dim> tempVector = v1 - v2;
433			return tempVector.length();
434			}
435
436			/**
437			* Returns the squared distance between two Vectors
438			* @param v1 first vector
439			* @param v2 second vector
440			* @return the squared distance between v1 and v2
441			*/
442	tim	1564	template<typename Real, unsigned int Dim>
443	tim	1563	inline Real distanceSquare( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
444			Vector<Real, Dim> tempVector = v1 - v2;
445			return tempVector.lengthSquare();
446			}
447
448			/**
449			* Write to an output stream
450			*/
451	tim	1564	template<typename Real, unsigned int Dim>
452	tim	1586	std::ostream &operator<< ( std::ostream& o, const Vector<Real, Dim>& v) {
453
454	tim	1603	o << "[ ";
455
456			for (unsigned int i = 0 ; i< Dim; i++) {
457			o << v[i];
458
459			if (i != Dim -1) {
460			o<< ", ";
461			}
462			}
463
464			o << " ]";
465	tim	1563	return o;
466			}
467
468			}
469			#endif