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( 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];
            }

            /**
             * 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:	1603
Committed:	Tue Oct 19 21:28:55 2004 UTC (19 years, 8 months ago) by tim
File size:	14669 byte(s)
Log Message:	more bugs get fixed at math library
#	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			/** default constructor */
69			inline Vector(){
70			for (unsigned int i = 0; i < Dim; i++)
71			data_[i] = 0.0;
72			}
73
74			/** Constructs and initializes a Vector from a vector */
75			inline Vector(const Vector<Real, Dim>& v) {
76			*this = v;
77			}
78
79			/** copy assignment operator */
80			inline Vector<Real, Dim>& operator=(const Vector<Real, Dim>& v) {
81			if (this == &v)
82			return *this;
83
84			for (unsigned int i = 0; i < Dim; i++)
85			data_[i] = v[i];
86
87			return *this;
88			}
89	tim	1594
90			template<typename T>
91			inline Vector(const T& s){
92			for (unsigned int i = 0; i < Dim; i++)
93			data_[i] = s;
94			}
95	tim	1563
96			/** Constructs and initializes a Vector from an array */
97	tim	1603	inline Vector( Real* v) {
98	tim	1586	for (unsigned int i = 0; i < Dim; i++)
99			data_[i] = v[i];
100	tim	1563	}
101
102			/**
103			* Returns reference of ith element.
104			* @return reference of ith element
105			* @param i index
106			*/
107	tim	1603	inline Real& operator[](unsigned int i) {
108	tim	1563	assert( i < Dim);
109			return data_[i];
110			}
111
112			/**
113			* Returns reference of ith element.
114			* @return reference of ith element
115			* @param i index
116			*/
117	tim	1603	inline Real& operator()(unsigned int i) {
118	tim	1563	assert( i < Dim);
119			return data_[i];
120			}
121
122			/**
123			* Returns constant reference of ith element.
124			* @return reference of ith element
125			* @param i index
126			*/
127	tim	1603	inline const Real& operator[](unsigned int i) const {
128	tim	1563	assert( i < Dim);
129			return data_[i];
130			}
131
132			/**
133			* Returns constant reference of ith element.
134			* @return reference of ith element
135			* @param i index
136			*/
137	tim	1603	inline const Real& operator()(unsigned int i) const {
138	tim	1563	assert( i < Dim);
139			return data_[i];
140			}
141
142	tim	1569	/**
143			* Tests if this vetor is equal to other vector
144			* @return true if equal, otherwise return false
145			* @param v vector to be compared
146			*/
147			inline bool operator ==(const Vector<Real, Dim>& v) {
148
149			for (unsigned int i = 0; i < Dim; i ++) {
150			if (!equal(data_[i], v[i])) {
151			return false;
152			}
153			}
154
155			return true;
156			}
157
158			/**
159			* Tests if this vetor is not equal to other vector
160			* @return true if equal, otherwise return false
161			* @param v vector to be compared
162			*/
163			inline bool operator !=(const Vector<Real, Dim>& v) {
164			return !(*this == v);
165			}
166
167	tim	1563	/** Negates the value of this vector in place. */
168			inline void negate() {
169	tim	1594	for (unsigned int i = 0; i < Dim; i++)
170			data_[i] = -data_[i];
171	tim	1563	}
172
173			/**
174			* Sets the value of this vector to the negation of vector v1.
175			* @param v1 the source vector
176			*/
177			inline void negate(const Vector<Real, Dim>& v1) {
178			for (unsigned int i = 0; i < Dim; i++)
179			data_[i] = -v1.data_[i];
180
181			}
182
183			/**
184			* Sets the value of this vector to the sum of itself and v1 (*this += v1).
185			* @param v1 the other vector
186			*/
187			inline void add( const Vector<Real, Dim>& v1 ) {
188	tim	1603	for (unsigned int i = 0; i < Dim; i++)
189			data_[i] += v1.data_[i];
190			}
191	tim	1563
192			/**
193			* Sets the value of this vector to the sum of v1 and v2 (*this = v1 + v2).
194			* @param v1 the first vector
195			* @param v2 the second vector
196			*/
197			inline void add( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
198	tim	1586	for (unsigned int i = 0; i < Dim; i++)
199			data_[i] = v1.data_[i] + v2.data_[i];
200	tim	1563	}
201
202			/**
203			* Sets the value of this vector to the difference of itself and v1 (*this -= v1).
204			* @param v1 the other vector
205			*/
206			inline void sub( const Vector<Real, Dim>& v1 ) {
207			for (unsigned int i = 0; i < Dim; i++)
208			data_[i] -= v1.data_[i];
209			}
210
211			/**
212			* Sets the value of this vector to the difference of vector v1 and v2 (*this = v1 - v2).
213			* @param v1 the first vector
214			* @param v2 the second vector
215			*/
216			inline void sub( const Vector<Real, Dim>& v1, const Vector &v2 ){
217			for (unsigned int i = 0; i < Dim; i++)
218			data_[i] = v1.data_[i] - v2.data_[i];
219			}
220
221			/**
222			* Sets the value of this vector to the scalar multiplication of itself (this = s).
223			* @param s the scalar value
224			*/
225	tim	1603	inline void mul( Real s ) {
226	tim	1586	for (unsigned int i = 0; i < Dim; i++)
227	tim	1563	data_[i] *= s;
228			}
229
230			/**
231			* Sets the value of this vector to the scalar multiplication of vector v1
232			* (this = s v1).
233	tim	1594	* @param v1 the vector
234	tim	1563	* @param s the scalar value
235			*/
236	tim	1603	inline void mul( const Vector<Real, Dim>& v1, Real s) {
237	tim	1586	for (unsigned int i = 0; i < Dim; i++)
238	tim	1563	data_[i] = s * v1.data_[i];
239			}
240
241			/**
242			* Sets the value of this vector to the scalar division of itself (*this /= s ).
243			* @param s the scalar value
244			*/
245	tim	1603	inline void div( Real s) {
246	tim	1586	for (unsigned int i = 0; i < Dim; i++)
247	tim	1563	data_[i] /= s;
248			}
249
250			/**
251			* Sets the value of this vector to the scalar division of vector v1 (*this = v1 / s ).
252			* @param v1 the source vector
253			* @param s the scalar value
254			*/
255	tim	1603	inline void div( const Vector<Real, Dim>& v1, Real s ) {
256	tim	1586	for (unsigned int i = 0; i < Dim; i++)
257	tim	1563	data_[i] = v1.data_[i] / s;
258			}
259
260			/** @see #add */
261	tim	1564	inline Vector<Real, Dim>& operator +=( const Vector<Real, Dim>& v1 ) {
262	tim	1563	add(v1);
263			return *this;
264			}
265
266			/** @see #sub */
267	tim	1564	inline Vector<Real, Dim>& operator -=( const Vector<Real, Dim>& v1 ) {
268	tim	1563	sub(v1);
269			return *this;
270			}
271
272			/** @see #mul */
273	tim	1603	inline Vector<Real, Dim>& operator *=( Real s) {
274	tim	1563	mul(s);
275			return *this;
276			}
277
278			/** @see #div */
279	tim	1603	inline Vector<Real, Dim>& operator /=( Real s ) {
280	tim	1563	div(s);
281			return *this;
282			}
283
284			/**
285			* Returns the length of this vector.
286			* @return the length of this vector
287			*/
288	tim	1603	inline Real length() {
289	tim	1597	return sqrt(lengthSquare());
290	tim	1563	}
291
292			/**
293			* Returns the squared length of this vector.
294			* @return the squared length of this vector
295			*/
296	tim	1603	inline Real lengthSquare() {
297	tim	1563	return dot(this, this);
298			}
299
300			/** Normalizes this vector in place */
301			inline void normalize() {
302	tim	1603	Real len;
303	tim	1563
304			len = length();
305	tim	1595
306			//if (len < oopse:epsilon)
307			// throw();
308
309	tim	1563	*this /= len;
310			}
311	tim	1586
312			/**
313			* Tests if this vector is normalized
314			* @return true if this vector is normalized, otherwise return false
315			*/
316	tim	1597	inline bool isNormalized() {
317			return equal(lengthSquare(), 1.0);
318	tim	1586	}
319	tim	1563
320			protected:
321	tim	1603	Real data_[Dim];
322	tim	1563
323			};
324
325			/** unary minus*/
326	tim	1564	template<typename Real, unsigned int Dim>
327	tim	1563	inline Vector<Real, Dim> operator -(const Vector<Real, Dim>& v1){
328	tim	1594	Vector<Real, Dim> tmp(v1);
329			tmp.negate();
330			return tmp;
331	tim	1563	}
332
333			/**
334			* Return the sum of two vectors (v1 - v2).
335			* @return the sum of two vectors
336			* @param v1 the first vector
337			* @param v2 the second vector
338			*/
339	tim	1564	template<typename Real, unsigned int Dim>
340	tim	1563	inline Vector<Real, Dim> operator +(const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2) {
341			Vector<Real, Dim> result;
342
343			result.add(v1, v2);
344			return result;
345			}
346
347			/**
348			* Return the difference of two vectors (v1 - v2).
349			* @return the difference of two vectors
350			* @param v1 the first vector
351			* @param v2 the second vector
352			*/
353	tim	1564	template<typename Real, unsigned int Dim>
354	tim	1563	Vector<Real, Dim> operator -(const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2) {
355			Vector<Real, Dim> result;
356			result.sub(v1, v2);
357			return result;
358			}
359
360			/**
361			* Returns the vaule of scalar multiplication of this vector v1 (v1 * r).
362			* @return the vaule of scalar multiplication of this vector
363			* @param v1 the source vector
364			* @param s the scalar value
365			*/
366	tim	1564	template<typename Real, unsigned int Dim>
367	tim	1603	Vector<Real, Dim> operator * ( const Vector<Real, Dim>& v1, Real s) {
368	tim	1563	Vector<Real, Dim> result;
369	tim	1594	result.mul(v1,s);
370	tim	1563	return result;
371			}
372
373			/**
374			* Returns the vaule of scalar multiplication of this vector v1 (v1 * r).
375			* @return the vaule of scalar multiplication of this vector
376			* @param s the scalar value
377			* @param v1 the source vector
378			*/
379	tim	1564	template<typename Real, unsigned int Dim>
380	tim	1603	Vector<Real, Dim> operator * ( Real s, const Vector<Real, Dim>& v1 ) {
381	tim	1563	Vector<Real, Dim> result;
382	tim	1594	result.mul(v1, s);
383	tim	1563	return result;
384			}
385
386			/**
387			* Returns the value of division of a vector by a scalar.
388			* @return the vaule of scalar division of this vector
389			* @param v1 the source vector
390			* @param s the scalar value
391			*/
392	tim	1564	template<typename Real, unsigned int Dim>
393	tim	1603	Vector<Real, Dim> operator / ( const Vector<Real, Dim>& v1, Real s) {
394	tim	1563	Vector<Real, Dim> result;
395			result.div( v1,s);
396			return result;
397			}
398
399			/**
400			* Returns the dot product of two Vectors
401			* @param v1 first vector
402			* @param v2 second vector
403			* @return the dot product of v1 and v2
404			*/
405	tim	1564	template<typename Real, unsigned int Dim>
406	tim	1563	inline Real dot( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
407	tim	1586	Real tmp;
408			tmp = 0;
409	tim	1563
410	tim	1586	for (unsigned int i = 0; i < Dim; i++)
411	tim	1603	tmp += v1[i] * v2[i];
412	tim	1586
413			return tmp;
414	tim	1563	}
415
416			/**
417			* Returns the distance between two Vectors
418			* @param v1 first vector
419			* @param v2 second vector
420			* @return the distance between v1 and v2
421			*/
422	tim	1564	template<typename Real, unsigned int Dim>
423	tim	1563	inline Real distance( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
424			Vector<Real, Dim> tempVector = v1 - v2;
425			return tempVector.length();
426			}
427
428			/**
429			* Returns the squared distance between two Vectors
430			* @param v1 first vector
431			* @param v2 second vector
432			* @return the squared distance between v1 and v2
433			*/
434	tim	1564	template<typename Real, unsigned int Dim>
435	tim	1563	inline Real distanceSquare( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
436			Vector<Real, Dim> tempVector = v1 - v2;
437			return tempVector.lengthSquare();
438			}
439
440			/**
441			* Write to an output stream
442			*/
443	tim	1564	template<typename Real, unsigned int Dim>
444	tim	1586	std::ostream &operator<< ( std::ostream& o, const Vector<Real, Dim>& v) {
445
446	tim	1603	o << "[ ";
447
448			for (unsigned int i = 0 ; i< Dim; i++) {
449			o << v[i];
450
451			if (i != Dim -1) {
452			o<< ", ";
453			}
454			}
455
456			o << " ]";
457	tim	1563	return o;
458			}
459
460			}
461			#endif