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];
            }

            /** Copy the internal data to an array*/
            void getArray(Real* array) {
                for (unsigned int i = 0; i < Dim; i ++) {
                    array[i] = 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:	151
Committed:	Mon Oct 25 22:46:19 2004 UTC (20 years, 6 months ago) by tim
File size:	15141 byte(s)
Log Message:	add getArray function to RectMatrix and Vector classes
#	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	tim	110
59	tim	76
60	tim	70	/**
61			* @class Vector Vector.hpp "math/Vector.hpp"
62			* @brief Fix length vector class
63			*/
64	tim	71	template<typename Real, unsigned int Dim>
65	tim	70	class Vector{
66			public:
67
68	tim	137	typedef Real ElemType;
69			typedef Real* ElemPoinerType;
70
71	tim	70	/** 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	101
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	70
99			/** Constructs and initializes a Vector from an array */
100	tim	110	inline Vector( Real* v) {
101	tim	93	for (unsigned int i = 0; i < Dim; i++)
102			data_[i] = v[i];
103	tim	70	}
104
105			/**
106			* Returns reference of ith element.
107			* @return reference of ith element
108			* @param i index
109			*/
110	tim	110	inline Real& operator[](unsigned int i) {
111	tim	70	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	110	inline Real& operator()(unsigned int i) {
121	tim	70	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	110	inline const Real& operator[](unsigned int i) const {
131	tim	70	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	110	inline const Real& operator()(unsigned int i) const {
141	tim	70	assert( i < Dim);
142			return data_[i];
143			}
144
145	tim	151	/** Copy the internal data to an array*/
146			void getArray(Real* array) {
147			for (unsigned int i = 0; i < Dim; i ++) {
148			array[i] = data_[i];
149			}
150			}
151
152	tim	137	/** Returns the pointer of internal array */
153			Real* getArrayPointer() {
154			return data_;
155			}
156
157	tim	76	/**
158			* Tests if this vetor is 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
164			for (unsigned int i = 0; i < Dim; i ++) {
165			if (!equal(data_[i], v[i])) {
166			return false;
167			}
168			}
169
170			return true;
171			}
172
173			/**
174			* Tests if this vetor is not equal to other vector
175			* @return true if equal, otherwise return false
176			* @param v vector to be compared
177			*/
178			inline bool operator !=(const Vector<Real, Dim>& v) {
179			return !(*this == v);
180			}
181
182	tim	70	/** Negates the value of this vector in place. */
183			inline void negate() {
184	tim	101	for (unsigned int i = 0; i < Dim; i++)
185			data_[i] = -data_[i];
186	tim	70	}
187
188			/**
189			* Sets the value of this vector to the negation of vector v1.
190			* @param v1 the source vector
191			*/
192			inline void negate(const Vector<Real, Dim>& v1) {
193			for (unsigned int i = 0; i < Dim; i++)
194			data_[i] = -v1.data_[i];
195
196			}
197
198			/**
199			* Sets the value of this vector to the sum of itself and v1 (*this += v1).
200			* @param v1 the other vector
201			*/
202			inline void add( const Vector<Real, Dim>& v1 ) {
203	tim	110	for (unsigned int i = 0; i < Dim; i++)
204			data_[i] += v1.data_[i];
205			}
206	tim	70
207			/**
208			* Sets the value of this vector to the sum of v1 and v2 (*this = v1 + v2).
209			* @param v1 the first vector
210			* @param v2 the second vector
211			*/
212			inline void add( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
213	tim	93	for (unsigned int i = 0; i < Dim; i++)
214			data_[i] = v1.data_[i] + v2.data_[i];
215	tim	70	}
216
217			/**
218			* Sets the value of this vector to the difference of itself and v1 (*this -= v1).
219			* @param v1 the other vector
220			*/
221			inline void sub( const Vector<Real, Dim>& v1 ) {
222			for (unsigned int i = 0; i < Dim; i++)
223			data_[i] -= v1.data_[i];
224			}
225
226			/**
227			* Sets the value of this vector to the difference of vector v1 and v2 (*this = v1 - v2).
228			* @param v1 the first vector
229			* @param v2 the second vector
230			*/
231			inline void sub( const Vector<Real, Dim>& v1, const Vector &v2 ){
232			for (unsigned int i = 0; i < Dim; i++)
233			data_[i] = v1.data_[i] - v2.data_[i];
234			}
235
236			/**
237			* Sets the value of this vector to the scalar multiplication of itself (this = s).
238			* @param s the scalar value
239			*/
240	tim	110	inline void mul( Real s ) {
241	tim	93	for (unsigned int i = 0; i < Dim; i++)
242	tim	70	data_[i] *= s;
243			}
244
245			/**
246			* Sets the value of this vector to the scalar multiplication of vector v1
247			* (this = s v1).
248	tim	101	* @param v1 the vector
249	tim	70	* @param s the scalar value
250			*/
251	tim	110	inline void mul( const Vector<Real, Dim>& v1, Real s) {
252	tim	93	for (unsigned int i = 0; i < Dim; i++)
253	tim	70	data_[i] = s * v1.data_[i];
254			}
255
256			/**
257			* Sets the value of this vector to the scalar division of itself (*this /= s ).
258			* @param s the scalar value
259			*/
260	tim	110	inline void div( Real s) {
261	tim	93	for (unsigned int i = 0; i < Dim; i++)
262	tim	70	data_[i] /= s;
263			}
264
265			/**
266			* Sets the value of this vector to the scalar division of vector v1 (*this = v1 / s ).
267			* @param v1 the source vector
268			* @param s the scalar value
269			*/
270	tim	110	inline void div( const Vector<Real, Dim>& v1, Real s ) {
271	tim	93	for (unsigned int i = 0; i < Dim; i++)
272	tim	70	data_[i] = v1.data_[i] / s;
273			}
274
275			/** @see #add */
276	tim	71	inline Vector<Real, Dim>& operator +=( const Vector<Real, Dim>& v1 ) {
277	tim	70	add(v1);
278			return *this;
279			}
280
281			/** @see #sub */
282	tim	71	inline Vector<Real, Dim>& operator -=( const Vector<Real, Dim>& v1 ) {
283	tim	70	sub(v1);
284			return *this;
285			}
286
287			/** @see #mul */
288	tim	110	inline Vector<Real, Dim>& operator *=( Real s) {
289	tim	70	mul(s);
290			return *this;
291			}
292
293			/** @see #div */
294	tim	110	inline Vector<Real, Dim>& operator /=( Real s ) {
295	tim	70	div(s);
296			return *this;
297			}
298
299			/**
300			* Returns the length of this vector.
301			* @return the length of this vector
302			*/
303	tim	110	inline Real length() {
304	tim	104	return sqrt(lengthSquare());
305	tim	70	}
306
307			/**
308			* Returns the squared length of this vector.
309			* @return the squared length of this vector
310			*/
311	tim	110	inline Real lengthSquare() {
312	tim	70	return dot(this, this);
313			}
314
315			/** Normalizes this vector in place */
316			inline void normalize() {
317	tim	110	Real len;
318	tim	70
319			len = length();
320	tim	102
321			//if (len < oopse:epsilon)
322			// throw();
323
324	tim	70	*this /= len;
325			}
326	tim	93
327			/**
328			* Tests if this vector is normalized
329			* @return true if this vector is normalized, otherwise return false
330			*/
331	tim	104	inline bool isNormalized() {
332			return equal(lengthSquare(), 1.0);
333	tim	93	}
334	tim	70
335			protected:
336	tim	110	Real data_[Dim];
337	tim	70
338			};
339
340			/** unary minus*/
341	tim	71	template<typename Real, unsigned int Dim>
342	tim	70	inline Vector<Real, Dim> operator -(const Vector<Real, Dim>& v1){
343	tim	101	Vector<Real, Dim> tmp(v1);
344			tmp.negate();
345			return tmp;
346	tim	70	}
347
348			/**
349			* Return the sum of two vectors (v1 - v2).
350			* @return the sum of two vectors
351			* @param v1 the first vector
352			* @param v2 the second vector
353			*/
354	tim	71	template<typename Real, unsigned int Dim>
355	tim	70	inline Vector<Real, Dim> operator +(const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2) {
356			Vector<Real, Dim> result;
357
358			result.add(v1, v2);
359			return result;
360			}
361
362			/**
363			* Return the difference of two vectors (v1 - v2).
364			* @return the difference of two vectors
365			* @param v1 the first vector
366			* @param v2 the second vector
367			*/
368	tim	71	template<typename Real, unsigned int Dim>
369	tim	70	Vector<Real, Dim> operator -(const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2) {
370			Vector<Real, Dim> result;
371			result.sub(v1, v2);
372			return result;
373			}
374
375			/**
376			* Returns the vaule of scalar multiplication of this vector v1 (v1 * r).
377			* @return the vaule of scalar multiplication of this vector
378			* @param v1 the source vector
379			* @param s the scalar value
380			*/
381	tim	71	template<typename Real, unsigned int Dim>
382	tim	110	Vector<Real, Dim> operator * ( const Vector<Real, Dim>& v1, Real s) {
383	tim	70	Vector<Real, Dim> result;
384	tim	101	result.mul(v1,s);
385	tim	70	return result;
386			}
387
388			/**
389			* Returns the vaule of scalar multiplication of this vector v1 (v1 * r).
390			* @return the vaule of scalar multiplication of this vector
391			* @param s the scalar value
392			* @param v1 the source vector
393			*/
394	tim	71	template<typename Real, unsigned int Dim>
395	tim	110	Vector<Real, Dim> operator * ( Real s, const Vector<Real, Dim>& v1 ) {
396	tim	70	Vector<Real, Dim> result;
397	tim	101	result.mul(v1, s);
398	tim	70	return result;
399			}
400
401			/**
402			* Returns the value of division of a vector by a scalar.
403			* @return the vaule of scalar division of this vector
404			* @param v1 the source vector
405			* @param s the scalar value
406			*/
407	tim	71	template<typename Real, unsigned int Dim>
408	tim	110	Vector<Real, Dim> operator / ( const Vector<Real, Dim>& v1, Real s) {
409	tim	70	Vector<Real, Dim> result;
410			result.div( v1,s);
411			return result;
412			}
413
414			/**
415			* Returns the dot product of two Vectors
416			* @param v1 first vector
417			* @param v2 second vector
418			* @return the dot product of v1 and v2
419			*/
420	tim	71	template<typename Real, unsigned int Dim>
421	tim	70	inline Real dot( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
422	tim	93	Real tmp;
423			tmp = 0;
424	tim	70
425	tim	93	for (unsigned int i = 0; i < Dim; i++)
426	tim	110	tmp += v1[i] * v2[i];
427	tim	93
428			return tmp;
429	tim	70	}
430
431			/**
432			* Returns the distance between two Vectors
433			* @param v1 first vector
434			* @param v2 second vector
435			* @return the distance between v1 and v2
436			*/
437	tim	71	template<typename Real, unsigned int Dim>
438	tim	70	inline Real distance( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
439			Vector<Real, Dim> tempVector = v1 - v2;
440			return tempVector.length();
441			}
442
443			/**
444			* Returns the squared distance between two Vectors
445			* @param v1 first vector
446			* @param v2 second vector
447			* @return the squared distance between v1 and v2
448			*/
449	tim	71	template<typename Real, unsigned int Dim>
450	tim	70	inline Real distanceSquare( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
451			Vector<Real, Dim> tempVector = v1 - v2;
452			return tempVector.lengthSquare();
453			}
454
455			/**
456			* Write to an output stream
457			*/
458	tim	71	template<typename Real, unsigned int Dim>
459	tim	93	std::ostream &operator<< ( std::ostream& o, const Vector<Real, Dim>& v) {
460
461	tim	110	o << "[ ";
462
463			for (unsigned int i = 0 ; i< Dim; i++) {
464			o << v[i];
465
466			if (i != Dim -1) {
467			o<< ", ";
468			}
469			}
470
471			o << " ]";
472	tim	70	return o;
473			}
474
475			}
476			#endif