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;
            }
            
            /** 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() {
                data_[0] = -data_[0];
                data_[1] = -data_[1];
                data_[2] = -data_[2];
            }

            /**
            * 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 s the scalar value
            * @param v1 the vector
            */
            inline void mul( double s, const Vector<Real, Dim>& v1 ) {
                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(lengthSquared());  
            }
            
            /**
             * Returns the squared length of this vector.
             * @return the squared length of this vector
             */
             inline double lengthSquared() {
                return dot(*this, *this);
            }
            
            /** Normalizes this vector in place */
            inline void normalize() {
                double len;

                len = length();
                *this /= len;
            }
            
        protected:
            double data_[3];
        
    };

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

    /**
     * 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(s, v1);
        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(s, v1);
        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  value of division of a vector by a scalar. 
     * @return  the vaule of scalar division of this vector
     * @param s the scalar value
     * @param v1 the source vector
     */
    template<typename Real, unsigned int Dim>        
    inline Vector<Real, Dim> operator /( double s, const Vector<Real, Dim>& v1 ) {
        Vector<Real, Dim> result;
        result.div( v1,s);
        return result;           
    }

    /** fuzzy comparson */
    template<typename Real, unsigned int Dim>        
    inline bool epsilonEqual( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {

    }

    
    /**
     * 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>& v1 ) {
        
        return o;        
    }
    
}
#endif
Revision:	76
Committed:	Thu Oct 14 23:28:09 2004 UTC (20 years, 6 months ago) by tim
File size:	14462 byte(s)
Log Message:	math library in progress
#	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
89			/** Constructs and initializes a Vector from an array */
90			inline Vector( double* v) {
91			for (unsigned int i = 0; i < Dim; i++)
92			data_[i] = v[i];
93			}
94
95			/**
96			* Returns reference of ith element.
97			* @return reference of ith element
98			* @param i index
99			*/
100			inline double& operator[](unsigned int i) {
101			assert( i < Dim);
102			return data_[i];
103			}
104
105			/**
106			* Returns reference of ith element.
107			* @return reference of ith element
108			* @param i index
109			*/
110			inline double& operator()(unsigned int i) {
111			assert( i < Dim);
112			return data_[i];
113			}
114
115			/**
116			* Returns constant reference of ith element.
117			* @return reference of ith element
118			* @param i index
119			*/
120			inline const double& operator[](unsigned int i) const {
121			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			inline const double& operator()(unsigned int i) const {
131			assert( i < Dim);
132			return data_[i];
133			}
134
135	tim	76	/**
136			* Tests if this vetor is equal to other vector
137			* @return true if equal, otherwise return false
138			* @param v vector to be compared
139			*/
140			inline bool operator ==(const Vector<Real, Dim>& v) {
141
142			for (unsigned int i = 0; i < Dim; i ++) {
143			if (!equal(data_[i], v[i])) {
144			return false;
145			}
146			}
147
148			return true;
149			}
150
151			/**
152			* Tests if this vetor is not equal to other vector
153			* @return true if equal, otherwise return false
154			* @param v vector to be compared
155			*/
156			inline bool operator !=(const Vector<Real, Dim>& v) {
157			return !(*this == v);
158			}
159
160	tim	70	/** Negates the value of this vector in place. */
161			inline void negate() {
162			data_[0] = -data_[0];
163			data_[1] = -data_[1];
164			data_[2] = -data_[2];
165			}
166
167			/**
168			* Sets the value of this vector to the negation of vector v1.
169			* @param v1 the source vector
170			*/
171			inline void negate(const Vector<Real, Dim>& v1) {
172			for (unsigned int i = 0; i < Dim; i++)
173			data_[i] = -v1.data_[i];
174
175			}
176
177			/**
178			* Sets the value of this vector to the sum of itself and v1 (*this += v1).
179			* @param v1 the other vector
180			*/
181			inline void add( const Vector<Real, Dim>& v1 ) {
182			for (unsigned int i = 0; i < Dim; i++)
183			data_[i] += v1.data_[i];
184			}
185
186			/**
187			* Sets the value of this vector to the sum of v1 and v2 (*this = v1 + v2).
188			* @param v1 the first vector
189			* @param v2 the second vector
190			*/
191			inline void add( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
192			for (unsigned int i = 0; i < Dim; i++)
193			data_[i] = v1.data_[i] + v2.data_[i];
194			}
195
196			/**
197			* Sets the value of this vector to the difference of itself and v1 (*this -= v1).
198			* @param v1 the other vector
199			*/
200			inline void sub( const Vector<Real, Dim>& v1 ) {
201			for (unsigned int i = 0; i < Dim; i++)
202			data_[i] -= v1.data_[i];
203			}
204
205			/**
206			* Sets the value of this vector to the difference of vector v1 and v2 (*this = v1 - v2).
207			* @param v1 the first vector
208			* @param v2 the second vector
209			*/
210			inline void sub( const Vector<Real, Dim>& v1, const Vector &v2 ){
211			for (unsigned int i = 0; i < Dim; i++)
212			data_[i] = v1.data_[i] - v2.data_[i];
213			}
214
215			/**
216			* Sets the value of this vector to the scalar multiplication of itself (this = s).
217			* @param s the scalar value
218			*/
219			inline void mul( double s ) {
220			for (unsigned int i = 0; i < Dim; i++)
221			data_[i] *= s;
222			}
223
224			/**
225			* Sets the value of this vector to the scalar multiplication of vector v1
226			* (this = s v1).
227			* @param s the scalar value
228			* @param v1 the vector
229			*/
230			inline void mul( double s, const Vector<Real, Dim>& v1 ) {
231			for (unsigned int i = 0; i < Dim; i++)
232			data_[i] = s * v1.data_[i];
233			}
234
235			/**
236			* Sets the value of this vector to the scalar division of itself (*this /= s ).
237			* @param s the scalar value
238			*/
239			inline void div( double s) {
240			for (unsigned int i = 0; i < Dim; i++)
241			data_[i] /= s;
242			}
243
244			/**
245			* Sets the value of this vector to the scalar division of vector v1 (*this = v1 / s ).
246			* @param v1 the source vector
247			* @param s the scalar value
248			*/
249			inline void div( const Vector<Real, Dim>& v1, double s ) {
250			for (unsigned int i = 0; i < Dim; i++)
251			data_[i] = v1.data_[i] / s;
252			}
253
254			/** @see #add */
255	tim	71	inline Vector<Real, Dim>& operator +=( const Vector<Real, Dim>& v1 ) {
256	tim	70	add(v1);
257			return *this;
258			}
259
260			/** @see #sub */
261	tim	71	inline Vector<Real, Dim>& operator -=( const Vector<Real, Dim>& v1 ) {
262	tim	70	sub(v1);
263			return *this;
264			}
265
266			/** @see #mul */
267	tim	71	inline Vector<Real, Dim>& operator *=( double s) {
268	tim	70	mul(s);
269			return *this;
270			}
271
272			/** @see #div */
273	tim	71	inline Vector<Real, Dim>& operator /=( double s ) {
274	tim	70	div(s);
275			return *this;
276			}
277
278			/**
279			* Returns the length of this vector.
280			* @return the length of this vector
281			*/
282			inline double length() {
283			return sqrt(lengthSquared());
284			}
285
286			/**
287			* Returns the squared length of this vector.
288			* @return the squared length of this vector
289			*/
290			inline double lengthSquared() {
291			return dot(this, this);
292			}
293
294			/** Normalizes this vector in place */
295			inline void normalize() {
296			double len;
297
298			len = length();
299			*this /= len;
300			}
301
302			protected:
303			double data_[3];
304
305			};
306
307			/** unary minus*/
308	tim	71	template<typename Real, unsigned int Dim>
309	tim	70	inline Vector<Real, Dim> operator -(const Vector<Real, Dim>& v1){
310			Vector tmp(v1);
311			return tmp.negate();
312			}
313
314			/**
315			* Return the sum of two vectors (v1 - v2).
316			* @return the sum of two vectors
317			* @param v1 the first vector
318			* @param v2 the second vector
319			*/
320	tim	71	template<typename Real, unsigned int Dim>
321	tim	70	inline Vector<Real, Dim> operator +(const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2) {
322			Vector<Real, Dim> result;
323
324			result.add(v1, v2);
325			return result;
326			}
327
328			/**
329			* Return the difference of two vectors (v1 - v2).
330			* @return the difference of two vectors
331			* @param v1 the first vector
332			* @param v2 the second vector
333			*/
334	tim	71	template<typename Real, unsigned int Dim>
335	tim	70	Vector<Real, Dim> operator -(const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2) {
336			Vector<Real, Dim> result;
337			result.sub(v1, v2);
338			return result;
339			}
340
341			/**
342			* Returns the vaule of scalar multiplication of this vector v1 (v1 * r).
343			* @return the vaule of scalar multiplication of this vector
344			* @param v1 the source vector
345			* @param s the scalar value
346			*/
347	tim	71	template<typename Real, unsigned int Dim>
348	tim	70	Vector<Real, Dim> operator * ( const Vector<Real, Dim>& v1, double s) {
349			Vector<Real, Dim> result;
350			result.mul(s, v1);
351			return result;
352			}
353
354			/**
355			* Returns the vaule of scalar multiplication of this vector v1 (v1 * r).
356			* @return the vaule of scalar multiplication of this vector
357			* @param s the scalar value
358			* @param v1 the source vector
359			*/
360	tim	71	template<typename Real, unsigned int Dim>
361	tim	70	Vector<Real, Dim> operator * ( double s, const Vector<Real, Dim>& v1 ) {
362			Vector<Real, Dim> result;
363			result.mul(s, v1);
364			return result;
365			}
366
367			/**
368			* Returns the value of division of a vector by a scalar.
369			* @return the vaule of scalar division of this vector
370			* @param v1 the source vector
371			* @param s the scalar value
372			*/
373	tim	71	template<typename Real, unsigned int Dim>
374	tim	70	Vector<Real, Dim> operator / ( const Vector<Real, Dim>& v1, double s) {
375			Vector<Real, Dim> result;
376			result.div( v1,s);
377			return result;
378			}
379
380			/**
381			* Returns the value of division of a vector by a scalar.
382			* @return the vaule of scalar division of this vector
383			* @param s the scalar value
384			* @param v1 the source vector
385			*/
386	tim	71	template<typename Real, unsigned int Dim>
387	tim	70	inline Vector<Real, Dim> operator /( double s, const Vector<Real, Dim>& v1 ) {
388			Vector<Real, Dim> result;
389			result.div( v1,s);
390			return result;
391			}
392
393			/** fuzzy comparson */
394	tim	71	template<typename Real, unsigned int Dim>
395	tim	70	inline bool epsilonEqual( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
396
397			}
398
399
400			/**
401			* Returns the dot product of two Vectors
402			* @param v1 first vector
403			* @param v2 second vector
404			* @return the dot product of v1 and v2
405			*/
406	tim	71	template<typename Real, unsigned int Dim>
407	tim	70	inline Real dot( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
408			Real tmp;
409			tmp = 0;
410
411			for (unsigned int i = 0; i < Dim; i++)
412			tmp += v1[i] + v2[i];
413
414			return tmp;
415			}
416
417			/**
418			* Returns the distance between two Vectors
419			* @param v1 first vector
420			* @param v2 second vector
421			* @return the distance between v1 and v2
422			*/
423	tim	71	template<typename Real, unsigned int Dim>
424	tim	70	inline Real distance( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
425			Vector<Real, Dim> tempVector = v1 - v2;
426			return tempVector.length();
427			}
428
429			/**
430			* Returns the squared distance between two Vectors
431			* @param v1 first vector
432			* @param v2 second vector
433			* @return the squared distance between v1 and v2
434			*/
435	tim	71	template<typename Real, unsigned int Dim>
436	tim	70	inline Real distanceSquare( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
437			Vector<Real, Dim> tempVector = v1 - v2;
438			return tempVector.lengthSquare();
439			}
440
441			/**
442			* Write to an output stream
443			*/
444	tim	71	template<typename Real, unsigned int Dim>
445	tim	70	std::ostream &operator<< ( std::ostream& o, const Vector<Real, Dim>& v1 ) {
446
447			return o;
448			}
449
450			}
451			#endif