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source: code/trunk/src/libraries/util/Math.cc @ 8384

Last change on this file since 8384 was 7401, checked in by landauf, 14 years ago

merged doc branch back to trunk

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[1505]1/*
2 *   ORXONOX - the hottest 3D action shooter ever to exist
3 *                    > www.orxonox.net <
4 *
5 *
6 *   License notice:
7 *
8 *   This program is free software; you can redistribute it and/or
9 *   modify it under the terms of the GNU General Public License
10 *   as published by the Free Software Foundation; either version 2
11 *   of the License, or (at your option) any later version.
12 *
13 *   This program is distributed in the hope that it will be useful,
14 *   but WITHOUT ANY WARRANTY; without even the implied warranty of
15 *   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
16 *   GNU General Public License for more details.
17 *
18 *   You should have received a copy of the GNU General Public License
19 *   along with this program; if not, write to the Free Software
20 *   Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
21 *
22 *   Author:
23 *      Fabian 'x3n' Landau
24 *   Co-authors:
25 *      ...
26 *
27 */
28
[1791]29/**
[2087]30    @file
[1791]31    @brief Implementation of several math-functions.
32*/
33
[2087]34#include "Math.h"
35
[1564]36#include <OgrePlane.h>
[3196]37
[2087]38#include "MathConvert.h"
39#include "SubString.h"
[3196]40// Do not remove this include, it avoids linker errors.
[2171]41#include "mbool.h"
[1505]42
[2171]43namespace orxonox
[1505]44{
[6417]45#if OGRE_VERSION < 0x010603
[2171]46    /**
47        @brief Function for writing a Radian to a stream.
48    */
49    std::ostream& operator<<(std::ostream& out, const orxonox::Radian& radian)
50    {
51        out << radian.valueRadians();
52        return out;
53    }
[1505]54
[2171]55    /**
[6417]56        @brief Function for writing a Degree to a stream.
57    */
58    std::ostream& operator<<(std::ostream& out, const orxonox::Degree& degree)
59    {
60        out << degree.valueDegrees();
61        return out;
62    }
63#endif
64
65    /**
[2171]66        @brief Function for reading a Radian from a stream.
67    */
68    std::istream& operator>>(std::istream& in, orxonox::Radian& radian)
69    {
70        float temp;
71        in >> temp;
72        radian = temp;
73        return in;
74    }
[1505]75
[2171]76    /**
77        @brief Function for reading a Degree from a stream.
78    */
79    std::istream& operator>>(std::istream& in, orxonox::Degree& degree)
80    {
81        float temp;
82        in >> temp;
83        degree = temp;
84        return in;
85    }
[1564]86
[1791]87
[2171]88    /**
89        @brief Gets the angle between my viewing direction and the direction to the position of the other object.
90        @param myposition My position
91        @param mydirection My viewing direction
92        @param otherposition The position of the other object
[7401]93        @return The angle in radian
[1564]94
[7401]95        Examples:
96         - If the other object is exactly in front of me, the function returns 0.
97         - If the other object is exactly behind me, the function returns pi.
98         - If the other object is exactly right/left to me (or above/below), the function returns pi/2.
[2171]99    */
100    float getAngle(const orxonox::Vector3& myposition, const orxonox::Vector3& mydirection, const orxonox::Vector3& otherposition)
101    {
102        orxonox::Vector3 distance = otherposition - myposition;
103        float distancelength = distance.length();
104        if (distancelength == 0)
105            return 0;
106        else
107            return acos(clamp<float>(mydirection.dotProduct(distance) / distancelength, -1, 1));
108    }
[1791]109
[2171]110    /**
111        @brief Gets the 2D viewing direction (up/down, left/right) to the position of the other object.
112        @param myposition My position
113        @param mydirection My viewing direction
114        @param myorthonormal My orthonormalvector (pointing upwards through my head)
115        @param otherposition The position of the other object
116        @return The viewing direction
[1564]117
[7401]118        Examples:
119         - If the other object is exactly in front of me, the function returns <tt>Vector2(0, 0)</tt>.
120         - If the other object is exactly at my left, the function returns <tt>Vector2(-1, 0)</tt>.
121         - If the other object is exactly at my right, the function returns <tt>Vector2(1, 0)</tt>.
122         - If the other object is only a bit at my right, the function still returns <tt>Vector2(1, 0)</tt>.
123         - If the other object is exactly above me, the function returns <tt>Vector2(0, 1)</tt>.
[2171]124    */
125    orxonox::Vector2 get2DViewdirection(const orxonox::Vector3& myposition, const orxonox::Vector3& mydirection, const orxonox::Vector3& myorthonormal, const orxonox::Vector3& otherposition)
126    {
127        orxonox::Vector3 distance = otherposition - myposition;
[1564]128
[2171]129        // project difference vector on our plane
130        orxonox::Vector3 projection = Ogre::Plane(mydirection, myposition).projectVector(distance);
[1608]131
[2171]132        float projectionlength = projection.length();
[3049]133        if (projectionlength == 0)
134        {
135            if (myposition.dotProduct(otherposition) >= 0)
136                return orxonox::Vector2(0, 0);
137            else
138                return orxonox::Vector2(0, 1);
139        }
[6417]140
[3304]141        float cos_value = clamp<float>(myorthonormal.dotProduct(projection) / projectionlength, -1, 1);
142        float sin_value = sqrt( 1 - cos_value*cos_value );
[6417]143
[2171]144        if ((mydirection.crossProduct(myorthonormal)).dotProduct(distance) > 0)
[3304]145            return orxonox::Vector2( sin_value, cos_value );
[2171]146        else
[3304]147            return orxonox::Vector2( -sin_value, cos_value );
[2171]148    }
[1791]149
[2171]150    /**
151        @brief Gets the 2D viewing direction (up/down, left/right) to the position of the other object, multiplied with the viewing distance to the object (0° = 0, 180° = 1).
152        @param myposition My position
153        @param mydirection My viewing direction
154        @param myorthonormal My orthonormalvector (pointing upwards through my head)
155        @param otherposition The position of the other object
156        @return The viewing direction
[1564]157
[7401]158        Examples:
159         - If the other object is exactly in front of me, the function returns <tt>Vector2(0, 0)</tt>.
160         - If the other object is exactly at my left, the function returns <tt>Vector2(-0.5, 0)</tt>.
161         - If the other object is exactly at my right, the function returns <tt>Vector2(0.5, 0)</tt>.
162         - If the other object is only a bit at my right, the function still returns <tt>Vector2(0.01, 0)</tt>.
163         - If the other object is exactly above me, the function returns <tt>Vector2(0, 0.5)</tt>.
[2171]164    */
165    orxonox::Vector2 get2DViewcoordinates(const orxonox::Vector3& myposition, const orxonox::Vector3& mydirection, const orxonox::Vector3& myorthonormal, const orxonox::Vector3& otherposition)
166    {
167        orxonox::Vector3 distance = otherposition - myposition;
[1564]168
[2171]169        // project difference vector on our plane
170        orxonox::Vector3 projection = Ogre::Plane(mydirection, myposition).projectVector(distance);
[1608]171
[2171]172        float projectionlength = projection.length();
[3049]173        if (projectionlength == 0)
174        {
175            if (myposition.dotProduct(otherposition) >= 0)
176                return orxonox::Vector2(0, 0);
177            else
178                return orxonox::Vector2(0, 1);
179        }
[3304]180        //float angle = acos(clamp<float>(myorthonormal.dotProduct(projection) / projectionlength, -1, 1));
[6417]181
[3304]182        float cos_value = clamp<float>(myorthonormal.dotProduct(projection) / projectionlength, -1, 1);
183        float sin_value = sqrt( 1 - cos_value*cos_value );
[1608]184
[2171]185        float distancelength = distance.length();
186        if (distancelength == 0) return orxonox::Vector2(0, 0);
[7184]187        float radius = acos(clamp<float>(mydirection.dotProduct(distance) / distancelength, -1, 1)) / math::pi;
[1566]188
[2171]189        if ((mydirection.crossProduct(myorthonormal)).dotProduct(distance) > 0)
[3304]190            return orxonox::Vector2( sin_value * radius, cos_value * radius);
[2171]191        else
[3304]192            return orxonox::Vector2( -sin_value * radius, cos_value * radius);
[2171]193    }
[1791]194
[2171]195    /**
196        @brief Returns the predicted position I have to aim at, if I want to hit a moving target with a moving projectile.
197        @param myposition My position
198        @param projectilespeed The speed of my projectile
199        @param targetposition The position of my target
200        @param targetvelocity The velocity of my target
201        @return The predicted position
[1566]202
[2171]203        The function predicts the position based on a linear velocity of the target. If the target changes speed or direction, the projectile will miss.
204    */
205    orxonox::Vector3 getPredictedPosition(const orxonox::Vector3& myposition, float projectilespeed, const orxonox::Vector3& targetposition, const orxonox::Vector3& targetvelocity)
206    {
207        float squaredProjectilespeed = projectilespeed * projectilespeed;
208        orxonox::Vector3 distance = targetposition - myposition;
209        float a = distance.squaredLength();
210        float b = 2 * (distance.x + distance.y + distance.z) * (targetvelocity.x + targetvelocity.y + targetvelocity.z);
211        float c = targetvelocity.squaredLength();
[1566]212
[2171]213        float temp = 4*squaredProjectilespeed*c + a*a - 4*b*c;
214        if (temp < 0)
215            return orxonox::Vector3::ZERO;
[1625]216
[2171]217        temp = sqrt(temp);
218        float time = (temp + a) / (2 * (squaredProjectilespeed - b));
219        return (targetposition + targetvelocity * time);
220    }
[1625]221
[7401]222    /**
223        @brief Returns a unique number. This function will never return the same value twice.
224    */
[2171]225    unsigned long getUniqueNumber()
226    {
227        static unsigned long aNumber = 135;
228        return aNumber++;
229    }
[2087]230
231
[2171]232    //////////////////////////
233    // Conversion functions //
234    //////////////////////////
[2087]235
[2171]236    // std::string to Vector2
237    bool ConverterFallback<std::string, orxonox::Vector2>::convert(orxonox::Vector2* output, const std::string& input)
[2087]238    {
[7284]239        size_t opening_parenthesis, closing_parenthesis = input.find('}');
240        if ((opening_parenthesis = input.find('{')) == std::string::npos)
[2171]241            opening_parenthesis = 0;
242        else
243            opening_parenthesis++;
[2087]244
[2171]245        SubString tokens(input.substr(opening_parenthesis, closing_parenthesis - opening_parenthesis),
246                         ",", SubString::WhiteSpaces, false, '\\', true, '"', true, '\0', '\0', true, '\0');
247        if (tokens.size() >= 2)
248        {
[3196]249            if (!convertValue(&(output->x), tokens[0]))
[2171]250                return false;
[3196]251            if (!convertValue(&(output->y), tokens[1]))
[2171]252                return false;
253
254            return true;
255        }
256        return false;
[2087]257    }
258
[2171]259    // std::string to Vector3
260    bool ConverterFallback<std::string, orxonox::Vector3>::convert(orxonox::Vector3* output, const std::string& input)
[2087]261    {
[7284]262        size_t opening_parenthesis, closing_parenthesis = input.find('}');
263        if ((opening_parenthesis = input.find('{')) == std::string::npos)
[2171]264            opening_parenthesis = 0;
265        else
266            opening_parenthesis++;
[2087]267
[2171]268        SubString tokens(input.substr(opening_parenthesis, closing_parenthesis - opening_parenthesis),
269                         ",", SubString::WhiteSpaces, false, '\\', true, '"', true, '\0', '\0', true, '\0');
270        if (tokens.size() >= 3)
271        {
[3196]272            if (!convertValue(&(output->x), tokens[0]))
[2171]273                return false;
[3196]274            if (!convertValue(&(output->y), tokens[1]))
[2171]275                return false;
[3196]276            if (!convertValue(&(output->z), tokens[2]))
[2171]277                return false;
278
279            return true;
280        }
281        return false;
[2087]282    }
283
[2171]284    // std::string to Vector4
285    bool ConverterFallback<std::string, orxonox::Vector4>::convert(orxonox::Vector4* output, const std::string& input)
[2087]286    {
[7284]287        size_t opening_parenthesis, closing_parenthesis = input.find('}');
288        if ((opening_parenthesis = input.find('{')) == std::string::npos)
[2171]289            opening_parenthesis = 0;
290        else
291            opening_parenthesis++;
[2087]292
[2171]293        SubString tokens(input.substr(opening_parenthesis, closing_parenthesis - opening_parenthesis),
294                         ",", SubString::WhiteSpaces, false, '\\', true, '"', true, '\0', '\0', true, '\0');
295        if (tokens.size() >= 4)
296        {
[3196]297            if (!convertValue(&(output->x), tokens[0]))
[2171]298                return false;
[3196]299            if (!convertValue(&(output->y), tokens[1]))
[2171]300                return false;
[3196]301            if (!convertValue(&(output->z), tokens[2]))
[2171]302                return false;
[3196]303            if (!convertValue(&(output->w), tokens[3]))
[2171]304                return false;
305
306            return true;
307        }
308        return false;
[2087]309    }
310
[2171]311    // std::string to Quaternion
312    bool ConverterFallback<std::string, orxonox::Quaternion>::convert(orxonox::Quaternion* output, const std::string& input)
[2087]313    {
[7284]314        size_t opening_parenthesis, closing_parenthesis = input.find('}');
315        if ((opening_parenthesis = input.find('{')) == std::string::npos)
316            opening_parenthesis = 0;
317        else
318            opening_parenthesis++;
[2087]319
[2171]320        SubString tokens(input.substr(opening_parenthesis, closing_parenthesis - opening_parenthesis), ",", SubString::WhiteSpaces, false, '\\', true, '"', true, '\0', '\0', true, '\0');
321        if (tokens.size() >= 4)
322        {
[3196]323            if (!convertValue(&(output->w), tokens[0]))
[2171]324                return false;
[3196]325            if (!convertValue(&(output->x), tokens[1]))
[2171]326                return false;
[3196]327            if (!convertValue(&(output->y), tokens[2]))
[2171]328                return false;
[3196]329            if (!convertValue(&(output->z), tokens[3]))
[2171]330                return false;
331
332            return true;
333        }
334        return false;
[2087]335    }
336
[2171]337    // std::string to ColourValue
338    bool ConverterFallback<std::string, orxonox::ColourValue>::convert(orxonox::ColourValue* output, const std::string& input)
339    {
[7284]340        size_t opening_parenthesis, closing_parenthesis = input.find('}');
341        if ((opening_parenthesis = input.find('{')) == std::string::npos)
342            opening_parenthesis = 0;
343        else
344            opening_parenthesis++;
[2087]345
[2171]346        SubString tokens(input.substr(opening_parenthesis, closing_parenthesis - opening_parenthesis), ",", SubString::WhiteSpaces, false, '\\', true, '"', true, '\0', '\0', true, '\0');
347        if (tokens.size() >= 3)
[2087]348        {
[3196]349            if (!convertValue(&(output->r), tokens[0]))
[2087]350                return false;
[3196]351            if (!convertValue(&(output->g), tokens[1]))
[2171]352                return false;
[3196]353            if (!convertValue(&(output->b), tokens[2]))
[2171]354                return false;
355            if (tokens.size() >= 4)
356            {
[3196]357                if (!convertValue(&(output->a), tokens[3]))
[2171]358                    return false;
359            }
360            else
361                output->a = 1.0;
362
363            return true;
[2087]364        }
[2171]365        return false;
[2087]366    }
367}
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