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| Rev | Author | Line No. | Line |
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| 308 | osiair | 1 | /* |
| 2 | This program (files math.c and math.h) is free software; you can redistribute it and/or modify |
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| 3 | it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; |
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| 4 | either version 3 of the License, or (at your option) any later version. |
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| 5 | This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; |
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| 6 | without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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| 7 | GNU General Public License and GNU Lesser General Public License for more details. |
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| 8 | You should have received a copy of GNU General Public License (License_GPL.txt) and |
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| 9 | GNU Lesser General Public License (License_LGPL.txt) along with this program. |
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| 10 | If not, see <http://www.gnu.org/licenses/>. |
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| 11 | |||
| 12 | Please note: All the other files for the project "Mikrokopter" by H.Buss are under the license (license_buss.txt) published by www.mikrokopter.de |
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| 13 | */ |
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| 14 | /*++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
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| 15 | Peter Muehlenbrock |
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| 16 | Winkelfunktionen sin, cos und arctan in |
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| 17 | brute-force Art: Sehr Schnell, nicht sonderlich genau, aber ausreichend |
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| 18 | get_dist Funktion fuer Entfernungsermittlung |
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| 19 | Stand 12.10.2007 |
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| 20 | ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
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| 21 | */ |
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| 22 | #include "main.h" |
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| 23 | |||
| 24 | |||
| 25 | // arctan Funktion: Eingabewert x,y Rueckgabe =arctan(x,y) in grad |
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| 26 | int arctan_i( signed int x, signed int y) |
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| 27 | { |
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| 28 | short int change_xy = 0; |
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| 29 | signed int i; |
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| 30 | long signed int wert; |
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| 31 | int return_value; |
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| 32 | |||
| 33 | if ((abs(x)) > (abs(y))) // x,y Werte vertauschen damit arctan <45 grad bleibt |
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| 34 | { |
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| 35 | change_xy = 1; |
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| 36 | i = x; |
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| 37 | x = y; |
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| 38 | y = i; |
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| 39 | } |
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| 40 | |||
| 41 | // Quadranten ermitteln |
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| 42 | |||
| 43 | // Wert durch lineare Interpolation ermitteln |
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| 44 | if ((y == 0) && (x == 0)) wert =1; // Division durch 0 nicht erlaubt |
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| 45 | else wert= abs(((long)x*1000)/((long)y)); |
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| 46 | |||
| 47 | if (wert <=268) //0...0.0,268 entsprechend 0..15 Grad |
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| 48 | { |
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| 49 | return_value = (signed int)((wert*100)/(268-0)*(15-0)/100) +0; |
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| 50 | } |
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| 51 | else if (wert <=578) //0,268...0.0,568 entsprechend 15..30 Grad |
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| 52 | { |
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| 53 | return_value = (signed int)((((wert-268)*100)/(578-268)*(30-15))/100) +15; |
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| 54 | } |
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| 55 | else //0,568...1 entsprechend 30..45 Grad |
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| 56 | { |
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| 57 | return_value = (signed int)((((wert-578)*50)/(1000-578)*(45-30))/50) +30; |
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| 58 | } |
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| 59 | |||
| 60 | if (change_xy == 0) return_value = 90-return_value; //Quadrant 45..90 Grad |
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| 61 | if ((x >= 0) && (y <0)) return_value = - return_value; |
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| 62 | else if ((x < 0) && (y >= 0)) return_value = - return_value; |
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| 63 | |||
| 64 | return return_value; |
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| 65 | } |
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| 66 | |||
| 67 | |||
| 68 | // cosinus Funktion: Eingabewert Winkel in Grad, Rueckgabe =cos(winkel)*1000 |
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| 69 | signed int cos_i(signed int winkel) |
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| 70 | { |
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| 71 | winkel = sin_i(90-winkel); |
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| 72 | return winkel; |
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| 73 | } |
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| 74 | |||
| 75 | |||
| 76 | const unsigned int pgm_sinus[91] PROGMEM = {0,17,35,52,70,87,105,122,139,156,174,191,208,225,242,259,276,292,309,326,342,358,375,391,407,423,438,454,469,485,500,515,530,545,559,574,588,602,616,629,643,656,669,682,695,707,719,731,743,755,766,777,788,799,809,819,829,839,848,857,866,875,883,891,899,906,914,921,927,934,940,946,951,956,961,966,970,974,978,982,985,988,990,993,995,996,998,999,999,1000,1000}; |
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| 77 | //von Nick666, Stand 28.9.2007 |
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| 78 | // sinus Funktion: Eingabewert Winkel in Grad, Rueckgabe =sin(winkel)*1000 |
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| 79 | signed int sin_i(signed int winkel) |
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| 80 | { |
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| 81 | short int m,n; |
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| 82 | |||
| 83 | if (abs(winkel) >=360) winkel = winkel % 360; |
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| 84 | if (winkel < 0) |
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| 85 | { |
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| 86 | m = -1; |
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| 87 | winkel = abs(winkel); |
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| 88 | } |
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| 89 | else m = +1; |
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| 90 | n =1; |
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| 91 | |||
| 92 | // Quadranten auswerten |
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| 93 | if ((winkel > 90 ) && (winkel <= 180)) winkel = 180 - winkel; |
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| 94 | else if ((winkel > 180 ) && (winkel <= 270)) |
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| 95 | { |
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| 96 | winkel = winkel -180; |
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| 97 | n = -1; |
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| 98 | } |
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| 99 | else if ((winkel > 270) && (winkel <= 360)) |
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| 100 | { |
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| 101 | winkel = 360 - winkel; |
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| 102 | n = -1; |
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| 103 | } |
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| 104 | // else //0 - 90 Grad |
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| 105 | |||
| 106 | winkel = pgm_read_word(&pgm_sinus[winkel]); |
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| 107 | return (winkel*m*n); |
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| 108 | } |
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| 109 | |||
| 110 | // Aus x,y und Winkel Distanz ermitteln |
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| 111 | long get_dist(signed int x, signed int y, signed int phi) |
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| 112 | { |
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| 113 | long dist; |
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| 114 | if (abs(x) > abs(y) ) |
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| 115 | { |
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| 116 | dist = (long) x; //Groesseren Wert wegen besserer Genauigkeit nehmen |
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| 117 | dist = abs((dist *1000) / (long) sin_i(phi)); |
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| 118 | } |
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| 119 | else |
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| 120 | { |
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| 121 | dist = (long) y; |
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| 122 | dist = abs((dist *1000) / (long) cos_i(phi)); |
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| 123 | } |
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| 124 | return dist; |
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| 125 | } |
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| 126 | |||
| 127 | |||
| 128 | // noch mehr von Nick666 |
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| 129 | |||
| 130 | const uint8_t pgm_atan[270] PROGMEM = {0,1,2,3,5,6,7,8,9,10,11,12,13,15,16,17,18,19,20,21,22,23,24,25,26,27,27,28,29,30,31,32,33,33,34,35,36,37,37,38,39,39,40,41,41,42,43,43,44,44,45,46,46,47,47,48,48,49,49,50,50,51,51,52,52,52,53,53,54,54,54,55,55,56,56,56,57,57,57,58,58,58,59,59,59,60,60,60,60,61,61,61,61,62,62,62,62,63,63,63,63,64,64,64,64,65,65,65,65,65,66,66,66,66,66,67,67,67,67,67,67,68,68,68,68,68,68,69,69,69,69,69,69,69,70,70,70,70,70,70,70,70,71,71,71,71,71,71,71,71,72,72,72,72,72,72,72,72,72,73,73,73,73,73,73,73,73,73,73,74,74,74,74,74,74,74,74,74,74,74,74,75,75,75,75,75,75,75,75,75,75,75,75,75,76,76,76,76,76,76,76,76,76,76,76,76,76,76,76,77,77,77,77,77,77,77,77,77,77,77,77,77,77,77,77,77,78,78,78,78,78,78,78,78,78,78,78,78,78,78,78,78,78,78,78,78,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79,79}; |
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| 131 | |||
| 132 | // Arkustangens2 im Gradmaß |
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| 133 | signed int atan2_i(signed int x, signed int y) |
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| 134 | { |
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| 135 | int i,angle; |
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| 136 | int8_t m; |
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| 137 | |||
| 138 | if (!x && !y) return 0; //atan2 = 0 für x und y = 0 |
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| 139 | |||
| 140 | if (y < 0) m=-1; |
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| 141 | else m=1; |
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| 142 | |||
| 143 | if (x==0) return (90*m); // atan2 = 90° für x = 0 |
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| 144 | |||
| 145 | i = abs(((float)y / x) * 50); // Berechne i für die Lookup table (Schrittweite atan(x) ist 0.02 -> *50) |
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| 146 | |||
| 147 | if (i<270) angle = pgm_read_byte(&pgm_atan[i]); // Lookup für 1° bis 79° |
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| 148 | else if (i>5750) angle = 90; // Grenzwert ist 90° |
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| 149 | else if (i>=1910) angle = 89; // 89° bis 80° über Wertebereiche |
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| 150 | else if (i>=1150) angle = 88; |
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| 151 | else if (i>=820) angle = 87; |
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| 152 | else if (i>=640) angle = 86; |
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| 153 | else if (i>=520) angle = 85; |
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| 154 | else if (i>=440) angle = 84; |
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| 155 | else if (i>=380) angle = 83; |
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| 156 | else if (i>=335) angle = 82; |
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| 157 | else if (i>=299) angle = 81; |
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| 158 | else angle = 80; // (i>=270) |
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| 159 | |||
| 160 | if (x > 0) return (angle*m); // Quadrant I und IV |
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| 161 | else if ((x < 0) && (y >= 0)) return ((angle*-1) + 180); // Quadrant II |
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| 162 | else return (angle - 180); // x < 0 && y < 0 Quadrant III |
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| 163 | } |
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| 164 | |||
| 165 | |||
| 166 | |||
| 167 | |||
| 168 | |||
| 169 | const float pgm_sinus_f [91] PROGMEM = {0.000,0.017,0.035,0.052,0.070,0.087,0.105,0.122,0.139,0.156,0.174,0.191,0.208,0.225,0.242,0.259,0.276,0.292,0.309,0.326,0.342,0.358,0.375,0.391,0.407,0.423,0.438,0.454,0.469,0.485,0.500,0.515,0.530,0.545,0.559,0.574,0.588,0.602,0.616,0.629,0.643,0.656,0.669,0.682,0.695,0.707,0.719,0.731,0.743,0.755,0.766,0.777,0.788,0.799,0.809,0.819,0.829,0.839,0.848,0.857,0.866,0.875,0.883,0.891,0.899,0.906,0.914,0.921,0.927,0.934,0.940,0.946,0.951,0.956,0.961,0.966,0.970,0.974,0.978,0.982,0.985,0.988,0.990,0.993,0.995,0.996,0.998,0.999,0.999,1.000,1.000}; |
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| 170 | |||
| 171 | inline float pgm_read_float(const float *addr) |
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| 172 | { |
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| 173 | union |
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| 174 | { |
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| 175 | uint16_t i[2]; // 2 16-bit-Worte |
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| 176 | float f; |
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| 177 | } u; |
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| 178 | |||
| 179 | u.i[0]=pgm_read_word((PGM_P)addr); |
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| 180 | u.i[1]=pgm_read_word((PGM_P)addr+2); |
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| 181 | |||
| 182 | return u.f; |
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| 183 | } |
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| 184 | |||
| 185 | // Kosinusfunktion im Gradmaß |
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| 186 | float cos_f(signed int winkel) |
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| 187 | { |
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| 188 | return (sin_f(90-winkel)); |
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| 189 | } |
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| 190 | |||
| 191 | // Sinusfunktion im Gradmaß |
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| 192 | float sin_f(signed int winkel) |
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| 193 | { |
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| 194 | short int m,n; |
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| 195 | float sinus; |
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| 196 | |||
| 197 | //winkel = winkel % 360; |
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| 198 | |||
| 199 | if (winkel < 0) |
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| 200 | { |
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| 201 | m = -1; |
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| 202 | winkel = abs(winkel); |
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| 203 | } |
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| 204 | else m = +1; |
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| 205 | |||
| 206 | // Quadranten auswerten |
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| 207 | if ((winkel > 90 ) && (winkel <= 180)) {winkel = 180 - winkel; n = 1;} |
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| 208 | else if ((winkel > 180 ) && (winkel <= 270)) {winkel = winkel - 180; n = -1;} |
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| 209 | else if ((winkel > 270) && (winkel <= 360)) {winkel = 360 - winkel; n = -1;} |
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| 210 | else n = 1; //0 - 90 Grad |
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| 211 | |||
| 212 | sinus = pgm_read_float(&pgm_sinus_f[winkel]); |
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| 213 | |||
| 214 | return (sinus*m*n); |
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| 215 | } |
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| 216 | |||
| 217 | |||
| 218 | const uint8_t pgm_asin[201] PROGMEM = {0,0,1,1,1,1,2,2,2,3,3,3,3,4,4,4,5,5,5,5,6,6,6,7,7,7,7,8,8,8,9,9,9,9,10,10,10,11,11,11,12,12,12,12,13,13,13,14,14,14,14,15,15,15,16,16,16,17,17,17,17,18,18,18,19,19,19,20,20,20,20,21,21,21,22,22,22,23,23,23,24,24,24,25,25,25,25,26,26,26,27,27,27,28,28,28,29,29,29,30,30,30,31,31,31,32,32,32,33,33,33,34,34,34,35,35,35,36,36,37,37,37,38,38,38,39,39,39,40,40,41,41,41,42,42,42,43,43,44,44,44,45,45,46,46,46,47,47,48,48,49,49,49,50,50,51,51,52,52,53,53,54,54,55,55,56,56,57,57,58,58,59,59,60,60,61,62,62,63,64,64,65,66,66,67,68,68,69,70,71,72,73,74,75,76,77,79,80,82,84,90}; |
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| 219 | |||
| 220 | // Akurssinusfunktion im Gradmaß |
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| 221 | int8_t asin_i(signed int i) |
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| 222 | { |
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| 223 | signed char m; |
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| 224 | |||
| 225 | if (i < 0) {m=-1;i=abs(i);} |
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| 226 | else m=1; |
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| 227 | |||
| 228 | return (pgm_read_byte(&pgm_asin[i]) * m); |
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| 229 | } |