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205 | Nick666 | 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 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 for more details. You should have received a copy of the GNU General Public License |
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8 | along with this program. If not, see <http://www.gnu.org/licenses/>. |
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9 | |||
10 | 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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11 | */ |
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12 | |||
13 | #include "main.h" |
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14 | |||
15 | //----------------------------------------------- |
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226 | Nick666 | 16 | // Fast arctan2 with max error of .07 rads |
205 | Nick666 | 17 | // http://www.dspguru.com/comp.dsp/tricks/alg/fxdatan2.htm |
18 | //----------------------------------------------- |
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229 | Nick666 | 19 | signed int arctan_f(signed int x, signed int y) |
205 | Nick666 | 20 | { |
226 | Nick666 | 21 | float rad,r; |
22 | short int m; |
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23 | #define coeff_1 0.7854 |
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24 | #define coeff_2 2.3562 |
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25 | #define rad2grad 57.2958 |
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205 | Nick666 | 26 | |
27 | if (!x && !y) return 0; |
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28 | |||
29 | if (y < 0) {y = abs(y); m = -1;} |
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30 | else m = 1; |
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31 | |||
32 | if (x>=0) |
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33 | { |
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226 | Nick666 | 34 | r = (float)(x - y) / (float)(x + y); |
35 | rad = coeff_1 - coeff_1*r; |
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205 | Nick666 | 36 | } |
37 | else |
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38 | { |
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226 | Nick666 | 39 | r = (float)(x + y) / (float)(y - x); |
40 | rad = coeff_2 - coeff_1*r; |
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205 | Nick666 | 41 | } |
226 | Nick666 | 42 | |
43 | rad *= rad2grad; |
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44 | |||
214 | Nick666 | 45 | return(rad*m); |
205 | Nick666 | 46 | } |
47 | |||
214 | Nick666 | 48 | /*++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
49 | Peter Muehlenbrock |
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50 | arctan in brute-force Art |
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51 | Stand 1.10.2007 |
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52 | ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
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53 | */ |
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54 | // arctan Funktion: Eingabewert x,y Rueckgabe =arctan(x,y) in grad |
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226 | Nick666 | 55 | signed int arctan_i(signed int x, signed int y) |
214 | Nick666 | 56 | { |
57 | short int change_xy = 0; |
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58 | signed int i; |
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59 | long signed int wert; |
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60 | int return_value; |
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61 | |||
62 | if ((abs(x)) > (abs(y))) // x,y Werte vertauschen damit arctan <45 grad bleibt |
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63 | { |
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64 | change_xy = 1; |
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65 | i = x; |
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66 | x = y; |
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67 | y = i; |
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68 | } |
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69 | |||
70 | // Quadranten ermitteln |
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71 | |||
72 | // Wert durch lineare Interpolation ermitteln |
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226 | Nick666 | 73 | if (!y && !x) return 0; // Division durch 0 nicht erlaubt |
74 | |||
214 | Nick666 | 75 | else wert= abs((x*1000)/y); |
76 | |||
77 | if (wert <=268) //0...0.0,268 entsprechend 0..15 Grad |
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78 | { |
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79 | return_value = (signed int)((wert*100)/(268-0)*(15-0)/100) +0; |
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80 | } |
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81 | else if (wert <=578) //0,268...0.0,568 entsprechend 15..30 Grad |
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82 | { |
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83 | return_value = (signed int)((((wert-268)*100)/(578-268)*(30-15))/100) +15; |
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84 | } |
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85 | else //0,568...1 entsprechend 30..45 Grad |
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86 | { |
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87 | return_value = (signed int)((((wert-578)*50)/(1000-578)*(45-30))/50) +30; |
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88 | } |
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89 | |||
90 | if (change_xy == 0) return_value = 90-return_value; //Quadrant 45..90 Grad |
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91 | if ((x >= 0) && (y <0)) return_value = - return_value; |
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92 | else if ((x < 0) && (y >= 0)) return_value = - return_value; |
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93 | |||
94 | return return_value; |
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95 | } |
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96 | |||
226 | Nick666 | 97 | |
98 | |||
99 | |||
229 | Nick666 | 100 | |
101 | 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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102 | |||
103 | inline float pgm_read_float(const float *addr) |
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104 | { |
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105 | union |
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106 | { |
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107 | uint16_t i[2]; // 2 16-bit-Worte |
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108 | float f; |
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109 | } u; |
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110 | |||
111 | u.i[0]=pgm_read_word((PGM_P)addr); |
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112 | u.i[1]=pgm_read_word((PGM_P)addr+2); |
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113 | |||
114 | return u.f; |
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115 | } |
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116 | |||
117 | // cosinus Funktion: Eingabewert Winkel in Grad |
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118 | float cos_f(signed int winkel) |
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119 | { |
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120 | return (sin_f(90-winkel)); |
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205 | Nick666 | 121 | } |
122 | |||
229 | Nick666 | 123 | // sinus Funktion: Eingabewert Winkel in Grad |
124 | float sin_f(signed int winkel) |
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205 | Nick666 | 125 | { |
126 | short int m,n; |
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229 | Nick666 | 127 | float sinus; |
205 | Nick666 | 128 | |
129 | //winkel = winkel % 360; |
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130 | |||
131 | if (winkel < 0) |
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132 | { |
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133 | m = -1; |
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134 | winkel = abs(winkel); |
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135 | } |
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136 | else m = +1; |
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137 | |||
138 | // Quadranten auswerten |
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139 | if ((winkel > 90 ) && (winkel <= 180)) {winkel = 180 - winkel; n = 1;} |
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140 | else if ((winkel > 180 ) && (winkel <= 270)) {winkel = winkel - 180; n = -1;} |
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141 | else if ((winkel > 270) && (winkel <= 360)) {winkel = 360 - winkel; n = -1;} |
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142 | else n = 1; //0 - 90 Grad |
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143 | |||
229 | Nick666 | 144 | sinus = pgm_read_float(&pgm_sinus_f[winkel]); |
205 | Nick666 | 145 | |
229 | Nick666 | 146 | return (sinus*m*n); |
205 | Nick666 | 147 | } |
148 | |||
149 | |||
226 | Nick666 | 150 | |
151 | |||
152 | |||
229 | Nick666 | 153 | |
154 | 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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155 | |||
156 | // cosinus Funktion: Eingabewert Winkel in Grad, Rueckgabe =cos(winkel)*1000 |
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157 | signed int cos_i(signed int winkel) |
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158 | { |
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159 | return (sin_i(90-winkel)); |
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226 | Nick666 | 160 | } |
161 | |||
229 | Nick666 | 162 | // sinus Funktion: Eingabewert Winkel in Grad, Rueckgabe =sin(winkel)*1000 |
163 | signed int sin_i(signed int winkel) |
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226 | Nick666 | 164 | { |
165 | short int m,n; |
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166 | |||
167 | //winkel = winkel % 360; |
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168 | |||
169 | if (winkel < 0) |
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170 | { |
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171 | m = -1; |
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172 | winkel = abs(winkel); |
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173 | } |
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174 | else m = +1; |
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175 | |||
176 | // Quadranten auswerten |
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177 | if ((winkel > 90 ) && (winkel <= 180)) {winkel = 180 - winkel; n = 1;} |
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178 | else if ((winkel > 180 ) && (winkel <= 270)) {winkel = winkel - 180; n = -1;} |
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179 | else if ((winkel > 270) && (winkel <= 360)) {winkel = 360 - winkel; n = -1;} |
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180 | else n = 1; //0 - 90 Grad |
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181 | |||
229 | Nick666 | 182 | winkel = pgm_read_word(&pgm_sinus[winkel]); |
226 | Nick666 | 183 | |
229 | Nick666 | 184 | return (winkel*m*n); |
226 | Nick666 | 185 | } |