| 0,0 → 1,229 |
|---|
| /* |
| This program (files math.c and math.h) 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 3 of the License, or (at your option) any later version. |
| 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 General Public License and GNU Lesser General Public License for more details. |
| You should have received a copy of GNU General Public License (License_GPL.txt) and |
| GNU Lesser General Public License (License_LGPL.txt) along with this program. |
| If not, see <http://www.gnu.org/licenses/>. |
| |
| 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 |
| */ |
| /*++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| Peter Muehlenbrock |
| Winkelfunktionen sin, cos und arctan in |
| brute-force Art: Sehr Schnell, nicht sonderlich genau, aber ausreichend |
| get_dist Funktion fuer Entfernungsermittlung |
| Stand 12.10.2007 |
| ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| */ |
| #include "main.h" |
| |
| |
| // arctan Funktion: Eingabewert x,y Rueckgabe =arctan(x,y) in grad |
| int arctan_i( signed int x, signed int y) |
| { |
| short int change_xy = 0; |
| signed int i; |
| long signed int wert; |
| int return_value; |
| |
| if ((abs(x)) > (abs(y))) // x,y Werte vertauschen damit arctan <45 grad bleibt |
| { |
| change_xy = 1; |
| i = x; |
| x = y; |
| y = i; |
| } |
| |
| // Quadranten ermitteln |
| |
| // Wert durch lineare Interpolation ermitteln |
| if ((y == 0) && (x == 0)) wert =1; // Division durch 0 nicht erlaubt |
| else wert= abs(((long)x*1000)/((long)y)); |
| |
| if (wert <=268) //0...0.0,268 entsprechend 0..15 Grad |
| { |
| return_value = (signed int)((wert*100)/(268-0)*(15-0)/100) +0; |
| } |
| else if (wert <=578) //0,268...0.0,568 entsprechend 15..30 Grad |
| { |
| return_value = (signed int)((((wert-268)*100)/(578-268)*(30-15))/100) +15; |
| } |
| else //0,568...1 entsprechend 30..45 Grad |
| { |
| return_value = (signed int)((((wert-578)*50)/(1000-578)*(45-30))/50) +30; |
| } |
| |
| if (change_xy == 0) return_value = 90-return_value; //Quadrant 45..90 Grad |
| if ((x >= 0) && (y <0)) return_value = - return_value; |
| else if ((x < 0) && (y >= 0)) return_value = - return_value; |
| |
| return return_value; |
| } |
| |
| |
| // cosinus Funktion: Eingabewert Winkel in Grad, Rueckgabe =cos(winkel)*1000 |
| signed int cos_i(signed int winkel) |
| { |
| winkel = sin_i(90-winkel); |
| return winkel; |
| } |
| |
| |
| 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}; |
| //von Nick666, Stand 28.9.2007 |
| // sinus Funktion: Eingabewert Winkel in Grad, Rueckgabe =sin(winkel)*1000 |
| signed int sin_i(signed int winkel) |
| { |
| short int m,n; |
| |
| if (abs(winkel) >=360) winkel = winkel % 360; |
| if (winkel < 0) |
| { |
| m = -1; |
| winkel = abs(winkel); |
| } |
| else m = +1; |
| n =1; |
| |
| // Quadranten auswerten |
| if ((winkel > 90 ) && (winkel <= 180)) winkel = 180 - winkel; |
| else if ((winkel > 180 ) && (winkel <= 270)) |
| { |
| winkel = winkel -180; |
| n = -1; |
| } |
| else if ((winkel > 270) && (winkel <= 360)) |
| { |
| winkel = 360 - winkel; |
| n = -1; |
| } |
| // else //0 - 90 Grad |
| |
| winkel = pgm_read_word(&pgm_sinus[winkel]); |
| return (winkel*m*n); |
| } |
| |
| // Aus x,y und Winkel Distanz ermitteln |
| long get_dist(signed int x, signed int y, signed int phi) |
| { |
| long dist; |
| if (abs(x) > abs(y) ) |
| { |
| dist = (long) x; //Groesseren Wert wegen besserer Genauigkeit nehmen |
| dist = abs((dist *1000) / (long) sin_i(phi)); |
| } |
| else |
| { |
| dist = (long) y; |
| dist = abs((dist *1000) / (long) cos_i(phi)); |
| } |
| return dist; |
| } |
| |
| |
| // noch mehr von Nick666 |
| |
| 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}; |
| |
| // Arkustangens2 im Gradmaß |
| signed int atan2_i(signed int x, signed int y) |
| { |
| int i,angle; |
| int8_t m; |
| |
| if (!x && !y) return 0; //atan2 = 0 für x und y = 0 |
| |
| if (y < 0) m=-1; |
| else m=1; |
| |
| if (x==0) return (90*m); // atan2 = 90° für x = 0 |
| |
| i = abs(((float)y / x) * 50); // Berechne i für die Lookup table (Schrittweite atan(x) ist 0.02 -> *50) |
| |
| if (i<270) angle = pgm_read_byte(&pgm_atan[i]); // Lookup für 1° bis 79° |
| else if (i>5750) angle = 90; // Grenzwert ist 90° |
| else if (i>=1910) angle = 89; // 89° bis 80° über Wertebereiche |
| else if (i>=1150) angle = 88; |
| else if (i>=820) angle = 87; |
| else if (i>=640) angle = 86; |
| else if (i>=520) angle = 85; |
| else if (i>=440) angle = 84; |
| else if (i>=380) angle = 83; |
| else if (i>=335) angle = 82; |
| else if (i>=299) angle = 81; |
| else angle = 80; // (i>=270) |
| |
| if (x > 0) return (angle*m); // Quadrant I und IV |
| else if ((x < 0) && (y >= 0)) return ((angle*-1) + 180); // Quadrant II |
| else return (angle - 180); // x < 0 && y < 0 Quadrant III |
| } |
| |
| |
| |
| |
| |
| 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}; |
| |
| inline float pgm_read_float(const float *addr) |
| { |
| union |
| { |
| uint16_t i[2]; // 2 16-bit-Worte |
| float f; |
| } u; |
| |
| u.i[0]=pgm_read_word((PGM_P)addr); |
| u.i[1]=pgm_read_word((PGM_P)addr+2); |
| |
| return u.f; |
| } |
| |
| // Kosinusfunktion im Gradmaß |
| float cos_f(signed int winkel) |
| { |
| return (sin_f(90-winkel)); |
| } |
| |
| // Sinusfunktion im Gradmaß |
| float sin_f(signed int winkel) |
| { |
| short int m,n; |
| float sinus; |
| |
| //winkel = winkel % 360; |
| |
| if (winkel < 0) |
| { |
| m = -1; |
| winkel = abs(winkel); |
| } |
| else m = +1; |
| |
| // Quadranten auswerten |
| if ((winkel > 90 ) && (winkel <= 180)) {winkel = 180 - winkel; n = 1;} |
| else if ((winkel > 180 ) && (winkel <= 270)) {winkel = winkel - 180; n = -1;} |
| else if ((winkel > 270) && (winkel <= 360)) {winkel = 360 - winkel; n = -1;} |
| else n = 1; //0 - 90 Grad |
| |
| sinus = pgm_read_float(&pgm_sinus_f[winkel]); |
| |
| return (sinus*m*n); |
| } |
| |
| |
| 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}; |
| |
| // Akurssinusfunktion im Gradmaß |
| int8_t asin_i(signed int i) |
| { |
| signed char m; |
| |
| if (i < 0) {m=-1;i=abs(i);} |
| else m=1; |
| |
| return (pgm_read_byte(&pgm_asin[i]) * m); |
| } |