| 0,0 → 1,184 |
|---|
| /****************************************************************/ |
| /* */ |
| /* NG-Video 5,8GHz */ |
| /* */ |
| /* Copyright (C) 2011 - gebad */ |
| /* */ |
| /* This code is distributed under the GNU Public License */ |
| /* which can be found at http://www.gnu.org/licenses/gpl.txt */ |
| /* */ |
| /****************************************************************/ |
| |
| #include <stdio.h> |
| #include <stdlib.h> |
| #include <math.h> |
| #include <avr/pgmspace.h> |
| |
| #include "mymath.h" |
| |
| // http://www.mikrocontroller.net/articles/AVR_Arithmetik#avr-gcc_Implementierung_.2832_Bit.29 |
| unsigned int sqrt32(uint32_t q) |
| { uint16_t r, mask; |
| uint16_t i = 8*sizeof (r) -1; |
| |
| r = mask = 1 << i; |
| for (; i > 0; i--) { |
| mask >>= 1; |
| |
| if (q < (uint32_t) r*r) |
| r -= mask; |
| else |
| r += mask; |
| } |
| |
| if (q < (uint32_t) r*r) |
| r -= 1; |
| |
| return r; |
| } |
| |
| // aus Orginal MK source code |
| // sinus with argument in degree at an angular resolution of 1 degree and a discretisation of 13 bit. |
| const uint16_t sinlookup[91] = {0, 143, 286, 429, 571, 714, 856, 998, 1140, 1282, 1423, 1563, 1703, \ |
| 1843, 1982, 2120, 2258, 2395, 2531, 2667, 2802, 2936, 3069, 3201, 3332, \ |
| 3462, 3591, 3719, 3846, 3972, 4096, 4219, 4341, 4462, 4581, 4699, 4815, \ |
| 4930, 5043, 5155, 5266, 5374, 5482, 5587, 5691, 5793, 5893, 5991, 6088, \ |
| 6183, 6275, 6366, 6455, 6542, 6627, 6710, 6791, 6870, 6947, 7022, 7094, \ |
| 7165, 7233, 7299, 7363, 7424, 7484, 7541, 7595, 7648, 7698, 7746, 7791, \ |
| 7834, 7875, 7913, 7949, 7982, 8013, 8041, 8068, 8091, 8112, 8131, 8147, \ |
| 8161, 8172, 8181, 8187, 8191, 8192}; |
| |
| //double c_cos_8192(int16_t angle) |
| int16_t c_cos_8192(int16_t angle) |
| { |
| int8_t m,n; |
| int16_t sinus; |
| |
| angle = 90 - angle; |
| // avoid negative angles |
| if (angle < 0) |
| { |
| m = -1; |
| angle = -angle; |
| } |
| else m = +1; |
| |
| // fold angle to interval 0 to 359 |
| angle %= 360; |
| |
| // check quadrant |
| if (angle <= 90) n = 1; // first quadrant |
| else if ((angle > 90) && (angle <= 180)) {angle = 180 - angle; n = 1;} // second quadrant |
| else if ((angle > 180) && (angle <= 270)) {angle = angle - 180; n = -1;} // third quadrant |
| else {angle = 360 - angle; n = -1;} //fourth quadrant |
| // get lookup value |
| sinus = sinlookup[angle]; |
| // calculate sinus value |
| return (sinus * m * n); |
| } |
| |
| /* ---------------------------------------------------------------------------------------------- |
| |
| atan2.S |
| |
| Author: Reiner Patommel |
| |
| atan2.S uses CORDIC, an algorithm which was developed in 1956 by Jack Volder. |
| CORDIC can be used to calculate trigonometric, hyperbolic and linear |
| functions and is until today implemented in most pocket calculators. |
| The algorithm makes only use of simple integer arithmetic. |
| |
| The CORDIC equations in vectoring mode for trigonometric functions are: |
| Xi+1 = Xi - Si * (Yi * 1 / 2^i) |
| Yi+1 = Yi + Si * (Xi * 1 / 2^i) |
| Zi+1 = Zi - Si * atan(1 / 2^i) |
| where Si = +1 if Yi < 0 else Si = -1 |
| The rotation angles are limited to -PI/2 and PI/2 i.e. |
| -90 degrees ... +90 degrees |
| |
| For the calculation of atan2(x,y) we need a small pre-calculated table of |
| angles or radians with the values Tn = atan(1/2^i). |
| We rotate the vector(Xo,Yo) in steps to the x-axis i.e. we drive Y to 0 and |
| accumulate the rotated angles or radians in Z. The direction of the rotation |
| will be positive or negative depending on the sign of Y after the previous |
| rotation and the rotation angle will decrease from step to step. (The first |
| step is 45 degrees, the last step is 0.002036 degrees for n = 15). |
| |
| After n rotations the variables will have the following values: |
| Yn = ideally 0 |
| Xn = c*sqrt(Xo^2+Yo^2) (magnitude of the vector) |
| Zn = Zo+atan(Yo/Xo) (accumulated rotation angles or radians) |
| |
| c, the cordic gain, is the product Pn of sqrt(1+2^(-2i)) and amounts to |
| approx. 1.64676 for n = 15. |
| |
| In order to represent X, Y and Z as integers we introduce a scaling factor Q |
| which is chosen as follows: |
| 1. We normalize Xo and Yo (starting values) to be less than or equal to 1*Q and |
| set Zo = 0 i.e. Xomax = 1*Q, Yomax = 1*Q, Zo = 0. |
| 2. With Xo = 1*Q and Yo = 1*Q, Xn will be Xnmax = Q*c*sqrt(2) = 2.329*Q |
| 3. In order to boost accuracy we only cover the rotation angles between 0 and PI/2 |
| i.e. X and Z are always > 0 and therefore can be unsigned. |
| (We do the quadrant correction afterwards based on the initial signs of x and y) |
| 4. If X is an unsigned int, Xnmax = 65536, and Q = 65536/2.329 = 28140. |
| i.e. |
| Xnmax = 65536 --> unsigned int |
| Ynmax = +/- 28140 --> signed int |
| Znmax = PI/2 * 28140 = 44202 --> unsigned int |
| The systematic error is 90/44202 = 0.002036 degrees or 0.0000355 rad. |
| |
| Below is atan2 and atan in C: */ |
| |
| #define getAtanVal(x) (uint16_t)pgm_read_word(&atantab[x]) |
| //uint16_t atantab[T] PROGMEM = {22101,13047,6894,3499,1756,879,440,220,110,55,27,14,7,3,2,1}; // T 16 |
| // Genauigkeit etwas eingeschränkt, da Servos nur in 1° Abständen positioniert werden |
| uint16_t atantab[T] PROGMEM = {22101,13047,6894,3499,1756,879,440,220,110,55,27,14,7,3}; |
| |
| // max. Wert für y oder x ist 76314 |
| int16_t my_atan2(int32_t y, int32_t x) |
| { unsigned char i; |
| uint32_t x1; |
| int32_t y1; |
| uint32_t angle = 0; |
| uint32_t tmp; |
| |
| x1 = abs(x); |
| y1 = abs(y); |
| |
| if (y1 == 0) { |
| if (x < 0) |
| return (180); |
| else |
| return 0; |
| } |
| |
| if (x1 < y1) { |
| x1 = SCALED(x1) / y1; |
| y1 = Q; |
| } |
| else { |
| y1 = SCALED(y1) / x1; |
| x1 = Q; |
| } |
| |
| for (i = 0; i < T-1; i++) { |
| tmp = x1 >> i; |
| if (y1 < 0) { |
| x1 -= y1 >> i; |
| y1 += tmp; |
| angle -= getAtanVal(i); |
| } |
| else { |
| x1 += y1 >> i; |
| y1 -= tmp; |
| angle += getAtanVal(i); |
| } |
| } |
| |
| angle = angle/RQ; // RAD_TO_DEG * angle / Q |
| if (x <= 0) |
| angle = 180 - angle; |
| if (y <= 0) |
| return(-angle); |
| return(angle); |
| } |