Questions:
Hey there I have a pic16f882 and an MMA7360L accelerometer and i'm trying to convert the x and y axis readings into vectors to be able to calculate the accelerometers position from a given point at any given time. I already have the readings stored from the accelerometer but i'm not sure how i would now go about integrating these to reach position. Any help would be greatly appreciated, thanks in advance, ali+
Code:
+Method 2B. Accurate to -1.2%..+0.8%. Requires up to four constant multiplies. This method refines Levitt/Morris method. int magnitude2B(int x, int y) { int mx; int mn; x = abs(x); y = abs(y); mx = max(x, y); mn = min(x, y); if(mx >= 3*mn) return mx + mn/8; else if (mx >= 5/4*mn) return mx*7/8 + mn/2; else return mx*3/4 + mn*21/32; }
+There are several approximate methods for finding magnitude. They vary in their complexity and accuracy. Here is a list of some options: Method 1. Accurate up to -0..+8%. Requires a multiply by a constant. int magnitude_Robertson(int x, int y) { int mx; int mn; x = abs(x); y = abs(y); mx = max(x, y); mn = min(x, y); return mx + mn*k; } The method is apparently due to: Robertson, G.H., "A Fast Amplitude Approximation for Quadrature Pairs", Bell Sys. Tech. J., Vol. 50, Oct. 1971, pp.2849-2852. The constant k is chosen to minimize error in one of different ways (average error, absolute error, peak-to-peak error, standard deviation, etc) and efficient to compute the multiply. A few examples: 1/2, 3/8, 1/4: suggested by Robertson sqrt(2)-1 ~= 106/256: minimizes p-p error (also, zero error at multiples of 45 deg) Method 2. Accurate to 2.8%. Requires three constant multiplies. int magnitude_Levitt(int x, int y) { int mx; int mn; x = abs(x); y = abs(y); mx = max(x, y); mn = min(x, y); if(mx >= 3*mn) return mx + mn/8; else return mx*7/8 + mn/2; } See B.K Levitt, G.A. Morris, "An Improved Digital Algorithm for Fast Amplitude Approximations of Quadrature Pairs", DSN Progress Report 42-40, May and June 1977, pp 97-101. <a href="http://tmo.jpl.nasa.gov/progress_report2/42-40/40L.PDF">http://tmo.jpl.nasa.gov/progress_report2/42-40/40L.PDF</a> Method 3. Accurate up to -1.5%...+0%. Requires a divide, multiply, and a constant multiply. int magnitude3(int x, int y) { int mx; int mn; x = abs(x); y = abs(y); mx = max(x, y); mn = min(x, y); if(mx == 0) return mx; return mx + mn*mn/mx*k; } The constant k is chosen similarly to method 1. For example, k=sqrt(2)-1~=106/256 again minimizes the p-p error. The method is due to Nikolai Golovchenko. :) Method 4. Accurate up to -0.5%..+0%. Requires a divide, multiply, and two constant multiplies. This is a piecewise refinement of method 3. Vector (x,y) is assumed to be rotated to the range of 0 to 45 deg (i.e. x=mx and y=mn as in examples above) b = y/x if b <= 0.5 b += b * 0.14 // ~5/32 else b += (1-b) * 0.14 r = x + y * b * 106/256 Method 5: Theoretically arbitrary accuracy. Requires a divide and two multiplies. r = x + y * lookup(y/x) lookup() - a function that represents a table with linear interpolation.
file: /Techref/microchip/math/vector/index.htm, 4KB, , updated: 2009/5/26 08:48, local time: 2022/11/29 12:35, |
©2022 These pages are served without commercial sponsorship. (No popup ads, etc...).Bandwidth abuse increases hosting cost forcing sponsorship or shutdown. This server aggressively defends against automated copying for any reason including offline viewing, duplication, etc... Please respect this requirement and DO NOT RIP THIS SITE. Questions? <A HREF="http://piclist.com/techref/microchip/math/vector/index.htm"> PIC Microcontoller Basic Math Vector Math Methods</A> |
Did you find what you needed? |
PICList 2022 contributors:
o List host: MIT, Site host massmind.org, Top posters @none found - Page Editors: James Newton, David Cary, and YOU! * Roman Black of Black Robotics donates from sales of Linistep stepper controller kits. * Ashley Roll of Digital Nemesis donates from sales of RCL-1 RS232 to TTL converters. * Monthly Subscribers: Gregg Rew. on-going support is MOST appreciated! * Contributors: Richard Seriani, Sr. |
Welcome to piclist.com! |
.