Colony

% vectorSizeSpecs - Script used to help calculate the max scalar value by

% 		which to multiply the BOM unit vectors (thus increasing the

%		precision of the scaled vectors) such that in the worst case, the

%		total net sum will not overflow the data type used to represent

%		the net vector components.

%

%	Author: John Sexton, Colony Project, CMU Robotics Club

% Parameters

maxIntensity = 255;

dataBits = 16;

scalar = 25;

n = 0:8;

angle = n * 2 * pi / 16;

vector_components = sin(angle);

max_net_component = sum(vector_components);

% Formula for max_net_component (mnc), obtained by summing

% values from the unit circle at angles of 0 : pi/8 : pi

% in quadrants I and II

mnc = 1;									%sin(pi/2)

mnc = mnc + (2*  (1/2)*sqrt(2+sqrt(2)));	%sin(3pi/8) and sin(5pi/8)

mnc = mnc + (2*  sqrt(2)/2);				%sin(pi/4) and sin(3pi/4)

mnc = mnc + (2*  (1/2)*sqrt(2-sqrt(2)));	%sin(pi/8) and sin(7pi/8)

calc_scalar = (2^(dataBits-1)-1) / (max_net_component * maxIntensity);

% calc_scalar = 25.560 => use 25 as scalor

fprintf('With %d data bits, calculated scalar value: %.3f\n\n', dataBits, calc_scalar);

% Check worst case

scaled_vector_components = scalar * vector_components;

worst_case = scaled_vector_components * maxIntensity;

worst_sum = sum(worst_case);

fprintf('With scalar %d, max worst case sum: %d\n', scalar, worst_sum);

fprintf('Max number: 2^(%d-1) - 1 = %d\n', dataBits, (2^(dataBits-1)-1));