function [new_config, new_ctrm, new_norms,eyes,eyeN]  = buddy140_km(ctrm,sp_coords,Theta,subset)

% This code represents the kinematic model created by 'Build_data_frame' as a function.

%%% INPUTS %%%
% ctrm: the estimated 3 x 1 center of mass for the kinematic model configuration.
% sp_coords: a 4 x 1 vector for global rotation, [-pi,pi], and position, R3, in the spatial frame.
% Theta: a vector of N x 1 angles, where N is the number of rotation axes
% subset: a vector of M x 1 binary values, where M is the number of mesh segments for selecting only a subset of mesh segments [0 = not in subset, 1 = in subset].
%%% Outputs %%%
% new_config: a point cloud from the surface of the kinematic model in the new configuration.
% new_ctrm: a new center of mass estimate for the kinematic model (only computed if all mesh segments are updated).

% new_norms: a new norm associated with the model point is calculated to reflect the new pose.

%%% Sampled meshes for each segment
I1  = [  0.016710  0.079998  0.065090  0.076797  0.066876  0.067908  0.052268 -0.008804  0.048362  0.048249  0.010780  0.075961  0.055707  0.036800  0.055247  0.057802  0.072759  0.036514  0.010169 -0.010587  0.073263  0.075301  0.076046 -0.005668  0.009813  0.034130  0.077018 -0.004391  0.079350  0.037281  0.007429  0.018868  0.013095  0.053246  0.063061  0.078945  0.080936  0.046741  0.075314  0.069152  0.035702  0.062604  0.021105 -0.013515  0.065860  0.023166  0.074949  0.075578  0.074149  0.016313  0.047347 -0.006840  0.009263  0.001333  0.066615  0.046176 -0.003621  0.014920 -0.004711  0.057708  0.025084  0.017548  0.036196  0.036214  0.025588  0.016592 -0.003737  0.041681  0.033314  0.068589  0.066444  0.008481  0.002677  0.052540 -0.002285  0.049352  0.011633  0.058992  0.081956 -0.002575  0.041782  0.057772  0.009887  0.040963  0.042242  0.059181  0.010652  0.043588  0.075245  0.057602  0.030985  0.056862  0.024969  0.077004  0.083164  0.011604 -0.003052  0.049368 -0.004313 -0.003736  0.043039  0.036190  0.081022  0.055746 -0.016069  0.014688  0.081346  0.036342  0.006155  0.042119  0.056489  0.055176  0.050328  0.031422  0.015032  0.023883  0.043352  0.075948  0.055293  0.055976  0.077657 -0.004565  0.061948  0.079426  0.057190  0.074496  0.071775 -0.000603  0.016898  0.034584  0.079783 -0.009438 -0.011034  0.021752  0.008492  0.014256  0.009680  0.055852  0.078483  0.056193 -0.008874  0.016630  0.078627  0.069714  0.048800  0.040448  0.028187  0.006193  0.002631 -0.001808  0.016776 -0.015060  0.074591  0.024767 -0.007009  0.047063  0.064522  0.037403  0.068696  0.050747  0.048952  0.054864  0.054760  0.039541 -0.011437 -0.000363  0.021243  0.055545  0.033060  0.040364  0.081766  0.010982 -0.007772  0.075601 -0.003391  0.020489 -0.016851  0.038204  0.041791  0.070286  0.060538  0.078721  0.065119 -0.000095  0.061897  0.082642  0.015623  0.003790  0.079979  0.038972  0.078045  0.077845  0.052218 -0.014632  0.036231  0.029641  0.021934  0.007128  0.027449  0.040995
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N1  = [  0.314524  1.056327  0.647908  0.926424  0.884782  0.897755  0.580648  0.399493  0.669848  0.440639  0.560357  0.923087  0.747129  0.621766  0.846837  0.567166  1.062327  0.779219  0.425700  0.487906  1.061816  1.053073  0.846327  0.490008  0.284262  0.705258  1.055745  0.317785  0.909792  0.683196  0.542342  0.680107  0.253291  0.728301  0.892908  1.036218  1.054766  0.668227  1.009488  0.886755  0.701542  0.379342  0.353186  0.522282  0.847210  0.263362  1.063503  0.968624  0.927519  0.551226  0.838937  0.407008  0.694357  0.443097  0.649432  0.711710  0.410226  0.289369  0.665198  0.972773  0.816240  0.315362  0.939708  0.827371  0.689565  0.680568  0.673025  0.373116  0.418512  0.949798  0.924323  0.693575  0.634066  0.730702  0.319890  0.522307  0.546546  0.739942  0.907730  0.330410  0.573940  0.738721  0.366776  0.843731  0.710061  0.728432  0.695746  0.665074  0.924872  0.374340  0.554007  0.859633  0.458275  0.885811  1.011645  0.251800  0.329933  0.714903  0.491363  0.673026  0.664525  0.939701  0.906796  0.620609  0.357076  0.675927  0.911788  0.703439  0.335045  0.661287  0.837516  0.724427  0.582486  0.362857  0.430564  0.457189  0.721515  0.968993  0.620156  0.666662  0.788533  0.370813  0.853538  1.013600  0.826633  1.063050  0.782651  0.857575  0.314711  0.837352  1.033690  0.526360  0.430730  0.378642  0.031791  0.471961  0.269402  0.730907  0.789359  0.846573  0.530739  0.551826  1.035958  0.950924  0.441190  0.570703  0.483947  0.421725  0.100178  0.616182  0.678016  0.008079  1.063145  0.693416  0.532603  0.712597  0.647339  0.780108  0.886602  0.719998  0.441342  0.685071  0.754439  0.370977  0.625923  0.631025  0.685220  0.772008  0.704189  0.661850  1.039038  0.034281  0.400526  0.956810  0.410457  0.684465  0.356295  0.941716  0.663278  0.923656  0.787037  1.055049  0.883435  0.441670  0.703333  1.056472  0.431154  0.392167  1.058705  0.703535  0.942501  0.895449  0.693654  0.500760  0.504047  0.485401  0.281656  0.030428  0.412647  0.445648
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%%% points and normals for eyes
eyes = [ -0.074303 -0.073086
          0.170921  0.078070
         -0.102810 -0.174956
          1.000000  1.000000];
     
eyeN = [  0.259084  0.279511
          1.090339  0.246279
         -0.311433 -1.095489
          1.000000  1.000000];
     
%%% Ordered transformation matrices
%Root Node
% Global rotation operator
w1a = [0.994421 0.094730 -0.046401]';
q1a = [ctrm(1) ctrm(2) ctrm(3)]';
t1a = twist_matrix(w1a,q1a,sp_coords(1));

% Global translation operator
t1b = t1a\twist_matrix(sp_coords(2:4),0,0)*t1a;

w1c = [0.206218 -0.011096 0.025543]';
q1c = [0.007455 -0.193970 0.228362]';
t1c = twist_matrix(w1c,q1c,Theta(1));

w1d = [-0.007811 0.160154 0.132631]';
q1d = [0.007455 -0.193970 0.228362]';
t1d = twist_matrix(w1d,q1d,Theta(2));

w1e = [-0.026731 -0.132397 0.158297]';
q1e = [0.007455 -0.193970 0.228362]';
t1e = twist_matrix(w1e,q1e,Theta(3));

w4a = [0.006539 0.163188 0.128952]';
q4a = [0.028378 -0.095224 0.102339]';
t4a = twist_matrix(w4a,q4a,Theta(4));

w4b = [0.026965 0.127261 -0.162416]';
q4b = [0.028378 -0.095224 0.102339]';
t4b = twist_matrix(w4b,q4b,Theta(5));

w4c = [-0.206232 0.021814 -0.017147]';
q4c = [0.028378 -0.095224 0.102339]';
t4c = twist_matrix(w4c,q4c,Theta(6));

w5a = [-0.038489 0.154098 0.134439]';
q5a = [-0.004649 -0.001896 -0.014092]';
t5a = twist_matrix(w5a,q5a,Theta(7));

w5b = [0.003627 -0.136263 0.157228]';
q5b = [-0.004649 -0.001896 -0.014092]';
t5b = twist_matrix(w5b,q5b,Theta(8));

w5c = [0.204467 0.031425 0.022517]';
q5c = [-0.004649 -0.001896 -0.014092]';
t5c = twist_matrix(w5c,q5c,Theta(9));

w6a = [-0.053929 0.151262 0.132337]';
q6a = [-0.006658 0.073573 -0.101173]';
t6a = twist_matrix(w6a,q6a,Theta(10));

w6b = [0.064774 0.142788 -0.136811]';
q6b = [-0.006658 0.073573 -0.101173]';
t6b = twist_matrix(w6b,q6b,Theta(11));

w6c = [-0.190256 0.005737 -0.084090]';
q6c = [-0.006658 0.073573 -0.101173]';
t6c = twist_matrix(w6c,q6c,Theta(12));

w7a = [0.012111 0.140829 0.152715]';
q7a = [0.002936 0.094724 -0.121438]';
t7a = twist_matrix(w7a,q7a,Theta(13));

w7b = [0.180690 -0.082620 0.061859]';
q7b = [0.002936 0.094724 -0.121438]';
t7b = twist_matrix(w7b,q7b,Theta(14));

w7c = [0.102499 0.129006 -0.127094]';
q7c = [0.002936 0.094724 -0.121438]';
t7c = twist_matrix(w7c,q7c,Theta(15));

%%% Construct kinematic chains of transformations
% if unspecified by user, select all mesh segments
if ~exist('subset','var') || isempty(subset)
	subset = ones(4,1);
end

% Initialize new_config and populate with the subset of mesh segment
new_config = [];
new_norms  = [];
if subset(1)
	U          = t1a*t1b*t1c*t1d*t1e*I1;
	new_config = [new_config U(1:3,:)];
	V          = t1a*t1b*t1c*t1d*t1e*N1;
	V = V-U;
	new_norms  = [new_norms V(1:3,:)];
end

if subset(2)
	U          = t1a*t1b*t1c*t1d*t1e*t4a*t4b*t4c*I4;
	new_config = [new_config U(1:3,:)];
	V          = t1a*t1b*t1c*t1d*t1e*t4a*t4b*t4c*N4;
	V = V-U;
	new_norms  = [new_norms V(1:3,:)];
end

if subset(3)
	U          = t1a*t1b*t1c*t1d*t1e*t4a*t4b*t4c*t5a*t5b*t5c*I5;
	new_config = [new_config U(1:3,:)];
	V          = t1a*t1b*t1c*t1d*t1e*t4a*t4b*t4c*t5a*t5b*t5c*N5;
	V = V-U;
	new_norms  = [new_norms V(1:3,:)];
end

if subset(4)
	U          = t1a*t1b*t1c*t1d*t1e*t4a*t4b*t4c*t5a*t5b*t5c*t6a*t6b*t6c*t7a*t7b*t7c*I7;
	new_config = [new_config U(1:3,:)];
	V          = t1a*t1b*t1c*t1d*t1e*t4a*t4b*t4c*t5a*t5b*t5c*t6a*t6b*t6c*t7a*t7b*t7c*N7;
	V = V-U;
	new_norms  = [new_norms V(1:3,:)];
    % Update eye model
    eyes       = t1a*t1b*t1c*t1d*t1e*t4a*t4b*t4c*t5a*t5b*t5c*t6a*t6b*t6c*t7a*t7b*t7c*eyes;
    eyes       = eyes(1:3,:);
    eyeN       = t1a*t1b*t1c*t1d*t1e*t4a*t4b*t4c*t5a*t5b*t5c*t6a*t6b*t6c*t7a*t7b*t7c*eyeN;
    eyeN       = eyeN(1:3,:);
    eyeN       = eyeN - eyes;
    
end

% Update center of mass estimate
if sum(subset) == 4
	new_ctrm = mean(new_config,2);
else
	new_ctrm = ctrm;
end


%%% Twist matrix function
function [twist] = twist_matrix(w,q,theta)
% Overview:
% This code generates an exponential map matrix for rotation and translation
% using the Rodrigues' formula for the matrix exponential, from "A Mathematical 
% Introduction to Robotic Manipulation" by Murray, Li, and Sastry (1994) p. 28. 
% The equation for the exponential map for twists is from Ibid. 42.
%
% [twist] = twist_matrix(w,q,theta)
% INPUTS %
% w: a 3d vector pointing: 1) in the direction of translation or 2) 
%      along the axis of rotation relative to the origin.
% q: a 3d point along the axis of rotation, providing the offset
% theta: the amount of rotation, in radians
%
% OUTPUTS %
% twist: the resulting matrix for left multiplication
%
% I treat 2 cases: 1) pure translation and 2) pure rotation
if numel(q) < 3 && (q == 0 || theta == 0)
    % 1) pure translation
    % In this case the input w now is a translation vector
	% check input
	if numel(w) < 3
		error('Input error: w must be a 3d vector.')
	end
	% we want column vectors
	if size(w,1)<size(w,2)
		w = w';
	end
	% pure translation in absolute frame
	twist = [eye(3) w;zeros(1,3) 1];
else
    % 2) pure rotation twist
    if numel(w)<3 || numel(q) < 3
        error('Input error: Both w and q must be 3d.')
    end
    if size(w) ~= size(q)
        error('Input error: w and q must be the same size.')
    end
    % we want column vectors
    if size(w,1)<size(w,2)
        w = w';
        q = q';
    end
    % correct for case where w is the origin
    if sum(w) == 0
        w = q;
    end
    
    % normalize
    if norm(w) ~= 1 && sum(w)~=0
        % make unit vector
        w = w/norm(w);
    end
    % Generate cross product operator so(3)
    w_hat = [0   -w(3) w(2);
             w(3) 0   -w(1);
            -w(2) w(1) 0];
    
    v = -w_hat*q;
    % Generate rotation matrix using the Rodrigues' equation pg. 28
    w_hat2 = w*w'-norm(w)^2*eye(3);
    R      = eye(3)+w_hat*sin(theta)+w_hat2*(1-cos(theta));

    % Generate relative frame twist, pg. 42
    twist  = [R (eye(3)-R)*w_hat*v+w*w'*v*theta;
              zeros(1,3) 1];
end
