function [new_config, new_ctrm, new_norms]  = buddy140_km(sp_coords,Theta)

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

%%% INPUTS %%%
% sp_coords: a 4 x 1 vector for global position, R3, and rotation, [-pi,pi], in the spatial frame.
% Theta: a vector of N x 1 angles, where N is the number of rotation axes.
%%% 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.

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

%%% Sampled meshes for each segment
I1  = [  0.042668  0.008804  0.021891  0.065928  0.034972  0.074829  0.081175  0.034728  0.079978  0.050247  0.021437  0.071164 -0.001745  0.029555  0.040909  0.076683  0.027158  0.020536 -0.009696  0.062486  0.081411  0.054269  0.064159  0.039813  0.007728  0.047312  0.066914  0.064873  0.066879 -0.014751  0.069189  0.078851  0.021590  0.070554  0.046166  0.012232 -0.002770  0.048246  0.078892  0.073743  0.073867  0.081527  0.048838  0.067273  0.033724  0.047463  0.011907  0.059370  0.072501  0.054678 -0.013678  0.079554  0.065737  0.052440  0.052323  0.021466  0.040315 -0.007985  0.054419  0.021871  0.039635  0.042520  0.081974  0.066521  0.020260  0.077682  0.035979  0.025840  0.048488  0.009416  0.025682  0.036704  0.076058  0.003820  0.066765  0.034686  0.076667  0.050321  0.026293  0.027117  0.037393  0.047265  0.081893  0.073411  0.060522  0.047496  0.002627  0.010477  0.068309  0.068341  0.059662  0.008837  0.080912  0.006536  0.073681  0.034169  0.080280  0.021844  0.010620  0.000114  0.059300  0.045595  0.019220  0.045651  0.041660  0.073971  0.082627  0.078197  0.076784  0.040268  0.052443  0.058747  0.022919  0.061428  0.026310 -0.010744  0.018785  0.051900  0.052095 -0.006916  0.025617  0.078672  0.025431  0.059506  0.033935  0.061758  0.030119  0.052360  0.026441  0.038158  0.075238  0.039255  0.024134  0.019988  0.051052  0.056715  0.080581  0.074947  0.030151  0.024576  0.081959  0.073124  0.052544 -0.008801  0.076049  0.075710  0.053344  0.061991  0.046494  0.078466 -0.000267  0.028688  0.080155 -0.014700  0.055137  0.079925  0.002263  0.062355  0.059244  0.080202  0.053658  0.054598  0.077581  0.010172  0.028457  0.055169  0.033438  0.050193  0.033686  0.034940  0.073624  0.034215  0.048325  0.081280  0.039331  0.040413 -0.010974  0.074481  0.067024  0.076439 -0.005236  0.021754  0.029850  0.041639  0.058888  0.001890  0.028571  0.008731  0.023622  0.076337  0.057374  0.037158 -0.019267  0.020055  0.060461 -0.012805  0.016334  0.004666  0.054978  0.026500  0.053770  0.038394  0.041553  0.066372  0.006698  0.082081  0.021817 -0.001660  0.038414  0.037197  0.061180  0.079917  0.037569  0.028897  0.065939  0.018583  0.048464 -0.010240  0.033932  0.015463  0.082623 -0.001268  0.024808  0.023963  0.013358 -0.008719  0.072497  0.077768  0.007784  0.010205  0.071572  0.080095  0.026395 -0.001482  0.073860  0.079865  0.010164  0.027691 -0.005349  0.077199  0.002621  0.066338  0.071860  0.009105  0.016684  0.038701  0.024887  0.040588 -0.000682  0.078689  0.081970  0.033036 -0.003450  0.037400  0.003987  0.061491
        -0.202568 -0.055086 -0.228179 -0.176634 -0.215429 -0.166701 -0.177039 -0.226099 -0.134747 -0.213482 -0.228205 -0.171671 -0.245019 -0.222128 -0.139824 -0.128020 -0.215959 -0.232287 -0.085928 -0.188221 -0.134331 -0.138176 -0.183051 -0.174779 -0.229640 -0.191370 -0.127974 -0.205742 -0.162954 -0.221341 -0.178485 -0.133180 -0.222853 -0.093585 -0.202437 -0.227570 -0.062237 -0.186041 -0.180692 -0.106237 -0.107141 -0.157173 -0.218406 -0.172931 -0.217272 -0.101656 -0.235740 -0.198252 -0.190389 -0.187292 -0.092587 -0.128425 -0.087605 -0.212553 -0.216765 -0.229081 -0.137933 -0.119246 -0.200404 -0.083084 -0.092455 -0.178489 -0.148126 -0.164606 -0.127601 -0.187197 -0.080421 -0.225796 -0.188948 -0.238593 -0.227232 -0.211775 -0.149344 -0.083121 -0.189160 -0.146582 -0.158526 -0.146207 -0.163842 -0.229297 -0.098342 -0.219979 -0.171602 -0.106676 -0.175656 -0.082892 -0.232623 -0.237235 -0.090273 -0.200770 -0.085300 -0.183729 -0.167794 -0.239785 -0.105989 -0.226782 -0.130558 -0.164818 -0.216197 -0.249031 -0.088622 -0.218587 -0.233247 -0.219678 -0.209148 -0.107753 -0.150654 -0.122009 -0.119140 -0.208887 -0.216972 -0.204244 -0.166345 -0.188530 -0.229452 -0.122792 -0.181092 -0.205523 -0.110145 -0.107550 -0.212201 -0.172118 -0.227398 -0.198858 -0.198932 -0.137422 -0.124458 -0.087924 -0.162239 -0.184582 -0.163654 -0.094403 -0.226937 -0.100175 -0.117834 -0.202736 -0.166215 -0.192280 -0.226747 -0.162824 -0.156274 -0.192543 -0.141869 -0.218518 -0.116517 -0.190396 -0.163706 -0.203088 -0.165290 -0.131653 -0.231985 -0.224072 -0.161180 -0.056329 -0.134841 -0.151274 -0.125450 -0.201594 -0.210896 -0.136063 -0.215479 -0.213490 -0.147689 -0.070504 -0.081508 -0.165778 -0.078360 -0.132755 -0.072345 -0.224406 -0.104970 -0.211540 -0.195573 -0.140384 -0.202733 -0.178662 -0.212689 -0.186324 -0.174848 -0.123367 -0.247507 -0.093757 -0.221406 -0.132467 -0.165132 -0.236836 -0.181140 -0.242348 -0.115572 -0.137609 -0.198263 -0.204975 -0.049732 -0.152174 -0.098744 -0.097723 -0.232626 -0.121313 -0.208197 -0.218389 -0.100778 -0.123058 -0.222388 -0.189173 -0.217447 -0.151371 -0.230994 -0.216435 -0.223230 -0.117871 -0.139453 -0.136924 -0.177587 -0.221955 -0.175628 -0.116153 -0.104591 -0.231058 -0.136256 -0.061738 -0.146911 -0.222612 -0.173864 -0.227897 -0.179345 -0.240356 -0.172478 -0.185217 -0.237728 -0.213314 -0.096290 -0.130575 -0.226032 -0.245568 -0.107079 -0.136220 -0.147564 -0.224058 -0.217287 -0.128992 -0.218387 -0.203415 -0.177884 -0.226200 -0.067540 -0.089248 -0.206694 -0.183632 -0.230033 -0.123560 -0.155040 -0.186079 -0.112218 -0.203289 -0.242945 -0.123435
         0.110791  0.207697  0.211340  0.198262  0.215134  0.109254  0.160065  0.144579  0.128019  0.133223  0.201794  0.106704  0.168416  0.230037  0.244193  0.195049  0.112332  0.154082  0.254037  0.112048  0.177580  0.230590  0.107949  0.235476  0.123258  0.100441  0.209631  0.165108  0.209634  0.109698  0.111103  0.152787  0.116754  0.166494  0.207461  0.120527  0.229687  0.221228  0.145150  0.157510  0.162586  0.122945  0.147485  0.199938  0.124722  0.210124  0.165368  0.123279  0.173715  0.101629  0.258785  0.164059  0.174092  0.136733  0.156458  0.178933  0.244852  0.264447  0.117473  0.223191  0.210426  0.231156  0.131602  0.209183  0.254670  0.153697  0.202443  0.223533  0.218984  0.193960  0.174873  0.224702  0.197982  0.242605  0.182514  0.249353  0.189059  0.232160  0.258080  0.147328  0.220363  0.142218  0.153043  0.175000  0.095414  0.192408  0.127604  0.187150  0.169924  0.155064  0.182674  0.270438  0.138259  0.181418  0.160460  0.146533  0.164716  0.262142  0.103692  0.210491  0.186037  0.177148  0.151881  0.173842  0.118652  0.163172  0.161807  0.173642  0.166174  0.117579  0.167562  0.135143  0.261299  0.110592  0.144828  0.266245  0.265166  0.191541  0.213761  0.260891  0.104361  0.128717  0.230453  0.186351  0.097876  0.219779  0.248192  0.192199  0.257817  0.234604  0.188843  0.212995  0.217993  0.242177  0.225346  0.187487  0.168911  0.167545  0.139716  0.259831  0.127497  0.147002  0.231459  0.105768  0.165617  0.151396  0.226472  0.139423  0.231426  0.137248  0.126300  0.186604  0.175779  0.234728  0.230028  0.185108  0.262272  0.181194  0.169615  0.129513  0.154382  0.176241  0.195407  0.223245  0.213101  0.224774  0.203489  0.235959  0.196371  0.168521  0.154845  0.234628  0.213806  0.129421  0.109229  0.233783  0.097037  0.137238  0.197955  0.150451  0.165485  0.235128  0.222677  0.242919  0.222476  0.135078  0.253455  0.209482  0.248277  0.198831  0.118902  0.110727  0.230352  0.261740  0.192405  0.260316  0.193337  0.260025  0.185637  0.115530  0.201844  0.242118  0.163319  0.183031  0.105030  0.134651  0.163804  0.103049  0.168441  0.239757  0.219977  0.154217  0.237799  0.241342  0.199880  0.251647  0.212133  0.124311  0.249313  0.206810  0.168896  0.112152  0.259496  0.224536  0.268032  0.139409  0.110262  0.166985  0.140986  0.099725  0.163518  0.163262  0.228224  0.171640  0.162115  0.134820  0.264465  0.224270  0.104097  0.194258  0.106192  0.157003  0.115712  0.118020  0.211858  0.208271  0.096719  0.231326  0.123224  0.183017  0.133668  0.244012  0.260705  0.230711  0.187895  0.215047
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N1  = [  0.351613  0.639868  0.745008  0.890966  0.797484  0.960892  1.053790  0.360419  1.037065  0.621179  0.683302  0.878328  0.615818  0.810930  0.673100  0.928149  0.711338  0.466782  0.487234  0.783612  1.063956  0.834929  0.776466  0.786462  0.066051  0.490998  0.852950  0.791522  0.934753  0.008651  0.811942  1.045472  0.393790  0.999341  0.855293  0.151481  0.617115  0.775679  1.011704  1.059599  1.056317  1.040941  0.771173  0.933664  0.563082  0.708749  0.523894  0.766484  0.882940  0.554952  0.371040  1.034041  0.865197  0.799173  0.641931  0.536275  0.672507  0.338931  0.593478  0.652521  0.692882  0.798608  1.081093  0.910578  0.458566  1.004203  0.691300  0.734963  0.827273  0.674598  0.447348  0.890810  0.990548  0.546519  0.837409  0.758038  0.978703  0.780670  0.747529  0.354329  0.708965  0.614499  1.064206  1.003475  0.607457  0.624963  0.055751  0.671050  0.936313  0.831524  0.778916  0.334004  1.070223  0.693027  1.059537  0.359859  1.053493  0.564053  0.120355  0.593917  0.683160  0.572176  0.478773  0.457638  0.373401  1.056421  1.081205  1.037685  1.029249  0.349677  0.652776  0.732910  0.744155  0.782553  0.644078  0.280544  0.603421  0.786770  0.728315  0.395806  0.411452  1.001658  0.768681  0.805031  0.655182  0.887101  0.506307  0.629827  0.817472  0.835242  0.977274  0.708021  0.738274  0.572246  0.728076  0.756061  1.026170  0.950092  0.397721  0.745812  1.079258  0.870878  0.801789  0.017395  1.028514  0.918736  0.616330  0.757948  0.749640  1.042395  0.052856  0.560192  1.039002  0.491256  0.835796  1.028487  0.352495  0.802446  0.705840  1.037289  0.643266  0.601904  0.998539  0.638596  0.681530  0.618156  0.671744  0.772629  0.651389  0.426122  1.059481  0.941042  0.861776  1.064240  0.393104  0.796501  0.016802  0.902477  0.914333  1.048262  0.683393  0.614864  0.761400  0.667339  0.702285  0.125465  0.893191  0.713313  0.509625  0.937038  0.770301  0.548749  0.333976  0.513890  0.705964  0.397438  0.667994  0.386860  0.693977  0.594767  0.688553  0.602476  0.375511  0.837016  0.059684  1.081200  0.425925  0.038252  0.372372  0.584350  0.885524  1.046537  0.870563  0.941824  0.906041  0.475826  0.698743  0.013974  0.598593  0.651759  1.081728  0.022080  0.763777  0.738103  0.430525  0.149792  0.912346  0.978269  0.249384  0.086712  1.040964  1.048622  0.807769  0.620528  1.056311  1.054204  0.337718  0.759241  0.020847  0.975884  0.031867  0.815520  0.866946  0.067428  0.641239  0.702973  0.462303  0.837672  0.031639  1.030614  1.081089  0.936290  0.381100  0.908987  0.664559  0.932719
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%%% Ordered transformation matrices
%Root Node
% Global rotation operator
w1a = [0.994421 0.094730 -0.046401]';
q1a = [0.0, 0.0, 0.0]';
t1b = twist_matrix_fast(w1a,q1a,sp_coords(4));

% Global translation operator
t1a = twist_matrix_fast(sp_coords(1:3),0,0);

w1c = [-0.976050 0.108532 -0.188538]';
q1c = [0.007455 -0.193970 0.228362]';
t1c = twist_matrix_fast(w1c,q1c,Theta(1));

w1d = [0.215380 0.604058 -0.767284]';
q1d = [0.007455 -0.193970 0.228362]';
t1d = twist_matrix_fast(w1d,q1d,Theta(2));

w1e = [0.030613 -0.789515 -0.612967]';
q1e = [0.007455 -0.193970 0.228362]';
t1e = twist_matrix_fast(w1e,q1e,Theta(3));

w4a = [-0.015574 -0.783500 -0.621196]';
q4a = [0.037034 -0.111011 0.122987]';
t4a = twist_matrix_fast(w4a,q4a,Theta(4));

w4b = [-0.227425 0.607763 -0.760856]';
q4b = [0.037034 -0.111011 0.122987]';
t4b = twist_matrix_fast(w4b,q4b,Theta(5));

w4c = [-0.973671 -0.129426 0.187652]';
q4c = [0.037034 -0.111011 0.122987]';
t4c = twist_matrix_fast(w4c,q4c,Theta(6));

w5a = [0.296047 -0.701196 -0.648598]';
q5a = [-0.001341 -0.008460 -0.005397]';
t5a = twist_matrix_fast(w5a,q5a,Theta(7));

w5b = [-0.123760 0.645154 -0.753962]';
q5b = [-0.001341 -0.008460 -0.005397]';
t5b = twist_matrix_fast(w5b,q5b,Theta(8));

w5c = [-0.947122 -0.303479 -0.104216]';
q5c = [-0.001341 -0.008460 -0.005397]';
t5c = twist_matrix_fast(w5c,q5c,Theta(9));

w6a = [0.090287 -0.749331 -0.656012]';
q6a = [-0.016873 0.072509 -0.100021]';
t6a = twist_matrix_fast(w6a,q6a,Theta(10));

w6b = [0.273043 0.652087 -0.707269]';
q6b = [-0.016873 0.072509 -0.100021]';
t6b = twist_matrix_fast(w6b,q6b,Theta(11));

w6c = [-0.957756 0.115262 -0.263475]';
q6c = [-0.016873 0.072509 -0.100021]';
t6c = twist_matrix_fast(w6c,q6c,Theta(12));

w7a = [-0.124623 -0.705034 -0.698137]';
q7a = [-0.001673 0.108810 -0.139394]';
t7a = twist_matrix_fast(w7a,q7a,Theta(13));

w7b = [-0.914105 0.355210 -0.195545]';
q7b = [-0.001673 0.108810 -0.139394]';
t7b = twist_matrix_fast(w7b,q7b,Theta(14));

w7c = [-0.385851 -0.613802 0.688743]';
q7c = [-0.001673 0.108810 -0.139394]';
t7c = twist_matrix_fast(w7c,q7c,Theta(15));

%%% Construct kinematic chains of transformations
% Generate new_config and new_norms
U1 = t1a*t1b*t1c*t1d*t1e*I1;
V1 = t1a*t1b*t1c*t1d*t1e*N1;
V1 = V1-U1;

U4 = t1a*t1b*t1c*t1d*t1e*t4a*t4b*t4c*I4;
V4 = t1a*t1b*t1c*t1d*t1e*t4a*t4b*t4c*N4;
V4 = V4-U4;

U5 = t1a*t1b*t1c*t1d*t1e*t4a*t4b*t4c*t5a*t5b*t5c*I5;
V5 = t1a*t1b*t1c*t1d*t1e*t4a*t4b*t4c*t5a*t5b*t5c*N5;
V5 = V5-U5;

U7 = t1a*t1b*t1c*t1d*t1e*t4a*t4b*t4c*t5a*t5b*t5c*t6a*t6b*t6c*t7a*t7b*t7c*I7;
V7 = t1a*t1b*t1c*t1d*t1e*t4a*t4b*t4c*t5a*t5b*t5c*t6a*t6b*t6c*t7a*t7b*t7c*N7;
V7 = V7-U7;

%%% Construct complete update
new_config = [U1(1:3,:) U4(1:3,:) U5(1:3,:) U7(1:3,:)];
new_norms  = [V1(1:3,:) V4(1:3,:) V5(1:3,:) V7(1:3,:)];

% Update center of mass estimate
new_ctrm = mean(new_config,2);

%%% Twist matrix function
function [twist] = twist_matrix_fast(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.
%
% This code has very little error checking to increase speed.
%
% [twist] = twist_matrix_fast(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)
    
    % we want column vectors
    if size(w,1)<size(w,2)
        w = w';
    end
    
    % 1) pure translation
	% pure translation in absolute frame
	twist = [eye(3) w;zeros(1,3) 1];
else
    % 2) pure rotation twist
    % correct for case where w is the origin
    if sum(w) == 0
        w = q;
        W = 0;
    else
        W = 1;
    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
    Id3x3  = eye(3);
    w_hat2 = w*w'-W*Id3x3;
    R      = Id3x3+w_hat*sin(theta)+w_hat2*(1-cos(theta));
    
    % Generate relative frame twist, pg. 42
    twist  = [R (Id3x3-R)*w_hat*v+w*w'*v*theta;
              zeros(1,3) 1];
end
