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msm/ShoulderModel_rTSA/TOOLBOX_Kinematics/KINEMATICS_TOOL_build_TS.m
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KINEMATICS_TOOL_build_TS.m
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function TS = KINEMATICS_TOOL_build_TS(AI, M4, REDATA, BLDATA)
% Function for obtaining the location of the point TS
%--------------------------------------------------------------------------
% Syntax
% TS = KINEMATICS_TOOL_build_TS(AI, M4, REDATA, BLDATA)
%--------------------------------------------------------------------------
%
% EPFL - LA - LBO SHOULDER MODEL
% Created by : David Ingram (LA - EPFL)
%
% File Description :
% This function computes the location of the point TS on the scapula's
% medial border given the location of the point AI and the value of the
% fourth minimal coordinate.
%--------------------------------------------------------------------------
% Initialise the output
TS = [];
%--------------------------------------------------------------------------
% Build Sphere Quadric around AI
%--------------------------------------------------------------------------
AIx = AI(1) - REDATA.Centre(1);
AIy = AI(2) - REDATA.Centre(2);
AIz = AI(3) - REDATA.Centre(3);
% Sphere Radii
R = norm(BLDATA.Initial_Points.TS - BLDATA.Initial_Points.AI);
% Quadric Matrix
T = [1, 0, 0, -AIx;
0, 1, 0, -AIy;
0, 0, 1, -AIz;
-AIx, -AIy, -AIz, AIx^2+AIy^2+AIz^2-R^2];
%--------------------------------------------------------------------------
% Build Ellipsoid Quadric
%--------------------------------------------------------------------------
% Get the Ellipsoid Axes
Ax = REDATA.TSaxes(1,1); Ay = REDATA.TSaxes(2,1); Az = REDATA.TSaxes(3,1);
% Quadric Matrix
S = [1/Ax^2, 0, 0, 0;
0, 1/Ay^2, 0, 0;
0, 0, 1/Az^2, 0;
0, 0, 0, -1];
%--------------------------------------------------------------------------
% Identify the type of intersection quadric
%--------------------------------------------------------------------------
IQuad = KINEMATICS_TOOL_intersection_identification(S, T);
% Construct the ruled surface
RSDATA = KINEMATICS_TOOL_ruled_surface_parameters(IQuad);
% Get the lower and upper bounds on the ruled surface u parameter
[Ubounds, RSDATA] = KINEMATICS_TOOL_parameter_bounds(RSDATA);
% Compute the Value of u
u = 0;
if M4 < 0.5
u = Ubounds.Umin + 2*M4*(Ubounds.Umax - Ubounds.Umin);
elseif M4 >= 0.5
u = Ubounds.Umax - 2*(M4 - 0.5)*(Ubounds.Umax - Ubounds.Umin);
end
% Compute the value of v
Vval = KINEMATICS_TOOL_v_of_u(RSDATA, u);
v = 0;
if M4 < 0.5
v = Vval.vp;
elseif M4 >= 0.5
v = Vval.vn;
end
% Build the Position of the Point
if isequal(RSDATA.Type, 'Hyperbolic-Cylinder')
% Get the Normalised Quadric Parameters
a = RSDATA.NPa;
b = RSDATA.NPb;
x0 = RSDATA.Centre(1);
y0 = RSDATA.Centre(2);
pu = [];
qu = [0; 0; 1; 0];
% Compute parameters depending on the type of parameterisation
if RSDATA.ParamType == 1
pu = [a*cosh(u)+x0; b*sinh(u)+y0; 0; 1];
elseif RSDATA.ParamType == 1
pu = [-a*cosh(u)+x0; b*sinh(u)+y0; 0; 1];
elseif RSDATA.ParamType == 3
pu = [a*sinh(u)+x0; b*cosh(u)+y0; 0; 1];
elseif RSDATA.ParamType == 4
pu = [a*sinh(u)+x0; -b*cosh(u)+y0; 0; 1];
end
% Compute the position of the point
TS = pu + v*qu;
% Make the Index Switch
TS = TS(RSDATA.IdS,1);
elseif isequal(RSDATA.Type, 'Hyperbolic Paraboloid')
% Get the Normalised Quadric Parameters
a = RSDATA.NPa;
b = RSDATA.NPb;
c = RSDATA.NPc;
ss = sign(RSDATA.Coef(3));
x0 = RSDATA.Centre(1);
y0 = RSDATA.Centre(2);
z0 = RSDATA.Centre(3);
% Build the parameterisation
pu = [a*u/c+x0; b*u/c+y0; z0; 1];
qu = [-ss*a/c; ss*b/c; 4*u; 0];
TS = pu + v*qu;
% Make the Index Switch
TS = TS(RSDATA.IdS,1);
end
% Take only the first three values
TS = TS(1:3,1);
return;
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