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msm/ShoulderModel/TOOLBOX_Kinematics/KINEMATICS_TOOL_v_of_u.m
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KINEMATICS_TOOL_v_of_u.m
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function Vval = KINEMATICS_TOOL_v_of_u(RSDATA, u)
% Function for computing the v's associated to the u for the ruled surface
%--------------------------------------------------------------------------
% Syntax
% Vval = KINEMATICS_TOOL_v_of_u(RSDATA, u)
%--------------------------------------------------------------------------
%
% EPFL - LA - LBO SHOULDER MODEL
% Created by : David Ingram (LA - EPFL)
%
% File Description :
% This function computes the two values of v for a given value of u for the
% ruled surface resulting from the sphere-ellipsoid intersection.
%--------------------------------------------------------------------------
% Initialise the output
Vval.vp = 0;
Vval.vn = 0;
%--------------------------------------------------------------------------
% The Quadric is a Hyperbolic-Cylinder
%--------------------------------------------------------------------------
if isequal(RSDATA.Type, 'Hyperbolic-Cylinder')
% Get the normalised quadric data
a = RSDATA.NPa;
b = RSDATA.NPb;
x0 = RSDATA.Centre(1);
y0 = RSDATA.Centre(2);
S = RSDATA.S;
pu = [];
% Use the correct 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
qu = [0; 0; 1; 0];
% Construct the polynomial coefficients
p0 = pu'*S*pu;
p1 = 2*pu'*S*qu;
p2 = qu'*S*qu;
% Compute the values of v
Vval.vp = -p1/(2*p2) + sqrt(abs(p1^2 - 4*p0*p2))/(2*p2);
Vval.vn = -p1/(2*p2) - sqrt(abs(p1^2 - 4*p0*p2))/(2*p2);
% Allways set the smaller value of v as vp
if Vval.vp < Vval.vn;
vn = Vval.vp;
vp = Vval.vn;
Vval.vp = vp;
Vval.vn = vn;
end
%--------------------------------------------------------------------------
% The Quadric is a Hyperbolic Paraboloid
%--------------------------------------------------------------------------
elseif isequal(RSDATA.Type, 'Hyperbolic Paraboloid')
% Get the normalised quadric data
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);
S = RSDATA.S;
% Build the parameterisation
pu = [a*u/c+x0; b*u/c+y0; z0; 1];
qu = [-ss*a/c; ss*b/c; 4*u; 0];
% Construct the polynomial coefficients
p0 = pu'*S*pu;
p1 = 2*pu'*S*qu;
p2 = qu'*S*qu;
% Compute the values of v
Vval.vp = -p1/(2*p2) + sqrt(abs(p1^2 - 4*p0*p2))/(2*p2);
Vval.vn = -p1/(2*p2) - sqrt(abs(p1^2 - 4*p0*p2))/(2*p2);
% Allways set the smaller value of v as vp
if Vval.vp < Vval.vn;
vn = Vval.vp;
vp = Vval.vn;
Vval.vp = vp;
Vval.vn = vn;
end
else
end
return;
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