Dear author, - Githubissues

Dear Author, I am recently reading the code about openface, Would you please tell me where the dxdR in the function CalcRigidJacobian come from? dxdR = [ 0, R(1,3), -R(1,2); -R(1,3), 0, R(1,1); R(1,2), -R(1,1), 0];

Is dxdR the jacobi matrix R(1,:) with respect to theta{x},theta{y} and $\theta$_{z}? If so, I am really puzzled about this result.

Looking forward to your reply. Thanks very much.

###########################################33 function J = CalcRigidJacobian(M, V, p, p_global)

n = size(M, 1)/3;

% Get the current 3D shape (not affected by global transform, as this
% is how the Jacobian was derived (for derivation please see
% ../derivations/orthoJacobian
shape3D = GetShape3D(M, V, p);

% Get the rotation matrix corresponding to current global orientation
R = Euler2Rot(p_global(2:4));
s = p_global(1);

% Rigid Jacobian is laid out as follows
% dx_1/ds, dx_1/dr1, dx_1/dr2, dx_1/dr3, dx_1/dtx, dx_1/dty
% dx_2/ds, dx_2/dr1, dx_2/dr2, dx_2/dr3, dx_2/dtx, dx_2/dty
% ...
% dx_n/ds, dx_n/dr1, dx_n/dr2, dx_n/dr3, dx_n/dtx, dx_n/dty
% dy_1/ds, dy_1/dr1, dy_1/dr2, dy_1/dr3, dy_1/dtx, dy_1/dty
% ...
% dy_n/ds, dy_n/dr1, dy_n/dr2, dy_n/dr3, dy_n/dtx, dy_n/dty

J = zeros(n*2, 6);

% dx/ds = X * r11  + Y * r12 + Z * r13
% dx/dr1 =  s*(r13 * Y - r12 * Z)
% dx/dr2 = -s*(r13 * X - r11 * Z)
% dx/dr3 =  s*(r12 * X - r11 * Y)
% dx/dtx = 1
% dx/dty = 0

% dy/ds = X * r21  + Y * r22 + Z * r23
% dy/dr1 =  s * (r23 * Y - r22 * Z)
% dy/dr2 = -s * (r23 * X - r21 * Z)
% dy/dr3 =  s * (r22 * X - r21 * Y)
% dy/dtx = 0
% dy/dty = 1

% set the Jacobian for x's

% with respect to scaling factor
J(1:n,1) = shape3D * R(1,:)';

% with respect to angular rotation around x, y, and z axes

% Change of x with respect to change in axis angle rotation
dxdR = [      0,  R(1,3), -R(1,2);
                     -R(1,3),       0,  R(1,1);
                    R(1,2), -R(1,1),      0];

J(1:n,2:4) = s*(dxdR * shape3D')';

% with respect to translation
J(1:n,5) = 1;
J(1:n,6) = 0;

% set the Jacobian for y's

% with respect to scaling factor
J(n+1:end,1) = shape3D * R(2,:)';

 % with respect to angular rotation around x, y, and z axes

% Change of y with respect to change in axis angle rotation
dydR = [      0,  R(2,3), -R(2,2);
        -R(2,3),       0,  R(2,1);
         R(2,2), -R(2,1),      0];

 J(n+1:end,2:4) = s*(dydR * shape3D')';

 % with respect to translation
 J(n+1:end,5) = 0;
 J(n+1:end,6) = 1;

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function [Rot] = Euler2Rot(euler) rx = euler(1); ry = euler(2); rz = euler(3); Rx = [1 0 0; ... 0 cos(rx) -sin(rx); 0 sin(rx) cos(rx)]; Ry = [cos(ry) 0 sin(ry); 0 1 0; -sin(ry) 0 cos(ry)]; Rz = [cos(rz) -sin(rz) 0; sin(rz) cos(rz) 0; 0 0 1];

Rot = Rx * Ry * Rz;

TadasBaltrusaitis / OpenFace

Dear author, #597