How I calculate the angles projected (plane xy, yz, xz) of a human segment in space?

Hello, I need calculate the angles projections of a segment in space by planes. For example the segment foot and shank, where the foot is defined by P1 and P2 and shank is defined by P2 and P3 in the space, I need obtain the angle between the segments, but I need too of your projections, anyone help me? Thanks for your attention. Best wishes.

    % Example:
P1(68,7910000000000  -79,5270000000000  18,0130000000000)
P2(40,3690000000000  57,5610000000000  -86,0590000000000)
P3(-94,3560000000000  109,322000000000  78,3600000000000)

If you see the image, I need the angle projection in xy, xz and yz plane. Do you understand my question?

Answer 1

[Jan]

No, I do not understand the question.

Do you want to project the two vectors into a specified plane an determine the angle between the projected vectors? This would equal the view through a 2D X-ray image.

Such "projection angles" can be calculated by the following code:

function Angle = ProjAngleV(L1, L2, LP)
% Angle between 2 vectors projected into plane
% Angle = ProjAngleV(L1, L2, LP)
% INPUT:
%   L1, L2, LP: Vectors of dimension [T x 3] or [1 x 3].
%               They need not be normalized.
% OUTPUT:
%   Angle: Angle between L1 and L2 projected into the plane orthogonal to LP.
%      In other words: the angle between L1 and L2 when looking along LP.
%      The sign of the angle is positive, if [L1, L2, LP] is a right handed
%      system, so the sign changes if L1 and L2 are interchanged.
%      Range of output: -180 < Angle <= 180:
%        L1 = L2  => Angle = 0
%        L1 ~= L2, L1 <-> L2 => Angle <-> -Angle
%      Discontinuity at antiparallel lines:
%        L1 = -L2 => Angle = 180
%        L1 = -L2 + [0,eps,0] => Angle = -180
% Author: Jan Simon, Heidelberg, (C) 2005-2013 [e-mail]
% License: Use, copy, modify as you like, don't blame me for troubles

% General algorithm:
%   A = L1 x LP;
%   B = L2 x LP;
%   Angle = ATAN2(Norm(A x B), Dot(A, B)) * sign(Dot(L1 x L2, LP))

% Project L1 and L2 into plane perpendicular to LP:
A = CrossTx3(L1, LP);
B = CrossTx3(L2, LP);

% Dot product between projected lines:
AdotB = A(:,1).*B(:,1) + A(:,2).*B(:,2) + A(:,3).*B(:,3);

AxB = [A(:, 2) .* B(:, 3) - A(:, 3) .* B(:, 2), ...
       A(:, 3) .* B(:, 1) - A(:, 1) .* B(:, 3), ...
       A(:, 1) .* B(:, 2) - A(:, 2) .* B(:, 1)];

Angle = atan2(NormTx3(AxB), AdotB);

% Sign(LX) is zero for LX==0, but this would destroy Inf values.
negS        = (DotTx3(AxB, LP) < 0);
Angle(negS) = -Angle(negS);

% Care for infinite values:
% Angle(isinf(AdotB)) = Inf;    % -Inf -> Inf
Angle(~isfinite(AdotB)) = Inf;  % NaN and -Inf -> Inf

% No valid angle for to0 short input vectors::
Small = 1.490116119384766e-008;   % SQRT(EPS)
Angle(sum(L1 .* L1, 2) < Small) = Inf;
Angle(sum(L2 .* L2, 2) < Small) = Inf;
Angle(sum(LP .* LP, 2) < Small) = Inf;

function R = CrossTx3(X, Y)
R = [ X(:,2) .* Y(:,3) - X(:,3) .* Y(:,2), ...
      X(:,3) .* Y(:,1) - X(:,1) .* Y(:,3), ...
      X(:,1) .* Y(:,2) - X(:,2) .* Y(:,1)];

function R = NormTx3(X)
R = sqrt(X(:, 1) .* X(:, 1) + X(:, 2) .* X(:, 2) + X(:, 3) .* X(:, 3));

function R = DotTx3(X, Y)
R = X(:, 1) .* Y(:, 1) + X(:, 2) .* Y(:, 2) + X(:, 3) .* Y(:, 3);

[Paulo Oliveira]

Hi, You understood my question, very well, but I have a question. What means 'LP' for you? For me is a "plan vector", is right?