Auswertung Experiment

Database tüddelei
DBHanlder läuft gut für DIESE Datanbank struktur...
App begonnen aber weit entfernt von gutem Stand

Libs/mat2tikz/test/examples/example_quivers.m

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+%% Quiver calculations
+% These are calculations for the quiver dimensions as implemented in MATLAB
+% (HG1) as in the |quiver.m| function.
+%
+% For HG2 and Octave, the situation might be different.
+%
+% A single quiver is defined as:
+%
+%                   C
+%                    \
+%                     \
+%  A ----------------- B 
+%                     /
+%                    /
+%                   D
+%
+% To know the dimensions of the arrow head, MATLAB defines the quantities
+%  alpha = beta = 0.33 that determine the coordinates of C and D as given below.
+
+clc; 
+clear variables;
+close all;
+
+%% Parameters
+try
+    syms x y z u v w alpha beta epsilon real
+catch
+    warning('Symbolic toolbox not found. Interpret the values with care!');
+    x = randn(); y = randn(); z = randn();
+    u = randn(); v = randn(); w = randn();
+end
+alpha = 0.33;
+beta = alpha;
+epsilon = 0;
+is2D = true;
+
+%% Coordinates as defined in MATLAB
+% Note that in 3D, the arrow head is oriented in a weird way. Let' just ignore
+% that and only focus on 2D and use the same in 3D. Due to the lack
+% of [u,v,w]-symmetry in those equations, the angle is bound to depend on the
+% length of |delta|, i.e. something we don't know beforehand.
+A = [x y z].';
+delta = [u v w].';
+B = A + delta;
+C = B - alpha*[u+beta*(v+epsilon);
+               v-beta*(u+epsilon)
+               w];
+D = B - alpha*[u-beta*(v+epsilon);
+               v+beta*(u+epsilon)
+               w];
+
+if is2D
+    A = A(1:2);
+    B = B(1:2);
+    C = C(1:2);
+    D = D(1:2);
+    delta = delta(1:2);
+end
+
+%% Calculating the angle of the arrowhead
+% Calculate the cos(angle) using the inner product
+unitVector = @(v) v/norm(v);
+cosAngleBetween = @(a,b,c) unitVector(a-b).' * unitVector(c-b);
+
+cosTwiceTheta = cosAngleBetween(C,B,D);
+if isa(cosTwiceTheta, 'sym')
+    cosTwiceTheta = simplify(cosTwiceTheta);
+end
+
+theta = acos(cosTwiceTheta) / 2
+
+radToDeg = @(rads) (rads * 180 / pi);
+
+thetaVal = radToDeg(theta)
+try
+    thetaVal = double(thetaVal)
+end
+
+% For the MATLAB parameters alpha=beta=0.33, we get theta = 18.263 degrees.
+