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