Generate Small Circles

Generate a true small circle, a loxomdromic small circle, and the limiting case of a great circle.

Display the map axes with an orthographic projection.

figure;
axesm ortho; gridm on; framem on
setm(gca,'Origin', [45 30 30], 'MLineLimit', [75 -75],...
'MLineException',[0 90 180 270])

Define three center points on the sphere.

A = [45 90];
B = [0 60];
C = [0 30];

Create the three small circles around the three center points. The first, sca, is a true small circle. The second, scb, is a loxomdromic small circle. The third, scc, is a great circle as the limiting case of a small circle.

sca = scircle1(A(1), A(2), 20);
scb = scircle2(B(1), B(2), 0, 150);
scc = scircle1('rh',C(1), C(2), 20);

Display the points and their corresponding small circles with different colors. Label the small circles.

plotm(A(1), A(2),'ro','MarkerFaceColor','r')
plotm(B(1), B(2),'bo','MarkerFaceColor','b')
plotm(C(1), C(2),'mo','MarkerFaceColor','m')

plotm(sca(:,1), sca(:,2),'r')
plotm(scb(:,1), scb(:,2),'b--')
plotm(scc(:,1), scc(:,2),'m')

textm(50,0,'Normal Small Circle')
textm(46,6,'(20\circ from point A)')
textm(4.5,-10,'Loxodromic Small Circle')
textm(4,-6,'(20\circ from point C')
textm(-2,-4,'in rhumb line sense)')
textm(40,-60,'Great Circle as Small Circle')
textm(45,-50,'(90\circ from point B)')

See Also

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