Polarplot - plot arc between points instead of line

Hi,

I would like to plot line plot in polar plot, but to have arcs between points instead of straight lines. Like for example, if I have two points with same radius, the line between them shouldn't be straight, but an arc, with the radius same as the two points. If they dont have same radius, it should lineary interpolate separately radius and angle, instead of x and y coordinates.

Answer 1

[Star Strider]

Define the two points you want, crate an angle vector connecting them, and then interpolate to create the radius vector —

points_r = rand*[1;1];
points_a = rand(2,1)*2*pi;

a_vct = linspace(points_a(1), points_a(2));
r_vct = interp1(points_a, points_r, a_vct);

figure
polarplot(points_a, points_r, 'pm')
hold on
polarplot(a_vct, r_vct, '-b')
hold off
title('Points With Equal Radii')

points_r = rand(2,1);
points_a = rand(2,1)*2*pi;

[a_vct,r_vct] = interp_line(points_a,points_r);

figure
polarplot(points_a, points_r, 'pm')
hold on
polarplot(a_vct, r_vct, '-b')
hold off
title('Points With Different Radii')

function [a_vct,r_vct] = interp_line(points_a,points_r)
a_vct = linspace(points_a(1), points_a(2));
r_vct = interp1(points_a, points_r, a_vct);
end

It would be straightforward to write a function to do the interpolation, so in the second plot, I did just that.

.

[Tomas Brezina]

Thank you very much sir.

[Star Strider]

As always, my pleasure!

Answer 2

[chicken vector]

point1 = [3, 4];
point2 = [10, 0];
radius = 6;
dir = 'Up';
nPoints = 50;

[x, y, c] = getArc(point1, point2, radius, dir, nPoints);

figure;
grid on;
hold on;
scatter(point1(1), point1(2), 50, 'k', 'filled')
scatter(point2(1), point2(2), 50, 'k', 'filled')
plot(x, y, 'r', 'LineWidth', 2)
scatter(c(1), c(2), 50, 'x', 'r')
plot([c(1) point1(1)], [c(2) point1(2)], 'k', 'LineWidth', 1, 'LineStyle', ':')
plot([c(1) point2(1)], [c(2) point2(2)], 'k', 'LineWidth', 1, 'LineStyle', ':')

dir = 'Down';
[x, y, c] = getArc(point1, point2, radius, dir, nPoints);

plot(x, y, 'b', 'LineWidth', 2)
scatter(c(1), c(2), 50, 'x', 'b')
plot([c(1) point1(1)], [c(2) point1(2)], 'k', 'LineWidth', 1, 'LineStyle', ':')
plot([c(1) point2(1)], [c(2) point2(2)], 'k', 'LineWidth', 1, 'LineStyle', ':')
hold off;
axis equal;

xlim([0 12])
ylim([-3 7])

function [x, y, c] = getArc(point1, point2, radius, dir, nPoints)

midPoint = (point2 - point1) / 2;
a = sqrt(sum(midPoint.^2));
b = sqrt(radius^2 - a^2);

xC12 = point1(1) + midPoint(1) + [1 -1] * b * midPoint(2) / a;
yC12 = point1(2) + midPoint(2) + [-1 1] * b * midPoint(1) / a;
[yC, idx] = sort(yC12);
xC = xC12(idx);

if ~diff(yC)
    xC = sort(xC);
end

c = zeros(1,2);
switch lower(dir)
    case 'up'
        c(1) = xC(2);
        c(2) = yC(2);
        th1 = atan2(point1(2) - c(2), point1(1) - c(1));
        th2 = atan2(point2(2) - c(2), point2(1) - c(1));
    case 'down'
        c(1) = xC(1);
        c(2) = yC(1);
        th1 = atan2(point2(2) - c(2), point2(1) - c(1));
        th2 = atan2(point1(2) - c(2), point1(1) - c(1));
    otherwise
        error("Use ''Up'' or ''Down'' for centre direction.")
end

th = linspace(th1, th2, nPoints);
x = radius * cos(th) + c(1);
y = radius * sin(th) + c(2);

end

Result: