Polarplot - plot arc between points instead of line

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Tomas Brezina
Tomas Brezina 2023-4-27
评论： Star Strider 2023-4-27
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.

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采纳的回答

Star Strider
Star Strider 2023-4-27
Ran in:
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.
.

更多回答（1 个）

chicken vector
chicken vector 2023-4-27
编辑：chicken vector 2023-4-27
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:

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