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matlabplotoctave

Plot Bezier Curve in Octave

I'm trying to plot Bezier Curves in Octave. A Bezier curve is defined by a number of control points, for example:

image

I'm trying to plot something like this. I found out about a function: drawBezierCurve but the function needs four control points and I need to plot a a Bezier curve with just three points. The control points are: a(1,2), b(4,-1), c(8,6). Any ideas?

Solution

  • Take the lines ab and bc:

    a = [1 2];
b = [4 -1];
c = [8 6];

    ab and ac

    Create n equidistant points on them:

    npoints = 10;
line1 = linspace(a, b, npoints);
line2 = linspace(b, c, npoints);

    n points

    For the kth point on the Bézier curve, take k / n parts from first line and (n - k) / n parts from the second line.

    weights = linspace(1, 0, npoints);
curve = line1 .* weights + line2 .* (1 - weights);

    points on bezier curve

    Connect the obtained points to draw the curve:

    plot(curve(1, :), curve(2, :))

    bezier curve

    The complete code:

    a = [1 2];
b = [4 -1];
c = [8 6];

npoints = 10; % modify this
line1 = linspace(a, b, npoints);
line2 = linspace(b, c, npoints);
weights = linspace(1, 0, npoints);

curve = line1 .* weights + line2 .* (1 - weights);
plot(curve(1, :), curve(2, :))

    Additional code to draw the figures in this answer:

    fig = figure;
hold on

% figure 1
plot([a(1) b(1)], [a(2) b(2)])
plot([b(1) c(1)], [b(2) c(2)])

% figure 2
plot(line1(1, :), line1(2, :), 'ok')
plot(line2(1, :), line2(2, :), 'or')

% figure 3
plot([line1(1,:); line2(1, :)], [line1(2, :); line2(2, :)], 'm--')

plot(curve(1, :), curve(2, :), 'oc')

% figure 4
plot(curve(1, :), curve(2, :), 'b', 'linewidth', 2)