Matlab 怎麼填充曲線相交的區域呢？

01-08

比如這個問題里的陰影部分（http://www.zhihu.com/question/20626673）
我只會畫成下面的樣子

代碼如下：
x=0:0.01:1; hold on plot(x, sqrt(2.*x-x.^2)) plot(x, 1-sqrt(2.*x-x.^2))
x=0:0.01:0.5; plot(x, (1+sqrt(1-4.*x.^2))/2 ) plot(x, (1-sqrt(1-4.*x.^2))/2 ) line([0 0], [0 1]) line([0 1], [0 0]) line([1 1], [0 1]) line([1 0], [1 1])
axis([-0.2,1.2,-0.2,1.2]) axis equal;

@吳運生

t = [-50:50 -50]/100*pi; [x1,y1] = poly2cw(cos(t)/2, sin(t)/2 + .5); t = [50:100 200 50]/100*pi; [x2,y2] = poly2cw(cos(t).*(t~=2*pi) + 1, sin(t)); [x3,y3] = poly2cw(x2, -y2 + 1); [Ex, Ey] = polybool("intersection", x1, y1, x2, y2); [Ex, Ey] = polybool("intersection", Ex, Ey, x3, y3);

plot(x1, y1, "r", x2, y2, "g", x3, y3, "b", "linewidth", 2) patch(Ex, Ey, "y", "linewidth", 3), axis image off

瀉藥，這種填充指定區域的作圖一般我會選用「patch」或「fill」函數來實現：

%% hold on grid on axis equal


f1 = @(x) -sqrt(0.25-x.^2) + 0.5;

f2 = @(x) 1 - f1(x);

f3 = @(x) 1 - sqrt(2*x-x.^2);

f4 = @(x) 1 - f3(x);
x1 = linspace(0, 0.5, 500);

plot(x1, f1(x1), "-.", "LineWidth", 1.2)

plot(x1, f2(x1), "LineWidth", 1.2)
x2 = linspace(0, 1, 500);

plot(x2, f3(x2), "LineWidth", 1.5)

plot(x2, f4(x2), "LineWidth", 1.5)
xlabel("$x$", "interpreter", "latex", "FontSize", 13)

ylabel("$y$", "interpreter", "latex", "FontSize", 13)

title("Illustration to show the usage of function patch", ...

      "FontName", "Arial", "FontSize", 14)

labels = {"$f_1(x)$", "$f_2(x)$", "$f_3(x)$", "$f_4(x)$"};

legend(labels, "interpreter", "latex", "FontSize", 12)

x_range = x2((f4(x2)&>f3(x2)) (x2&<=0.5)); % 確定待填充區域的x範圍 [y1, y2, y3, y4] = deal(f1(x_range), f2(x_range), f3(x_range), f4(x_range)); y_upper = min(y2, y4); % 填充區域的上邊界 y_lower = max(y1, y3); % 填充區域的下邊界 patch([x_range, fliplr(x_range)], [y_lower, fliplr(y_upper)], "r") alpha(0.65)

如果不要坐標軸的話，稍微改改也行：

x1=0:0.01:1;

hold on

y11=sqrt(2.*x1-x1.^2);

y12=1-sqrt(2.*x1-x1.^2);

plot(x1,y11)

plot(x1,y12)

x2=0:0.01:0.5;

y21=(1+sqrt(1-4.*x2.^2))/2;

y22=(1-sqrt(1-4.*x2.^2))/2;

plot(x2,y21)

plot(x2,y22)

x3=[0.13403 x1(15:41) x2(41:end) x2(end:-1:41) x1(41:-1:15) 0.13403];

y3=[0.5 y11(15:41) y21(41:end) y22(end:-1:41) y12(41:-1:15) 0.5];

fill(x3,y3,[1 1 0])

line([0 0], [0 1])

line([0 1], [0 0])

line([1 1], [0 1])

line([1 0], [1 1])

axis([-0.2,1.2,-0.2,1.2])

axis equal;

FILL(X,Y,C) fills the 2-D polygon defined by vectors X and Y

with the color specified by C. The vertices of the polygon

are specified by pairs of components of X and Y. If necessary,

the polygon is closed by connecting the last vertex to the first.

If C is a single character string chosen from the list "r","g","b",

"c","m","y","w","k", or an RGB row vector triple, [r g b], the

polygon is filled with the constant specified color.

fill()函數，可以填充由X,Y向量相交形成的區域。

作水平線y=0.5，可以得到與弧線相交的兩個點A,B.

你可以先求出A,B的坐標，然後把上弧AB和下弧AB的點，分別放在向量X,Y裡面

然後fill(X,Y,"y")