如何在MATLAB中绘制某个多边形区域之外的点

Question

我一直在寻找一种方法来绘制多边形区域之外的点（在我的例子中是六边形）。这是我想要实现的场景，我有一个小六边形位于一个大六边形内。图片如下：

在图片中，我创建了一个小六边形（其区域以淡红色表示）并使用inpolygon 在其中生成一个随机点（在我的例子中为三个）。当我想在大六边形（以淡紫色表示）不接触小六边形区域中绘制点（红色三角形）时，就会出现问题。我在网上四处寻找这个简单的解决方案 3 天无济于事。

如果能得到任何帮助或指导，我将不胜感激。非常感谢！

我的代码如下：

clear
clc

bighexagon = 20;
smallhexagon = 4;

axis_min = 0;
axis_max = 40; 
axis([axis_min axis_max axis_min axis_max],'square');
hold on

L = linspace(30,390,7); 
bhex_x = bighexagon * (1+cosd(L))'; 
bhex_y = bighexagon*(1+sind(L))';

L2 = linspace(30,390,7); 
shex_x = smallhexagon * (1+cosd(L2))'; 
shex_y = smallhexagon * (1+sind(L2))';

plot(bhex_x,bhex_y,'LineWidth',3);

%---Move small hexagon into big hexagon
shex_vertices_x2(:,1) = shex_x + 16;
shex_vertices_y2(:,1) = shex_y + 16;
plot(shex_vertices_x2(:,1),shex_vertices_y2(:,1),'--k','LineWidth',3);


%---Plot points in small hexagon
no = 3;
point_x2 = (smallhexagon+20) - rand(1,9*no)*2*smallhexagon;
point_y2 = (smallhexagon+20) - rand(1,9*no)*2*smallhexagon;       

inside = inpolygon(point_x2,point_y2,shex_vertices_x2,shex_vertices_y2);

point_x2 = point_x2(inside);
point_y2 = point_y2(inside);

idx2 = randperm(length(point_x2));

point_x2 = point_x2(idx2(1:no));
point_y2 = point_y2(idx2(1:no));

plot(point_x2,point_y2,'ro','MarkerSize',1.5,'LineWidth',1, ...
'MarkerFaceColor','r');

%---Plot points in big hexagon
no2 = 4;
point_x = (bighexagon+20) - rand(1,9*no2)*2*bighexagon;
point_y = (bighexagon+20) - rand(1,9*no2)*2*bighexagon;

inside2 = inpolygon(point_x,point_y,bhex_x,bhex_y);

point_x = point_x(inside2);
point_y = point_y(inside2);

idx = randperm(length(point_x));

point_x = point_x(idx(1:no2));
point_y = point_y(idx(1:no2));

plot(point_x,point_y,'g^','MarkerSize',3,'LineWidth',3, ...
'MarkerFaceColor','g');

Answer 1

更新

感谢Hoki的建议，我终于可以解决了。

请注意，我在代码中更改了这部分：

validpoint = inpolygon(point_x,point_y,bhex_x,bhex_y) & ~inpolygon(point_x,point_y,shex_vertices_x2,shex_vertices_y2);

希望这能消除困惑，也能帮助其他用户。我要感谢Hoki 和xenoclast 的帮助。

代码如下：

clear
clc

bighexagon = 20;
smallhexagon = 4;

axis_min = 0;
axis_max = 40; 
axis([axis_min axis_max axis_min axis_max],'square');
hold on

L = linspace(30,390,7); 
bhex_x = bighexagon * (1+cosd(L))'; 
bhex_y = bighexagon*(1+sind(L))';

L2 = linspace(30,390,7); 
shex_x = smallhexagon * (1+cosd(L2))'; 
shex_y = smallhexagon * (1+sind(L2))';

plot(bhex_x,bhex_y,'LineWidth',3);

%---Move small hexagon into big hexagon
shex_vertices_x2(:,1) = shex_x + 16;
shex_vertices_y2(:,1) = shex_y + 16;
plot(shex_vertices_x2(:,1),shex_vertices_y2(:,1),'--k','LineWidth',3);


%---Plot points in small hexagon
no = 3;
point_x2 = (smallhexagon+20) - rand(1,9*no)*2*smallhexagon;
point_y2 = (smallhexagon+20) - rand(1,9*no)*2*smallhexagon;       

inside = inpolygon(point_x2,point_y2,shex_vertices_x2,shex_vertices_y2);

point_x2 = point_x2(inside);
point_y2 = point_y2(inside);

idx2 = randperm(length(point_x2));

point_x2 = point_x2(idx2(1:no));
point_y2 = point_y2(idx2(1:no));

plot(point_x2,point_y2,'ro','MarkerSize',1.5,'LineWidth',1, ...
'MarkerFaceColor','r');

%---Plot points in big hexagon
no2 = 30;
point_x = (bighexagon+20) - rand(1,9*no2)*2*bighexagon;
point_y = (bighexagon+20) - rand(1,9*no2)*2*bighexagon;

%---As per Hoki's suggestion, it ensure the points are outside the small hexagon

validpoint = inpolygon(point_x,point_y,bhex_x,bhex_y) & ...
    ~inpolygon(point_x,point_y,shex_vertices_x2,shex_vertices_y2);

point_x = point_x(validpoint);
point_y = point_y(validpoint);

idx = randperm(length(point_x));

point_x = point_x(idx(1:no2));
point_y = point_y(idx(1:no2));

plot(point_x,point_y,'g^','MarkerSize',3,'LineWidth',3, ...
'MarkerFaceColor','g');

Answer 2

如果您的内六边形由顶点定义，那么您可以使用inpolygon (link) 来测试给定点是否在其中。

Answer 3

请在inside2 = inpolygon(point_x,point_y,bhex_x,bhex_y);后添加以下两行检查

in1 = inpolygon(point_x,point_y,shex_vertices_x2,shex_vertices_y2);
inside2= logical(inside2-in1);