create and rotate a line up to a convex polygon vertex

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dediydi 2011-12-29

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https://ww2.mathworks.cn/matlabcentral/answers/24936-create-and-rotate-a-line-up-to-a-convex-polygon-vertex

采纳的回答： Sean de Wolski

在 MATLAB Online 中打开

Hello,

how can i create and rotate a line up to a convex polygon vertex ?

line is tangent to vertex and rotate the line by the smallest angle between the line and the segment following the vertex it passes through (in clockwise order.)

step1: create a convex polygon step2: find the leftmost point of the polygon step3:create a line that is tangent to the leftmost point of the polygon. step4:rotate the line by the smallest angle between the line and the segment following the vertex it passes through (in clockwise order.)

step 1,2 and 3 ok, but i have problems with step 4.

i have already tried

*angle = atan2(norm(cross(v1,v2)),dot(v1,v2));*

that method but when i find the direction of vector it equal to 0 0 0 .

please help me.

thanks

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dediydi 2011-12-29

not two edges. i use the angle to rotate (in clockwise) that vertical lines by the smaller angle. so it is enough to calculate the angle between the vertical line and the above edge. maybe a another picture necessary here :)

http://www.freeimagehosting.net/0f9f9

thanks for your interest.

dediydi 2011-12-29

this is not correct. i will use this algorithm to draw the convex hull of two convex polygon.

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采纳的回答

Sean de Wolski 2011-12-29

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/24936-create-and-rotate-a-line-up-to-a-convex-polygon-vertex#answer_32783

在 MATLAB Online 中打开

So to calculate you're angle, v1 will always be a unit vector vertical:

v1 = [0 1 0];

v2 needs to be turned into a unit vector:

v2 = [dx dy 0]; %dx,dy are the differences in the vertex we care about and the next one over
v2 = v2./norm(v2); %make unit vector

Then calculate the angle

ang = atan2(norm(cross(v1,v2)),dot(v1,v2))

To rotate it you can use hgtransform:

x = [0 1 1 0];
y = [0 0 1 1];
h = fill(x,y,'c');
t = hgtransform('Parent',gca);
set(h,'Parent',t);
rot = makehgtform('zrotate',ang);
set(t,'matrix',rot)

So something along the lines of:

P(1,:) = [1.5 2.0 0]; 
P(2,:) = [0.7 3.2 0]; 
P(3,:) = [0.5 4.5 0]; 
P(4,:) = [0.7 5.2 0]; 
P(5,:) = [1.7 5.3 0]; 
P(6,:) = [2.5 5.0 0]; 
P(7,:) = [3.0 4.5 0];
fill(P(:,1),P(:,2),'c');
v1 = [0 1 0];
v2 = P(4,:);
v2 = v2./norm(v2);
ang = atan2(norm(cross(v1,v2)),dot(v1,v2));
lineH = line([0 2],[0 10]);
pause(2) %demo
t = hgtransform('Parent',gca);
set(lineH,'Parent',t);
rot = makehgtform('zrotate',ang);
set(t,'matrix',rot)