这是一个用刀模拟裁布的过程，因为刀尖是受刀的控制点控制，为了达到尽量精确，只能把刀尖点转换为控制点，然后插补过去。

% 计算线段的角度
function theta = get_line_angle(point1, point2)    
    v_x = point2(1) - point1(1);
    v_y = point2(2) - point1(2); 
    L = sqrt(v_x^2 + v_y^2);
    
    %防止线段长度为零的情况
    if L < 1e-4
        theta = 0;
        return
    end
    theta = acos(v_x / L)*180/pi;
    if v_y < 0
        theta = 360 - theta;
    end

% 计算线段之间的夹角在-180-180度之间
function theta = get_inter_angle(v1_x, v1_y, v2_x, v2_y)
    
    new_x = (v1_x * v2_x + v1_y * v2_y);
    new_y = (v1_x * v2_y - v2_x * v1_y);

    theta = acos(new_x / sqrt(new_x^2 + new_y^2))*180/pi;
    if new_y < 0
        theta =  -theta ;
    end

%得到刀的控制点中心
function new_points = get_control_points(L, points)

new_points = [];
n = size(points,1);
v_inter_step = 0;
for i = 1:n  
    pre_i = max(1,i-1);
    next_i = min(n,i+1);
    point1 = points(pre_i,:);
    point2 = points(i,:);
    point3 = points(next_i,:);
    if norm(point3 - point1)<eps || v_inter_step == 1
        v_inter_step = v_inter_step + 1;
    else
        v_inter_step = 0;
    end
    if i == 1
        line_angle = get_line_angle(point2,point3); 
        inter_angle = 0;
    elseif i==n
        line_angle = new_points(end,3);
        inter_angle = 0;
    else
        v1_x = point2(1) - point1(1);
        v1_y = point2(2) - point1(2); 
        v2_x = point3(1) - point2(1);
        v2_y = point3(2) - point2(2);
        line_angle = new_points(end,3);
        if v_inter_step == 2       
            inter_angle = get_inter_angle(-v1_x,-v1_y,v2_x,v2_y);
        else         
            inter_angle = get_inter_angle(v1_x,v1_y,v2_x,v2_y);
        end        
    end   
    arc_angle = (line_angle +  inter_angle)*pi/180;
    knife_vect = L*[cos(arc_angle),sin(arc_angle)];
    max_inter_angle = 10;
    if abs(inter_angle)<20
         temp_points = [point2 - knife_vect,line_angle +  inter_angle,i];      
    elseif v_inter_step == 1
         temp_points = [point2 + knife_vect,line_angle - 180 + inter_angle,i] ;              
    else     
        m = floor(abs(inter_angle)/max_inter_angle)+1;
        temp_points = zeros(m,4);
        for j = 0:m
            new_angle = (line_angle + j*inter_angle/m)*pi/180;
            new_knife_vect = L*[cos(new_angle),sin(new_angle)];
            temp_points(j+1,:) = [point2 - new_knife_vect, line_angle + j*inter_angle/m,i];
        end        
    end
    new_points = [new_points;temp_points];     
end    

%main函数
%模拟刀的跟随裁剪
clc;clear all;
points = [0    0
490  0
500  20
510  0
1000 0
1000 1000
500  1000
500  995
500 1000
0    1000
0    500
5    500
0    500
0    0];
    
knife_e = 50;
new_points = get_control_points1(knife_e, points);
n = size(new_points,1);
for i = 1: n-1
    p1 = new_points(i,:);
    p2 = new_points(i+1,:);
    L = norm(p2 - p1);
    m = floor(L/10) + 1;
    for j = 0:m
        p = ((m - j)*p1 + j*p2 )/m;
        p_start = [p(1),p(2)];
        t = p(3)*pi/180;
        p_end = p_start + knife_e * [cos(t) sin(t)];
        plot(points(:,1),points(:,2),'-s')
        hold on
        axis equal;
        plot(new_points(:,1),new_points(:,2),'-*')
        plot([p_start(1),p_end(1)],[p_start(2),p_end(2)],'-*');
        text(p_start(1), p_start(2) ,'start')
        text(p_end(1), p_end(2) ,'end')
        hold off
        pause(0.1);
    end
    pause(0.3);
end    

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