GJK程序matlab

GJK算法是一种用于计算两个凸多边形之间最小距离的算法，它的实现可以使用Matlab语言。以下是一个简单的Matlab实现：

function [distance, simplex] = gjk(A, B, max_iterations)
    % A和B分别是两个凸多边形的顶点集合
    % max_iterations是最大迭代次数
    % distance是两个凸多边形之间的最小距离
    % simplex是最后一个包含原点的单纯形
    
    % 初始化
    direction = [1; 0]; % 任意方向
    point_A = support(A, direction);
    point_B = support(B, -direction);
    simplex = [point_A, point_B];
    direction = -point_B;
    
    % 迭代
    for i = 1:max_iterations
        point_A = support(A, direction);
        if dot(point_A, direction) < 0
            distance = norm(simplex(:, end));
            return;
        end
        
        simplex = [simplex, point_A];
        [simplex, direction] = do_simplex(simplex);
    end
    
    distance = norm(simplex(:, end));
end

function point = support(A, direction)
    % 返回A中距离方向最远的点
    [~, index] = max(dot(A, direction));
    point = A(:, index);
end

function [simplex, direction] = do_simplex(simplex)
    % 根据simplex的大小进行不同的操作
    n = size(simplex, 2);
    if n == 2
        [simplex, direction] = do_simplex_2(simplex);
    elseif n == 3
        [simplex, direction] = do_simplex_3(simplex);
    else
        [simplex, direction] = do_simplex_4(simplex);
    end
end

function [simplex, direction] = do_simplex_2(simplex)
    % 二维情况下的操作
    AB = simplex(:, 2) - simplex(:, 1);
    AO = -simplex(:, 1);
    if dot(AB, AO) > 0
        direction = cross([AB; 0], [AO; 0]);
        simplex = [simplex, simplex(:, 1)];
    else
        simplex = simplex(:, 1);
        direction = -AO;
    end
end

function [simplex, direction] = do_simplex_3(simplex)
    % 三维情况下的操作
    AB = simplex(:, 2) - simplex(:, 1);
    AC = simplex(:, 3) - simplex(:, 1);
    AO = -simplex(:, 1);
    ABC = cross(AB, AC);
    if dot(cross(ABC, AC), AO) > 0
        if dot(AC, AO) > 0
            simplex = [simplex(:, 1), simplex(:, 3)];
            direction = cross(cross(AC, AO), AC);
        else
            simplex = simplex(:, 1);
            direction = -AO;
        end
    else
        if dot(cross(AB, ABC), AO) > 0
            simplex = [simplex(:, 1), simplex(:, 2)];
            direction = cross(cross(AB, AO), AB);
        else
            simplex = [simplex(:, 1), simplex(:, 2), simplex(:, 3)];
            direction = ABC;
        end
    end
end

function [simplex, direction] = do_simplex_4(simplex)
    % 四维情况下的操作
    AB = simplex(:, 2) - simplex(:, 1);
    AC = simplex(:, 3) - simplex(:, 1);
    AD = simplex(:, 4) - simplex(:, 1);
    AO = -simplex(:, 1);
    ABC = cross(AB, AC);
    ACD = cross(AC, AD);
    ADB = cross(AD, AB);
    if dot(ABC, AO) > 0
        simplex = [simplex(:, 1), simplex(:, 2), simplex(:, 3)];
        direction = do_simplex_3(simplex(:, 1:3));
    elseif dot(ACD, AO) > 0
        simplex = [simplex(:, 1), simplex(:, 3), simplex(:, 4)];
        direction = do_simplex_3(simplex(:, 1:3));
    elseif dot(ADB, AO) > 0
        simplex = [simplex(:, 1), simplex(:, 4), simplex(:, 2)];
        direction = do_simplex_3(simplex(:, 1:3));
    else
        distance = dot(AO, ABC) / norm(ABC);
        direction = ABC;
    end
end