GJK算法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。在Matlab中，可以使用以下代码实现GJK算法：

function [distance, simplex] = gjk(A, B)
    % 初始化
    d = [1; -1];
    v = A(:, 1) - B(:, 1);
    simplex = v;
    % 迭代
    while true
        % 计算最靠近原点的点
        [~, i] = max(d .* dot(simplex, repmat(-v, 1, size(simplex, 2))));
        % 计算下一个点
        v = A(:, i) - B * simplex(:, i);
        % 判断是否相交
        if dot(v, simplex(:, i)) <= 0
            distance = norm(simplex(:, i));
            break;
        end
        % 更新simplex
        simplex = [simplex, v];
        % 判断是否包含原点
        if contains_origin(simplex)
            distance = 0;
            break;
        end
    end
end

function contains = contains_origin(simplex)
    % 判断simplex是否包含原点
    switch size(simplex, 2)
        case 2
            contains = contains_origin_2d(simplex);
        case 3
            contains = contains_origin_3d(simplex);
        case 4
            contains = contains_origin_4d(simplex);
    end
end

function contains = contains_origin_2d(simplex)
    % 判断2D simplex是否包含原点
    a = simplex(:, 2) - simplex(:, 1);
    b = -simplex(:, 1);
    ao = -simplex(:, 1);
    if dot(a, ao) <= 0
        contains = false;
    else
        ab = a / norm(a);
        ap = b - dot(b, ab) * ab;
        contains = dot(ap, ao) <= 0;
    end
end

function contains = contains_origin_3d(simplex)
    % 判断3D simplex是否包含原点
    a = simplex(:, 3) - simplex(:, 1);
    b = simplex(:, 2) - simplex(:, 1);
    c = cross(a, b);
    d = -simplex(:, 1);
    if dot(c, d) <= 0
        contains = false;
    else
        ab = cross(c, b);
        ac = cross(a, c);
        if dot(ab, d) <= 0
            contains = false;
        elseif dot(ac, d) <= 0
            contains = false;
        else
            contains = true;
        end
    end
end

function contains = contains_origin_4d(simplex)
    % 判断4D simplex是否包含原点
    a = simplex(:, 4) - simplex(:, 1);
    b = simplex(:, 3) - simplex(:, 1);
    c = simplex(:, 2) - simplex(:, 1);
    d = cross(c, cross(a, b));
    e = -simplex(:, 1);
    if dot(d, e) <= 0
        contains = false;
    else
        abc = cross(a, b);
        acd = cross(a, d);
        adb = cross(d, b);
        if dot(abc, c) * dot(abc, e) <= 0
            contains = false;
        elseif dot(acd, a) * dot(acd, e) <= 0
            contains = false;
        elseif dot(adb, b) * dot(adb, e) <= 0
            contains = false;
        else
            contains = true;
        end
    end
end

其中，A和B分别表示两个凸多边形的顶点坐标，distance表示两个凸多边形之间的最小距离，simplex表示GJK算法中的simplex。