写一段matlab判断六面体是否为凸的代码

以下是一段 Matlab 代码，用于判断六面体是否为凸：

function isConvex = isHexahedronConvex(vertices)
% vertices: 8 x 3 matrix, each row represents a vertex of the hexahedron

% Check if all faces are convex
for i = 1:6
    faceVertices = vertices(hexahedronFaces(i,:), :);
    if ~isConvexPolygon(faceVertices)
        isConvex = false;
        return;
    end
end

% Check if all edges are not intersecting
for i = 1:12
    for j = i+1:12
        if isEdgeIntersecting(vertices(hexahedronEdges(i,:), :), vertices(hexahedronEdges(j,:), :))
            isConvex = false;
            return;
        end
    end
end

isConvex = true;
end

function isConvex = isConvexPolygon(vertices)
% vertices: n x 3 matrix, each row represents a vertex of the polygon

% Compute the normal vector of the polygon
normal = cross(vertices(2,:)-vertices(1,:), vertices(3,:)-vertices(1,:));
normal = normal / norm(normal);

% Check if all other vertices are on the same side of the plane
for i = 4:size(vertices, 1)
    if dot(normal, vertices(i,:)-vertices(1,:)) < 0
        isConvex = false;
        return;
    end
end

isConvex = true;
end

function isIntersecting = isEdgeIntersecting(edge1, edge2)
% edge1, edge2: 2 x 3 matrix, each row represents a vertex of the edge

% Compute the direction vectors of the edges
dir1 = edge1(2,:) - edge1(1,:);
dir2 = edge2(2,:) - edge2(1,:);

% Compute the normal vector of the plane containing both edges
normal = cross(dir1, dir2);
normal = normal / norm(normal);

% Check if the edges are parallel
if norm(normal) == 0
    isIntersecting = false;
    return;
end

% Compute the intersection point of the two lines containing the edges
t1 = dot(cross(dir2, edge1(1,:)-edge2(1,:)), normal) / dot(cross(dir1, dir2), normal);
t2 = dot(cross(dir1, edge1(1,:)-edge2(1,:)), normal) / dot(cross(dir1, dir2), normal);
if t1 >= 0 && t1 <= 1 && t2 >= 0 && t2 <= 1
    isIntersecting = true;
else
    isIntersecting = false;
end
end

% Define the faces and edges of a hexahedron
hexahedronFaces = [1 2 3 4; 5 6 7 8; 1 2 6 5; 2 3 7 6; 3 4 8 7; 4 1 5 8];
hexahedronEdges = [1 2; 2 3; 3 4; 4 1; 5 6; 6 7; 7 8; 8 5; 1 5; 2 6; 3 7; 4 8];

你可以将六面体的顶点坐标存储在一个 8 x 3 的矩阵中，每行代表一个顶点的坐标。调用 `isHexahedronConvex` 函数即可判断六面体是否为凸。如果返回值为 true，则六面体为凸；如果返回值为 false，则六面体不为凸。