lua实现cocos多边形碰撞检测

定义几个数据类型和函数

function vec(x, y)

    return {x, y}
end


v = vec -- shortcut


function dot(v1, v2)
    return v1[1]*v2[1] + v1[2]*v2[2]
end


function normalize(v)
    local mag = math.sqrt(v[1]^2 + v[2]^2)
    return vec(v[1]/mag, v[2]/mag)
end


function perp(v)
    return {v[2],-v[1]}
end


function segment(a, b)
    local obj = {a=a, b=b, dir={b[1] - a[1], b[2] - a[2]}}
    obj[1] = obj.dir[1]; obj[2] = obj.dir[2]
    return obj
end


function polygon(vertices)
    local obj = {}
    obj.vertices = vertices
    obj.edges = {}
    for i=1,#vertices do
        table.insert(obj.edges, segment(vertices[i], vertices[1+i%(#vertices)]))
    end
    return obj
end
vec为矢量或者向量，也可表示点；dot为矢量点投影运算；normalize为求模运算；perp计算法线向量；segment表示线段；polygon为多边形，包括顶点vertices和边edges，所有点的顺序必须按顺时针或者逆时针


算法的判断函数
-- We keep a running range (min and max) values of the projection, and then use that as our shadow


function project(a, axis)
    axis = normalize(axis)
    local min = dot(a.vertices[1],axis)
    local max = min
    for i,v in ipairs(a.vertices) do
        local proj =  dot(v, axis) -- projection
        if proj < min then min = proj end
        if proj > max then max = proj end
    end


    return {min, max}
end


function contains(n, range)
    local a, b = range[1], range[2]
    if b < a then a = b; b = range[1] end
    return n >= a and n <= b
end


function overlap(a_, b_)
    if contains(a_[1], b_) then return true
    elseif contains(a_[2], b_) then return true
    elseif contains(b_[1], a_) then return true
    elseif contains(b_[2], a_) then return true
    end
    return false
end

project为计算投影函数，先计算所有边长的投影，然后算出投影的最大和最小点即起始点；overlap函数判断两条线段是否重合





算法实现函数，使用到上面的数据和函数
function sat(a, b)
    for i,v in ipairs(a.edges) do
        local axis = perp(v)
        local a_, b_ = project(a, axis), project(b, axis)
        if not overlap(a_, b_) then return false end
    end
    for i,v in ipairs(b.edges) do
        local axis = perp(v)
        local a_, b_ = project(a, axis), project(b, axis)
        if not overlap(a_, b_) then return false end
    end


    return true
end
遍历a和b两个多边形的所有边长，判断投影是否重合



a = polygon{v(0,0),v(0,5),v(5,4),v(3,0)}
b = polygon{v(4,4),v(4,6),v(6,6),v(6,4)}


print(sat(a,b)) -- true