碰撞算法8 --直线与圆的碰撞

--线与圆的碰撞
function LineToCircle(linePoint1,linePoint2,circlePos,radius)
    --这里需要分成两种情况，一种是线段两边的点是否在圆内
    --如果点到半径的距离
    if PointToCircle(linePoint1,circlePos,radius) then
        return true
    end

    if PointToCircle(linePoint2,circlePos,radius) then
        return true
    end

    --寻找圆心最近的点
    local lineVec = {x= (linePoint2.x - linePoint1.x) , y = (linePoint2.y - linePoint1.y)}
    local pointToLinePoint1 = {x= (circlePos.x - linePoint1.x) , y = (circlePos.y - linePoint1.y)}

    local lineLength = math.sqrt(lineVec.x * lineVec.x  + lineVec.y * lineVec.y)
    --点乘向量公式 相当于 lineLength * pointLinePoint1Length * cos角度
    local dot = lineVec.x  * pointToLinePoint1.x +  lineVec.y * pointToLinePoint1.y
    --这里就是pointLinePoint1Length * cos角度 及为lineVec 的投影长度，温馨提示pointLinePoint1ToLine可能为正负值 取决于向量的夹角的cos值
    --相当于到线段的投影比例
    local pointLinePoint1ToLine =  dot / lineLength
    local closestX = linePoint1.x + pointLinePoint1ToLine * (linePoint2.x - linePoint1.x)
    local closestY = linePoint1.y + pointLinePoint1ToLine * (linePoint2.y - linePoint1.y)

    local isInLine = PointToLine({ x = closestX,y =  closestY} , linePoint1, linePoint2)
    --如果点不在线上面（就是相当于他是在延长线 ） 直接returnfalse
    if not isInLine then
        return false;
    end
    --点跟圆的碰撞
    local result = PointToCircle({ x = closestX,y =  closestY},circlePos,radius)
    return result
end

--点与直线的碰撞
function PointToLine(point , linePoint1, linePoint2)
    --思想点与线两边线段的距离跟线的距离的判断，相等就是在同一直线
    local line1 = math.sqrt((linePoint1.x - point.x) * (linePoint1.x - point.x) + (linePoint1.y - point.y)* (linePoint1.y - point.y))
    local line2 = math.sqrt((linePoint2.x - point.x) * (linePoint2.x - point.x) + (linePoint2.y - point.y)* (linePoint2.y - point.y))
    local line = math.sqrt((linePoint2.x - linePoint1.x) * (linePoint2.x - linePoint1.x) + (linePoint2.y - linePoint1.y)* (linePoint2.y - linePoint1.y))
    return (line1 + line2) == line
end

--点跟圆是否碰撞
function PointToCircle (point,circlePos,radius)
    local sqr2  = (point.x - circlePos.x) * (point.x - circlePos.x) + (point.y - circlePos.y) * (point.y - circlePos.y)
    return radius * radius >= sqr2
end