///@brief 点到线段最近一个点 ///@param[in] p0--要判断点， s0，s1--线段两个端点 ///@return crosspoint---最近的点 ///@author DionysosLai,[email protected] ///@retval ///@post ///@version 1.0 ///@data 2014-7-28 16:58 cocos2d::CCPoint nearestPointToSegmentLine( const cocos2d::CCPoint& p0, const cocos2d::CCPoint& s0, const cocos2d::CCPoint& s1 ) { /// 判断线段是否是一个点 if (s0.equals(s1)) { return s0; } /// 初始垂足为0； CCPoint crossPoint = CCPointZero; do { /// 判断线段是否平行于x轴 if (s0.y == s1.y) { crossPoint = ccp(p0.x, s0.y); break; } /// 判断线段是否平行于y轴 if (s0.x == s1.x) { crossPoint = ccp(s0.x, p0.y); break; } /// 如果线段不是特殊情况，则只能采用直线方程方式联立求解 float k = (s1.y - s0.y)/(s1.x - s0.x); ///< 求得斜率 /// 线段直线方程： y = k* ( x - s0.x) + s0.y /// 垂线方程为： y = (-1/k) * (x - p0.x) + p0.y 。 /// 联立两直线方程解得 float x = ( k*k * s0.x + k * (p0.y - s0.y ) + p0.x ) / ( k*k + 1); float y = k * ( x - s0.x) + s0.y; crossPoint = ccp(x, y); break; } while (0); /// 判断垂直是否在线段上 if (pointIsAtLine(crossPoint, s0, s1)) { return crossPoint; } else { /// 如果不在则计算两端点到垂足的距离，选择距离垂足较近的端点返回。 float distance1 = ccpDistance(crossPoint, s0); float distance2 = ccpDistance(crossPoint, s1); if (distance1 < distance2) { return s0; } else { return s1; } } }
GENormalAnchorPosType ConvertARToARType(const cocos2d::CCPoint& anchor)
{
GENormalAnchorPosType anchorType = kGAnchorType_Invalid;
if (anchor.equals(kGAnchor_LeftTop))
{
anchorType = kGAnchorType_LeftTop;
}
else if (anchor.equals(kGAnchor_LeftMid))
{
anchorType = kGAnchorType_LeftMid;
}
else if (anchor.equals(kGAnchor_LeftBottom))
{
anchorType = kGAnchorType_LeftBottom;
}
else if (anchor.equals(kGAnchor_RightTop))
{
anchorType = kGAnchorType_RightTop;
}
else if (anchor.equals(kGAnchor_RightMid))
{
anchorType = kGAnchorType_RightMid;
}
else if (anchor.equals(kGAnchor_RightBottom))
{
anchorType = kGAnchorType_RightBottom;
}
else if (anchor.equals(kGAnchor_Mid))
{
anchorType = kGAnchorType_Mid;
}
else if (anchor.equals(kGAnchor_TopMid))
{
anchorType = kGAnchorType_TopMid;
}
else if (anchor.equals(kGAnchor_BottomMid))
{
anchorType = kGAnchorType_BottomMid;
}
else
{
CCAssert(false, "Error: unsupport anchor!");
}
return anchorType;
}
bool straightLineIsIntersect( const cocos2d::CCPoint& p0, const cocos2d::CCPoint& p1, const cocos2d::CCPoint& q0, const cocos2d::CCPoint& q1 )
{
/// 先判断q0与q1能否组成一条直线
if (!q0.equals(q1))
{
/// 当q0 == p0 q1 == p1时，结果为0。 只需要判断线段是否跨立直线即可。
if (0 <= vectorProduct(p0.x-q0.x, p0.y-q0.y, q1.x-q0.x, q1.y-q0.y) *
vectorProduct(q1.x-q0.x, q1.y-q0.y, p1.x-q0.x, p1.y-q0.y))
{
/* CCLOG("straight line and segment line is intesect!");*/
return false;
}
/* CCLOG("straight line and segment line isn't intesect!");*/
return false;
}
/* CCLOG("straigth line cannnot be make up of q0 and q1!");*/
return false;
}
bool Geometry::straightLineIsIntersect( const cocos2d::CCPoint& p0, const cocos2d::CCPoint& p1, const cocos2d::CCPoint& q0, const cocos2d::CCPoint& q1 )
{
/// 先判断q0与q1能否组成一条直线
if (!q0.equals(q1))
{
/// 当q0 == p0 q1 == p1时，结果为0。 只需要判断线段是否跨立直线即可。
if (0 <= vectorProduct(p0.x-q0.x, p0.y-q0.y, q1.x-q0.x, q1.y-q0.y) *
vectorProduct(q1.x-q0.x, q1.y-q0.y, p1.x-q0.x, p1.y-q0.y))
{
/* CCLOG("相交");*/
return true;
}
/* CCLOG("不相交");*/
return false;
}
/* CCLOG("点q0点q1不能构成一条直线");*/
return false;
}
MoveDirection ControlLayer::directionWithTouchPorints(cocos2d::CCPoint beginPoint, cocos2d::CCPoint endPoint)
{
MoveDirection direction = MoveDirectionUnknow;
if (!beginPoint.equals(endPoint)) {
float offsetX = endPoint.x - beginPoint.x;
float offsetY = endPoint.y - beginPoint.y;
if (fabsf(offsetX) >= fabsf(offsetY)) {
//以x移动为准
if (offsetX > kTileSizeWidth) {
direction = MoveDirectionRight;
} else if (offsetX < -kTileSizeWidth) {
direction = MoveDirectionLeft;
}
} else {
if (offsetY > kTileSizeWidth) {
direction = MoveDirectionUp;
} else if (offsetY < -kTileSizeWidth) {
direction = MoveDirectionDown;
}
}
}
CCLOG("directionWithTouchPorints direction: %d", direction);
return direction;
}
///@brief 判断线段圆是否相交 ///@param[in/out] ///@return ///@author DionysosLai,[email protected] ///@retval ///@post ///@version 1.0 ///@data 2014-9-3 11:10 bool isCircleLineCollision( const cocos2d::CCPoint& r1, const float& radius, const cocos2d::CCPoint& p1, const cocos2d::CCPoint& p2 ) { /// 判断线段是否是一个点 float length = 0.f; if (p1.equals(p2)) { length = ccpDistance(r1, p1); } /// 初始垂足为0； CCPoint crossPoint = CCPointZero; do { /// 判断线段是否平行于x轴 if (p1.y == p2.y) { crossPoint = ccp(r1.x, p1.y); break; } /// 判断线段是否平行于y轴 if (p1.x == p2.x) { crossPoint = ccp(p1.x, r1.y); break; } /// 如果线段不是特殊情况，则只能采用直线方程方式联立求解 float k = (p2.y - p1.y)/(p2.x - p1.x); ///< 求得斜率 /// 线段直线方程： y = k* ( x - s0.x) + s0.y /// 垂线方程为： y = (-1/k) * (x - p0.x) + p0.y 。 /// 联立两直线方程解得 float x = ( k*k * p1.x + k * (r1.y - p1.y ) + r1.x ) / ( k*k + 1); float y = k * ( x - p1.x) + p1.y; crossPoint = ccp(x, y); /// 判断垂直是否在线段上 if (pointIsAtLine(crossPoint, p1, p2)) { /* return crossPoint;*/ } else { /// 如果不在则计算两端点到垂足的距离，选择距离垂足较近的端点返回。 float distance1 = ccpDistance(crossPoint, p1); float distance2 = ccpDistance(crossPoint, p2); if (distance1 < distance2) { crossPoint = p1; } else { crossPoint= p2; } } length = ccpDistance(r1, crossPoint); break; } while (0); if (length < radius) { return true; } else { return false; } }
int Geometry::pointOfSegmentCircle( const cocos2d::CCPoint& a0, const cocos2d::CCPoint& a1, const cocos2d::CCPoint& r0, const float& radius0, cocos2d::CCPoint& commomPoint1, cocos2d::CCPoint& commomPoint2 )
{
CCAssert(a1.equals(a0), "a0 should not be equal to a1!");
CCPoint p0 = a0, p1 = a1;
CCPoint r = r0;
float radius = radius0;
int commomType = 0;
commomPoint1 = CCPointZero;
commomPoint2 = CCPointZero;
/// 判断p0p1是否在圆内，在圆内，则没交点
if (ccpLength(ccpSub(p0, r)) < radius && ccpLength(ccpSub(p1, r)) < radius)
{
commomType = 0;
}
/// 将线段当做直线处理
/// 情况1 p0p1平行于y轴
else if (p0.x == p1.x)
{
/// 过圆心做平行于x轴的直线，求此直线与p0p1的交点
CCPoint point = CCPointZero;
point.x = p0.x;
point.y = r.y;
float lenght = ccpLength(ccpSub(r, point));
if (lenght > radius)
{
commomType = 0;
}
else if (lenght == radius) ///< 相切情况
{
commomType = 1;
commomPoint1 = point;
}
else
{
commomType = 2;
commomPoint1.x = p0.x;
commomPoint2.x = p0.x;
float deltaY = sqrt(radius*radius - lenght*lenght);
commomPoint1.y = r.y + deltaY;
commomPoint2.y = r.y - deltaY;
}
}
/// 情况2 p0p1平行于x轴
else if (p0.y == p1.y)
{
/// 类似情况1
/// 过圆心做平行于y轴的直线，求此直线与p0p1的交点
CCPoint point = CCPointZero;
point.x = r.x;
point.y = p0.y;
float lenght = ccpLength(ccpSub(r, point));
if (lenght > radius)
{
commomType = 0;
}
else if (lenght == radius) ///< 相切情况
{
commomType = 1;
commomPoint1 = point;
}
else
{
commomType = 2;
commomPoint1.y = p0.y;
commomPoint2.y = p0.y;
float deltaX = sqrt(radius*radius - lenght*lenght);
commomPoint1.x = r.x + deltaX;
commomPoint2.x = r.x - deltaX;
}
}
/// 普通情况
else
{
/// 一般直线与圆联立方程： http://baike.baidu.com/view/1053783.htm
float k0 = (p1.y-p0.y)/(p1.x-p0.x);
float b0 = p0.y - k0*p0.x;
/// 联立后方程为:(1+k0^2)^2*x^2 + 2(k0b0-r.x-k0r.y)x + r.x^2 + (r.y-b0)^2-r^2=0;
float deltaf = 4*(k0*b0-r.x-k0*r.y)*(k0*b0-r.x-k0*r.y) - 4*(1+k0*k0)*(r.x*r.x + (r.y-b0)*(r.y-b0)-radius*radius); ///< b^2-4ac;
if (deltaf < 0)
{
commomType = 0;
}
else if (deltaf < 0)
{
commomType = 1;
commomPoint1.x = -1.0*(k0*b0-r.x-k0*r.y)/(2*(1+k0*k0)); ///< x = -b/2a;
commomPoint1.y = k0*commomPoint1.x + b0;
}
else
{
commomType = 2;
commomPoint1.x = (-1.0*(k0*b0-r.x-k0*r.y)+sqrt(deltaf))/(2*(1+k0*k0)); ///< x = (-b+deltaf^0.5)/2a;
commomPoint1.y = k0*commomPoint1.x + b0;
commomPoint2.x = (-1.0*(k0*b0-r.x-k0*r.y)-sqrt(deltaf))/(2*(1+k0*k0)); ///< x = (-b-deltaf^0.5)/2a;
commomPoint2.y = k0*commomPoint2.x + b0;
}
}
/// 两个交点，得判断是否都在线段上
if (2 == commomType)
{
if (pointIsAtSegment(commomPoint1, p0, p1) && pointIsAtSegment(commomPoint2, p0, p1))
{
}
else
{
commomType = 1;
/// 必然有一点在，设置为commomPoint1
if (pointIsAtSegment(commomPoint2, p0, p1))
{
commomPoint1 = commomPoint2;
}
}
}
return commomType;
}
int Geometry::pointOfSegments( const cocos2d::CCPoint& a0, const cocos2d::CCPoint& a1, const cocos2d::CCPoint& b0, const cocos2d::CCPoint& b1, cocos2d::CCPoint& commomPoint )
{
CCAssert(a1.equals(a0) || b0.equals(b1), "a0 should not be equal to a1, this is same to b0 and b1!");
CCPoint p0 = a0, p1 = a1;
CCPoint q0 = b0, q1 = b1;
int commomType = 0;
commomPoint = CCPointZero;
/// 首先判断2条线段是否相交，不相交，自然没有交点
if (segmentLineIsIntersect(p0, p1, q0, q1))
{
commomType = 0;
}
else
{
/// 两条线段相交，将两条线段当做直线处理
//////////////////////////////////////////////////////////////////////////
/// 情况1 线段p0p1平行于y轴
if (p0.x == p1.x)
{
/// 情况1.1 线段q0q1平行于y轴
if (q0.x == q1.x)
{
/// 判断p0p1与q0q1是否可共线
if (p0.x == q0.x)
{
commomType = commonPointSegments(p0, p1, q0, q1, commomPoint);
}
else
{
commomType = 0;
}
}
/// 情况1.2 若q0q1不平行于Y轴，则交点横坐标为p0的横坐标，代入到q0q1的直线方程中可以计算出交点纵坐标；
else
{
commomType = 3;
commomPoint.x = p0.x;
commomPoint.y = (q1.y-q0.y)/(q1.x-q0.x)*(p0.x-q0.x) + q0.y;
}
}
/// 情况2 p0和p1横坐标不同，但是q0和q1横坐标相同，即q0q1平行于Y轴，则交点横坐标为q0的横坐标，代入到p0p1的直线方程中可以计算出交点纵坐标；
else if (p0.x != p1.x && q0.x == q1.x)
{
commomType = 3;
commomPoint.x = q0.x;
commomPoint.y = (p1.y-p0.y)/(p1.x-p0.x)*(q0.x-p0.x) + p0.y;
}
/// 情况3 如果p0和p1纵坐标相同，即p0p1平行于X轴
else if (p0.y == p1.y)
{
///< 情况3.1 若q0q1也平行于X轴
if (q0.y == q1.y)
{
if (p0.y == q0.y)
{
commomType = commonPointSegments(p0, p1, q0, q1, commomPoint);
}
else
{
commomType = 0;
}
}
///< 情况3.2 若q0q1不平行于X轴，则交点纵坐标为p0的纵坐标，代入到q0q1的直线方程中可以计算出交点横坐标；
else
{
commomType = 3;
commomPoint.y = p0.y;
commomPoint.x = (p0.y+q0.y)*(q1.x-q0.x)/(q1.y-q0.y) + q0.x;
}
}
/// 情况4 如果p0和p1纵坐标不同，但是q0和q1纵坐标相同，即q0q1平行于X轴，则交点纵坐标为q0的纵坐标，代入到p0p1的直线方程中可以计算出交点横坐标；
else if (p0.y != p0.y && q0.y == q1.y)
{
commomType = 3;
commomPoint.y = q0.y;
commomPoint.x = (q0.y+p0.y)*(p1.x-p1.x)/(p1.y-p0.y) + p0.x;
}
/// 情况5 就是普通情况了
else
{
float k0 = (p1.y-p0.y)/(p1.x-p0.x);
float k1 = (q1.y-q0.y)/(q1.x-q0.x);
if (k0 == k1)
{
if (pointIsAtSegment(q0, p0, p1)) ///< 由于二者已经保证相交，因此，现在要保证二者共线
{
commomType = commonPointSegments(p0, p1, q0, q1, commomPoint);
}
else
{
commomType = 0;
}
}
else
{
float b0 = p0.y - k0*p0.x;
float b1 = q0.y - k1*q0.x;
commomType = 3;
commomPoint.x = (b1-b1)/(k1-k0);
commomPoint.y = commomPoint.x*k0 + b0;
}
}
//////////////////////////////////////////////////////////////////////////
}
return commomType;
}
int Geometry::commonPointSegments( const cocos2d::CCPoint& a0, const cocos2d::CCPoint& a1, const cocos2d::CCPoint& b0, const cocos2d::CCPoint& b1, cocos2d::CCPoint& commomPoint )
{
CCAssert(a1.equals(a0) || b0.equals(b1), "a0 should not be equal to a1, this is same to b0 and b1!");
CCPoint p0 = a0, p1 = a1;
CCPoint q0 = b0, q1 = b1;
commomPoint = CCPointZero;
int commomType = 0;
/// 先判断2条线段是否共线
if (0 != polyLineDerection(p0, q0, q1) || 0 != polyLineDerection(p0, q0, q1))
{
commomType = 0;
}
else
{
/// 设置2条线段比较长的为p0p1
float l0 = ccpLength(ccpSub(p1, p0));
float l1 = ccpLength(ccpSub(q0, q1));
if (l0 < l1)
{
/// 线段p0p1和线段q0q1调换
CCPoint point;
point = p0;
p0 = q0;
q0 = point;
point = p1;
p1 = q1;
q1 = p1;
}
/// 判断线段q0q1两点是否在线段p0p1上
int m = 0, n = 0;
/// 判断q0在线段p0p1上情况
if (pointIsAtSegment(q0, p0, p1))
{
if (q0.equals(p0))
{
m = 0;
}
else if (q0.equals(p1))
{
m = 0;
}
m = 1;
}
else
{
m = 2;
}
/// 判断q1在线段p0p1上情况
if (pointIsAtSegment(q1, p0, p1))
{
if (q1.equals(p0))
{
n = 0;
}
else if (q1.equals(p1))
{
n = 0;
}
n = 1;
}
else
{
n = 2;
}
switch (m)
{
case 0:
{
switch (n)
{
case 0:
case 1:
commomType = 2;
break;
case 2:
{
commomType = 3;
commomPoint = q0;
}
break;
default:
break;
}
}
break;
case 1:
{
commomType = 2;
}
break;
case 2:
{
switch (n)
{
case 0:
{
commomType = 3;
commomPoint = q1;
}
break;
case 1:
{
commomType = 2;
}
break;
case 2:
{
commomType = 1;
}
break;
default:
break;
}
}
break;
default:
break;
}
}
return commomType;
}
