Cocos2d宏的数学解释
/** Returns opposite of point.
@return CGPoint@since v0.7.2
*/
static inline CGPoint
ccpNeg(const CGPoint v) //计算关于原点的对称点
{
return ccp(-v.x, -v.y);
}
/** Calculates sum of two points.
@return CGPoint
@since v0.7.2
*/
static inline CGPoint
ccpAdd(const CGPoint v1, const CGPoint v2)//计算两个向量的和
{
return ccp(v1.x + v2.x, v1.y + v2.y);
}
/** Calculates difference of two points.
@return CGPoint
@since v0.7.2
*/
static inline CGPoint
ccpSub(const CGPoint v1, const CGPoint v2)// 计算两个向量的差
{
return ccp(v1.x - v2.x, v1.y - v2.y);
}
/** Returns point multiplied by given factor.
@return CGPoint
@since v0.7.2
*/
static inline CGPoint
ccpMult(const CGPoint v, const CGFloat s)// 给定一个因子，算向量的倍数
{
return ccp(v.x*s, v.y*s);
}
/** Calculates midpoint between two points.
@return CGPoint
@since v0.7.2
*/
static inline CGPoint
ccpMidpoint(const CGPoint v1, const CGPoint v2)// 计算两个点得中心点
{
return ccpMult(ccpAdd(v1, v2), 0.5f);
}
/** Calculates dot product of two points.
@return CGFloat
@since v0.7.2
*/
static inline CGFloat
ccpDot(const CGPoint v1, const CGPoint v2)// 计算两个向量的点乘积
{
return v1.x*v2.x + v1.y*v2.y;
}
/** Calculates cross product of two points.
@return CGFloat
@since v0.7.2
*/
static inline CGFloat
ccpCross(const CGPoint v1, const CGPoint v2)// 计算两个向量的叉乘积
{
return v1.x*v2.y - v1.y*v2.x;
}
/** Calculates perpendicular of v, rotated 90 degrees counter-clockwise -- cross(v, perp(v)) >= 0
@return CGPoint
@since v0.7.2
*/
static inline CGPoint
ccpPerp(const CGPoint v)// 向量逆时针旋转后的点坐标
{
return ccp(-v.y, v.x);
}
/** Calculates perpendicular of v, rotated 90 degrees clockwise -- cross(v, rperp(v)) <= 0
@return CGPoint
@since v0.7.2
*/
static inline CGPoint
ccpRPerp(const CGPoint v)// 向量顺时针旋转后的点坐标
{
return ccp(v.y, -v.x);
}
/** Calculates the projection of v1 over v2.
@return CGPoint
@since v0.7.2
*/
static inline CGPoint
ccpProject(const CGPoint v1, const CGPoint v2)// 计算向量V1在向量V2上的投影点
{
return ccpMult(v2, ccpDot(v1, v2)/ccpDot(v2, v2));
}
/** Rotates two points.
@return CGPoint
@since v0.7.2
*/
static inline CGPoint
ccpRotate(const CGPoint v1, const CGPoint v2)
{
return ccp(v1.x*v2.x - v1.y*v2.y, v1.x*v2.y + v1.y*v2.x);
}
/** Unrotates two points.
@return CGPoint
@since v0.7.2
*/
static inline CGPoint
ccpUnrotate(const CGPoint v1, const CGPoint v2)
{
return ccp(v1.x*v2.x + v1.y*v2.y, v1.y*v2.x - v1.x*v2.y);
}
/** Calculates the square length of a CGPoint (not calling sqrt() )
@return CGFloat
@since v0.7.2
*/
static inline CGFloat
ccpLengthSQ(const CGPoint v)// 计算一个向量长度的平方值
{
return ccpDot(v, v);
}
/** Calculates distance between point an origin
@return CGFloat
@since v0.7.2
*/
CGFloat ccpLength(const CGPoint v);// 计算点和原点的距离，但不知道函数体在哪里
/** Calculates the distance between two points
@return CGFloat
@since v0.7.2
*/
CGFloat ccpDistance(const CGPoint v1, const CGPoint v2);// 两点间距离
/** Returns point multiplied to a length of 1.
@return CGPoint
@since v0.7.2
*/
CGPoint ccpNormalize(const CGPoint v);
/** Converts radians to a normalized vector.
@return CGPoint
@since v0.7.2
*/
CGPoint ccpForAngle(const CGFloat a);
/** Converts a vector to radians.
@return CGFloat
@since v0.7.2
*/
CGFloat ccpToAngle(const CGPoint v);
/** Clamp a value between from and to.
@since v0.99.1
*/
float clampf(float value, float min_inclusive, float max_inclusive);
/** Clamp a point between from and to.
@since v0.99.1
*/
CGPoint ccpClamp(CGPoint p, CGPoint from, CGPoint to);
/** Quickly convert CGSize to a CGPoint
@since v0.99.1
*/
CGPoint ccpFromSize(CGSize s);
/** Run a math operation function on each point component
* absf, fllorf, ceilf, roundf
* any function that has the signature: float func(float);
* For example: let's try to take the floor of x,y
* ccpCompOp(p,floorf);
@since v0.99.1
*/
CGPoint ccpCompOp(CGPoint p, float (*opFunc)(float));
/** Linear Interpolation between two points a and b
@returns
alpha == 0 ? a
alpha == 1 ? b
otherwise a value between a..b
@since v0.99.1
*/
CGPoint ccpLerp(CGPoint a, CGPoint b, float alpha);
/** @returns if points have fuzzy equality which means equal with some degree of variance.
@since v0.99.1
*/
BOOL ccpFuzzyEqual(CGPoint a, CGPoint b, float variance);
/** Multiplies a nd b components, a.x*b.x, a.y*b.y
@returns a component-wise multiplication
@since v0.99.1
*/
CGPoint ccpCompMult(CGPoint a, CGPoint b);
/** @returns the signed angle in radians between two vector directions
@since v0.99.1
*/
float ccpAngleSigned(CGPoint a, CGPoint b);
/** @returns the angle in radians between two vector directions
@since v0.99.1
*/
float ccpAngle(CGPoint a, CGPoint b);
/** Rotates a point counter clockwise by the angle around a pivot
@param v is the point to rotate
@param pivot is the pivot, naturally
@param angle is the angle of rotation cw in radians
@returns the rotated point
@since v0.99.1
*/
CGPoint ccpRotateByAngle(CGPoint v, CGPoint pivot, float angle);
/** A general line-line intersection test
@param p1
is the startpoint for the first line P1 = (p1 - p2)
@param p2
is the endpoint for the first line P1 = (p1 - p2)
@param p3
is the startpoint for the second line P2 = (p3 - p4)
@param p4
is the endpoint for the second line P2 = (p3 - p4)
@param s
is the range for a hitpoint in P1 (pa = p1 + s*(p2 - p1))
@param t
is the range for a hitpoint in P3 (pa = p2 + t*(p4 - p3))
@return bool
indicating successful intersection of a line
note that to truly test intersection for segments we have to make
sure that s & t lie within [0..1] and for rays, make sure s & t > 0
the hit point is p3 + t * (p4 - p3);
the hit point also is p1 + s * (p2 - p1);
@since v0.99.1
*/
BOOL ccpLineIntersect(CGPoint p1, CGPoint p2,
CGPoint p3, CGPoint p4,
float *s, float *t);
/*
ccpSegmentIntersect returns YES if Segment A-B intersects with segment C-D
@since v1.0.0
*/
BOOL ccpSegmentIntersect(CGPoint A, CGPoint B, CGPoint C, CGPoint D);
/*
ccpIntersectPoint returns the intersection point of line A-B, C-D
@since v1.0.0
*/
CGPoint ccpIntersectPoint(CGPoint A, CGPoint B, CGPoint C, CGPoint D);