Cocos2d宏的数学解释

                                                Cocos2d宏的数学解释

    以下文字转载自：http://blog.csdn.net/cocoa_geforce/article/details/6913292，对原作者表示敬意。

   

/** 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);