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+/* cocos2d for iPhone
+ * http://www.cocos2d-iphone.org
+ *
+ * Copyright (c) 2007 Scott Lembcke
+ *
+ * Copyright (c) 2010 Lam Pham
+ * 
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ * 
+ * The above copyright notice and this permission notice shall be included in
+ * all copies or substantial portions of the Software.
+ * 
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+/*
+ * Some of the functions were based on Chipmunk's cpVect.h.
+ */
+
+/**
+ @file
+ CGPoint extensions based on Chipmunk's cpVect file.
+ These extensions work both with CGPoint and cpVect.
+ 
+ The "ccp" prefix means: "CoCos2d Point"
+ 
+ Examples:
+  - ccpAdd( ccp(1,1), ccp(2,2) ); // preferred cocos2d way
+  - ccpAdd( CGPointMake(1,1), CGPointMake(2,2) ); // also ok but more verbose
+  
+  - cpvadd( cpv(1,1), cpv(2,2) ); // way of the chipmunk
+  - ccpAdd( cpv(1,1), cpv(2,2) ); // mixing chipmunk and cocos2d (avoid)
+  - cpvadd( CGPointMake(1,1), CGPointMake(2,2) ); // mixing chipmunk and CG (avoid)
+ */
+
+#import <Availability.h>
+
+#ifdef __IPHONE_OS_VERSION_MAX_ALLOWED
+#import <CoreGraphics/CGGeometry.h>
+#elif defined(__MAC_OS_X_VERSION_MAX_ALLOWED)
+#import <Foundation/Foundation.h>
+#endif
+
+#import <math.h>
+#import <objc/objc.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif  
+
+/** Helper macro that creates a CGPoint
+ @return CGPoint
+ @since v0.7.2
+ */
+#define ccp(__X__,__Y__) CGPointMake(__X__,__Y__)
+
+
+/** Returns opposite of point.
+ @return CGPoint
+ @since v0.7.2
+ */
+static inline CGPoint
+ccpNeg(const CGPoint v)
+{
+        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)
+{
+        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)
+{
+        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)
+{
+        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)
+{
+        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)
+{
+        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)
+{
+        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)
+{
+        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)
+{
+        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)
+{
+        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)
+{
+        return ccpDot(v, v);
+}
+
+/** Calculates distance between point an origin
+ @return CGFloat
+ @since v0.7.2
+ */
+CGFloat ccpLength(const CGPoint v);
+
+/** Calculates the distance between two points
+ @return CGFloat
+ @since v0.7.2
+ */
+CGFloat ccpDistance(const CGPoint v1, const CGPoint v2);
+
+/** 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);
+
+#ifdef __cplusplus
+}
+#endif