axmol/cocos/math/Vector2.h

/**
 Copyright 2013 BlackBerry Inc.

 Licensed under the Apache License, Version 2.0 (the "License");
 you may not use this file except in compliance with the License.
 You may obtain a copy of the License at

 http://www.apache.org/licenses/LICENSE-2.0

 Unless required by applicable law or agreed to in writing, software
 distributed under the License is distributed on an "AS IS" BASIS,
 WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 See the License for the specific language governing permissions and
 limitations under the License.

 Original file from GamePlay3D: http://gameplay3d.org

 This file was modified to fit the cocos2d-x project
 */

#ifndef VECTOR2_H_
#define VECTOR2_H_

#include "CCMathBase.h"
#include "base/CCPlatformMacros.h"
#include "base/ccMacros.h"

NS_CC_MATH_BEGIN

/** Clamp a value between from and to.
 */

inline float clampf(float value, float min_inclusive, float max_inclusive)
{
    if (min_inclusive > max_inclusive) {
        CC_SWAP(min_inclusive, max_inclusive, float);
    }
    return value < min_inclusive ? min_inclusive : value < max_inclusive? value : max_inclusive;
}

class Matrix;

/**
 * Defines a 2-element floating point vector.
 */
class Vector2
{
public:

    /**
     * The x coordinate.
     */
    float x;

    /**
     * The y coordinate.
     */
    float y;

    /**
     * Constructs a new vector initialized to all zeros.
     */
    Vector2();

    /**
     * Constructs a new vector initialized to the specified values.
     *
     * @param xx The x coordinate.
     * @param yy The y coordinate.
     */
    Vector2(float xx, float yy);

    /**
     * Constructs a new vector from the values in the specified array.
     *
     * @param array An array containing the elements of the vector in the order x, y.
     */
    Vector2(const float* array);

    /**
     * Constructs a vector that describes the direction between the specified points.
     *
     * @param p1 The first point.
     * @param p2 The second point.
     */
    Vector2(const Vector2& p1, const Vector2& p2);

    /**
     * Constructs a new vector that is a copy of the specified vector.
     *
     * @param copy The vector to copy.
     */
    Vector2(const Vector2& copy);

    /**
     * Destructor.
     */
    ~Vector2();

    /**
     * Indicates whether this vector contains all zeros.
     *
     * @return true if this vector contains all zeros, false otherwise.
     */
    bool isZero() const;

    /**
     * Indicates whether this vector contains all ones.
     *
     * @return true if this vector contains all ones, false otherwise.
     */
    bool isOne() const;

    /**
     * Returns the angle (in radians) between the specified vectors.
     *
     * @param v1 The first vector.
     * @param v2 The second vector.
     * 
     * @return The angle between the two vectors (in radians).
     */
    static float angle(const Vector2& v1, const Vector2& v2);

    /**
     * Adds the elements of the specified vector to this one.
     *
     * @param v The vector to add.
     */
    void add(const Vector2& v);

    /**
     * Adds the specified vectors and stores the result in dst.
     *
     * @param v1 The first vector.
     * @param v2 The second vector.
     * @param dst A vector to store the result in.
     */
    static void add(const Vector2& v1, const Vector2& v2, Vector2* dst);

    /**
     * Clamps this vector within the specified range.
     *
     * @param min The minimum value.
     * @param max The maximum value.
     */
    void clamp(const Vector2& min, const Vector2& max);

    /**
     * Clamps the specified vector within the specified range and returns it in dst.
     *
     * @param v The vector to clamp.
     * @param min The minimum value.
     * @param max The maximum value.
     * @param dst A vector to store the result in.
     */
    static void clamp(const Vector2& v, const Vector2& min, const Vector2& max, Vector2* dst);

    /**
     * Returns the distance between this vector and v.
     *
     * @param v The other vector.
     * 
     * @return The distance between this vector and v.
     * 
     * @see distanceSquared
     */
    float distance(const Vector2& v) const;

    /**
     * Returns the squared distance between this vector and v.
     *
     * When it is not necessary to get the exact distance between
     * two vectors (for example, when simply comparing the
     * distance between different vectors), it is advised to use
     * this method instead of distance.
     *
     * @param v The other vector.
     * 
     * @return The squared distance between this vector and v.
     * 
     * @see distance
     */
    float distanceSquared(const Vector2& v) const;

    /**
     * Returns the dot product of this vector and the specified vector.
     *
     * @param v The vector to compute the dot product with.
     * 
     * @return The dot product.
     */
    float dot(const Vector2& v) const;

    /**
     * Returns the dot product between the specified vectors.
     *
     * @param v1 The first vector.
     * @param v2 The second vector.
     * 
     * @return The dot product between the vectors.
     */
    static float dot(const Vector2& v1, const Vector2& v2);

    /**
     * Computes the length of this vector.
     *
     * @return The length of the vector.
     * 
     * @see lengthSquared
     */
    float length() const;

    /**
     * Returns the squared length of this vector.
     *
     * When it is not necessary to get the exact length of a
     * vector (for example, when simply comparing the lengths of
     * different vectors), it is advised to use this method
     * instead of length.
     *
     * @return The squared length of the vector.
     * 
     * @see length
     */
    float lengthSquared() const;

    /**
     * Negates this vector.
     */
    void negate();

    /**
     * Normalizes this vector.
     *
     * This method normalizes this Vector2 so that it is of
     * unit length (in other words, the length of the vector
     * after calling this method will be 1.0f). If the vector
     * already has unit length or if the length of the vector
     * is zero, this method does nothing.
     * 
     * @return This vector, after the normalization occurs.
     */
    void normalize();

    /**
     * Normalizes this vector and stores the result in dst.
     *
     * If the vector already has unit length or if the length
     * of the vector is zero, this method simply copies the
     * current vector into dst.
     *
     * @param dst The destination vector.
     */
    Vector2 getNormalized() const;

    /**
     * Scales all elements of this vector by the specified value.
     *
     * @param scalar The scalar value.
     */
    void scale(float scalar);

    /**
     * Scales each element of this vector by the matching component of scale.
     *
     * @param scale The vector to scale by.
     */
    void scale(const Vector2& scale);

    /**
     * Rotates this vector by angle (specified in radians) around the given point.
     *
     * @param point The point to rotate around.
     * @param angle The angle to rotate by (in radians).
     */
    void rotate(const Vector2& point, float angle);

    /**
     * Sets the elements of this vector to the specified values.
     *
     * @param xx The new x coordinate.
     * @param yy The new y coordinate.
     */
    void set(float xx, float yy);

    /**
     * Sets the elements of this vector from the values in the specified array.
     *
     * @param array An array containing the elements of the vector in the order x, y.
     */
    void set(const float* array);

    /**
     * Sets the elements of this vector to those in the specified vector.
     *
     * @param v The vector to copy.
     */
    void set(const Vector2& v);

    /**
     * Sets this vector to the directional vector between the specified points.
     * 
     * @param p1 The first point.
     * @param p2 The second point.
     */
    void set(const Vector2& p1, const Vector2& p2);

    /**
     * Subtracts this vector and the specified vector as (this - v)
     * and stores the result in this vector.
     *
     * @param v The vector to subtract.
     */
    void subtract(const Vector2& v);

    /**
     * Subtracts the specified vectors and stores the result in dst.
     * The resulting vector is computed as (v1 - v2).
     *
     * @param v1 The first vector.
     * @param v2 The second vector.
     * @param dst The destination vector.
     */
    static void subtract(const Vector2& v1, const Vector2& v2, Vector2* dst);

    /**
     * Updates this vector towards the given target using a smoothing function.
     * The given response time determines the amount of smoothing (lag). A longer
     * response time yields a smoother result and more lag. To force this vector to
     * follow the target closely, provide a response time that is very small relative
     * to the given elapsed time.
     *
     * @param target target value.
     * @param elapsedTime elapsed time between calls.
     * @param responseTime response time (in the same units as elapsedTime).
     */
    void smooth(const Vector2& target, float elapsedTime, float responseTime);

    /**
     * Calculates the sum of this vector with the given vector.
     * 
     * Note: this does not modify this vector.
     * 
     * @param v The vector to add.
     * @return The vector sum.
     */
    inline const Vector2 operator+(const Vector2& v) const;

    /**
     * Adds the given vector to this vector.
     * 
     * @param v The vector to add.
     * @return This vector, after the addition occurs.
     */
    inline Vector2& operator+=(const Vector2& v);

    /**
     * Calculates the sum of this vector with the given vector.
     * 
     * Note: this does not modify this vector.
     * 
     * @param v The vector to add.
     * @return The vector sum.
     */
    inline const Vector2 operator-(const Vector2& v) const;

    /**
     * Subtracts the given vector from this vector.
     * 
     * @param v The vector to subtract.
     * @return This vector, after the subtraction occurs.
     */
    inline Vector2& operator-=(const Vector2& v);

    /**
     * Calculates the negation of this vector.
     * 
     * Note: this does not modify this vector.
     * 
     * @return The negation of this vector.
     */
    inline const Vector2 operator-() const;

    /**
     * Calculates the scalar product of this vector with the given value.
     * 
     * Note: this does not modify this vector.
     * 
     * @param s The value to scale by.
     * @return The scaled vector.
     */
    inline const Vector2 operator*(float s) const;

    /**
     * Scales this vector by the given value.
     * 
     * @param s The value to scale by.
     * @return This vector, after the scale occurs.
     */
    inline Vector2& operator*=(float s);
    
    /**
     * Returns the components of this vector divided by the given constant
     *
     * Note: this does not modify this vector.
     *
     * @param s the constant to divide this vector with
     * @return a smaller vector
     */
    inline const Vector2 operator/(float s) const;

    /**
     * Determines if this vector is less than the given vector.
     * 
     * @param v The vector to compare against.
     * 
     * @return True if this vector is less than the given vector, false otherwise.
     */
    inline bool operator<(const Vector2& v) const;

    /**
     * Determines if this vector is equal to the given vector.
     * 
     * @param v The vector to compare against.
     * 
     * @return True if this vector is equal to the given vector, false otherwise.
     */
    inline bool operator==(const Vector2& v) const;

    /**
     * Determines if this vector is not equal to the given vector.
     * 
     * @param v The vector to compare against.
     * 
     * @return True if this vector is not equal to the given vector, false otherwise.
     */
    inline bool operator!=(const Vector2& v) const;

    //code added compatible for Point
public:
      /**
     * @js NA
     * @lua NA
     */
    void setPoint(float xx, float yy);
    /**
     * @js NA
     */
    bool equals(const Vector2& target) const;
    
    /** @returns if points have fuzzy equality which means equal with some degree of variance.
     @since v2.1.4
     * @js NA
     * @lua NA
     */
    bool fuzzyEquals(const Vector2& target, float variance) const;

    /** Calculates distance between point an origin
     @return float
     @since v2.1.4
     * @js NA
     * @lua NA
     */
    inline float getLength() const {
        return sqrtf(x*x + y*y);
    };

    /** Calculates the square length of a Vector2 (not calling sqrt() )
     @return float
     @since v2.1.4
     * @js NA
     * @lua NA
     */
    inline float getLengthSq() const {
        return dot(*this); //x*x + y*y;
    };

    /** Calculates the square distance between two points (not calling sqrt() )
     @return float
     @since v2.1.4
     * @js NA
     * @lua NA
     */
    inline float getDistanceSq(const Vector2& other) const {
        return (*this - other).getLengthSq();
    };

    /** Calculates the distance between two points
     @return float
     @since v2.1.4
     * @js NA
     * @lua NA
     */
    inline float getDistance(const Vector2& other) const {
        return (*this - other).getLength();
    };

    /** @returns the angle in radians between this vector and the x axis
     @since v2.1.4
     * @js NA
     * @lua NA
     */
    inline float getAngle() const {
        return atan2f(y, x);
    };

    /** @returns the angle in radians between two vector directions
     @since v2.1.4
     * @js NA
     * @lua NA
     */
    float getAngle(const Vector2& other) const;

    /** Calculates cross product of two points.
     @return float
     @since v2.1.4
     * @js NA
     * @lua NA
     */
    inline float cross(const Vector2& other) const {
        return x*other.y - y*other.x;
    };

    /** Calculates perpendicular of v, rotated 90 degrees counter-clockwise -- cross(v, perp(v)) >= 0
     @return Vector2
     @since v2.1.4
     * @js NA
     * @lua NA
     */
    inline Vector2 getPerp() const {
        return Vector2(-y, x);
    };
    
    /** Calculates midpoint between two points.
     @return Vector2
     @since v3.0
     * @js NA
     * @lua NA
     */
    inline Vector2 getMidpoint(const Vector2& other) const
    {
        return Vector2((x + other.x) / 2.0f, (y + other.y) / 2.0f);
    }
    
    /** Clamp a point between from and to.
     @since v3.0
     * @js NA
     * @lua NA
     */
    inline Vector2 getClampPoint(const Vector2& min_inclusive, const Vector2& max_inclusive) const
    {
        return Vector2(clampf(x,min_inclusive.x,max_inclusive.x), clampf(y, min_inclusive.y, max_inclusive.y));
    }
    
    /** 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
     * p.compOp(floorf);
     @since v3.0
     * @js NA
     * @lua NA
     */
    inline Vector2 compOp(std::function<float(float)> function) const
    {
        return Vector2(function(x), function(y));
    }

    /** Calculates perpendicular of v, rotated 90 degrees clockwise -- cross(v, rperp(v)) <= 0
     @return Vector2
     @since v2.1.4
     * @js NA
     * @lua NA
     */
    inline Vector2 getRPerp() const {
        return Vector2(y, -x);
    };

    /** Calculates the projection of this over other.
     @return Vector2
     @since v2.1.4
     * @js NA
     * @lua NA
     */
    inline Vector2 project(const Vector2& other) const {
        return other * (dot(other)/other.dot(other));
    };

    /** Complex multiplication of two points ("rotates" two points).
     @return Vector2 vector with an angle of this.getAngle() + other.getAngle(),
     and a length of this.getLength() * other.getLength().
     @since v2.1.4
     * @js NA
     * @lua NA
     */
    inline Vector2 rotate(const Vector2& other) const {
        return Vector2(x*other.x - y*other.y, x*other.y + y*other.x);
    };

    /** Unrotates two points.
     @return Vector2 vector with an angle of this.getAngle() - other.getAngle(),
     and a length of this.getLength() * other.getLength().
     @since v2.1.4
     * @js NA
     * @lua NA
     */
    inline Vector2 unrotate(const Vector2& other) const {
        return Vector2(x*other.x + y*other.y, y*other.x - x*other.y);
    };

    /** Linear Interpolation between two points a and b
     @returns
        alpha == 0 ? a
        alpha == 1 ? b
        otherwise a value between a..b
     @since v2.1.4
     * @js NA
     * @lua NA
     */
    inline Vector2 lerp(const Vector2& other, float alpha) const {
        return *this * (1.f - alpha) + other * alpha;
    };

    /** Rotates a point counter clockwise by the angle around a pivot
     @param pivot is the pivot, naturally
     @param angle is the angle of rotation ccw in radians
     @returns the rotated point
     @since v2.1.4
     * @js NA
     * @lua NA
     */
    Vector2 rotateByAngle(const Vector2& pivot, float angle) const;

    /**
     * @js NA
     * @lua NA
     */
    static inline Vector2 forAngle(const float a)
    {
        return Vector2(cosf(a), sinf(a));
    }
    
    /** A general line-line intersection test
     @param A   the startpoint for the first line L1 = (A - B)
     @param B   the endpoint for the first line L1 = (A - B)
     @param C   the startpoint for the second line L2 = (C - D)
     @param D   the endpoint for the second line L2 = (C - D)
     @param S   the range for a hitpoint in L1 (p = A + S*(B - A))
     @param T   the range for a hitpoint in L2 (p = C + T*(D - C))
     @returns   whether these two lines interects.

     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        C + T * (D - C);
     the hit point also is   A + S * (B - A);
     @since 3.0
     * @js NA
     * @lua NA
     */
    static bool isLineIntersect(const Vector2& A, const Vector2& B,
                                 const Vector2& C, const Vector2& D,
                                 float *S = nullptr, float *T = nullptr);
    
    /**
     returns true if Line A-B overlap with segment C-D
     @since v3.0
     * @js NA
     * @lua NA
     */
    static bool isLineOverlap(const Vector2& A, const Vector2& B,
                                const Vector2& C, const Vector2& D);
    
    /**
     returns true if Line A-B parallel with segment C-D
     @since v3.0
     * @js NA
     * @lua NA
     */
    static bool isLineParallel(const Vector2& A, const Vector2& B,
                   const Vector2& C, const Vector2& D);
    
    /**
     returns true if Segment A-B overlap with segment C-D
     @since v3.0
     * @js NA
     * @lua NA
     */
    static bool isSegmentOverlap(const Vector2& A, const Vector2& B,
                                 const Vector2& C, const Vector2& D,
                                 Vector2* S = nullptr, Vector2* E = nullptr);
    
    /**
     returns true if Segment A-B intersects with segment C-D
     @since v3.0
     * @js NA
     * @lua NA
     */
    static bool isSegmentIntersect(const Vector2& A, const Vector2& B, const Vector2& C, const Vector2& D);
    
    /**
     returns the intersection point of line A-B, C-D
     @since v3.0
     * @js NA
     * @lua NA
     */
    static Vector2 getIntersectPoint(const Vector2& A, const Vector2& B, const Vector2& C, const Vector2& D);
    
    /** equals to Vector2(0,0) */
    static const Vector2 ZERO;
    /** equals to Vector2(1,1) */
    static const Vector2 ONE;
    /** equals to Vector2(1,0) */
    static const Vector2 UNIT_X;
    /** equals to Vector2(0,1) */
    static const Vector2 UNIT_Y;
    /** equals to Vector2(0.5, 0.5) */
    static const Vector2 ANCHOR_MIDDLE;
    /** equals to Vector2(0, 0) */
    static const Vector2 ANCHOR_BOTTOM_LEFT;
    /** equals to Vector2(0, 1) */
    static const Vector2 ANCHOR_TOP_LEFT;
    /** equals to Vector2(1, 0) */
    static const Vector2 ANCHOR_BOTTOM_RIGHT;
    /** equals to Vector2(1, 1) */
    static const Vector2 ANCHOR_TOP_RIGHT;
    /** equals to Vector2(1, 0.5) */
    static const Vector2 ANCHOR_MIDDLE_RIGHT;
    /** equals to Vector2(0, 0.5) */
    static const Vector2 ANCHOR_MIDDLE_LEFT;
    /** equals to Vector2(0.5, 1) */
    static const Vector2 ANCHOR_MIDDLE_TOP;
    /** equals to Vector2(0.5, 0) */
    static const Vector2 ANCHOR_MIDDLE_BOTTOM;
};

/**
 * Calculates the scalar product of the given vector with the given value.
 * 
 * @param x The value to scale by.
 * @param v The vector to scale.
 * @return The scaled vector.
 */
inline const Vector2 operator*(float x, const Vector2& v);

typedef Vector2 Point2;

NS_CC_MATH_END

#include "Vector2.inl"

#endif