Vector2.hpp

#pragma once

#define _USE_MATH_DEFINES
#include <math.h>

namespace Unity
{
    struct Vector2
    {
        union
        {
            struct
            {
                float X;
                float Y;
            };
            float data[2];
        };
    
    
        /**
         * Constructors.
         */
        inline Vector2();
        inline Vector2(float data[]);
        inline Vector2(float value);
        inline Vector2(float x, float y);
    
    
        /**
         * Constants for common vectors.
         */
        static inline Vector2 Zero();
        static inline Vector2 One();
        static inline Vector2 Right();
        static inline Vector2 Left();
        static inline Vector2 Up();
        static inline Vector2 Down();
    
    
        /**
         * Returns the angle between two vectors in radians.
         * @param a: The first vector.
         * @param b: The second vector.
         * @return: A scalar value.
         */
        static inline float Angle(Vector2 a, Vector2 b);
    
        /**
         * Returns a vector with its magnitude clamped to maxLength.
         * @param vector: The target vector.
         * @param maxLength: The maximum length of the return vector.
         * @return: A new vector.
         */
        static inline Vector2 ClampMagnitude(Vector2 vector, float maxLength);
    
        /**
         * Returns the component of a in the direction of b (scalar projection).
         * @param a: The target vector.
         * @param b: The vector being compared against.
         * @return: A scalar value.
         */
        static inline float Component(Vector2 a, Vector2 b);
    
        /**
         * Returns the distance between a and b.
         * @param a: The first point.
         * @param b: The second point.
         * @return: A scalar value.
         */
        static inline float Distance(Vector2 a, Vector2 b);
    
        /**
         * Returns the dot product of two vectors.
         * @param lhs: The left side of the multiplication.
         * @param rhs: The right side of the multiplication.
         * @return: A scalar value.
         */
        static inline float Dot(Vector2 lhs, Vector2 rhs);
    
        /**
         * Converts a polar representation of a vector into cartesian
         * coordinates.
         * @param rad: The magnitude of the vector.
         * @param theta: The angle from the X axis.
         * @return: A new vector.
         */
        static inline Vector2 FromPolar(float rad, float theta);
    
        /**
         * Returns a vector linearly interpolated between a and b, moving along
         * a straight line. The vector is clamped to never go beyond the end points.
         * @param a: The starting point.
         * @param b: The ending point.
         * @param t: The interpolation value [0-1].
         * @return: A new vector.
         */
        static inline Vector2 Lerp(Vector2 a, Vector2 b, float t);
    
        /**
         * Returns a vector linearly interpolated between a and b, moving along
         * a straight line.
         * @param a: The starting point.
         * @param b: The ending point.
         * @param t: The interpolation value [0-1] (no actual bounds).
         * @return: A new vector.
         */
        static inline Vector2 LerpUnclamped(Vector2 a, Vector2 b, float t);
    
        /**
         * Returns the magnitude of a vector.
         * @param v: The vector in question.
         * @return: A scalar value.
         */
        static inline float Magnitude(Vector2 v);
    
        /**
         * Returns a vector made from the largest components of two other vectors.
         * @param a: The first vector.
         * @param b: The second vector.
         * @return: A new vector.
         */
        static inline Vector2 Max(Vector2 a, Vector2 b);
    
        /**
         * Returns a vector made from the smallest components of two other vectors.
         * @param a: The first vector.
         * @param b: The second vector.
         * @return: A new vector.
         */
        static inline Vector2 Min(Vector2 a, Vector2 b);
    
        /**
         * Returns a vector "maxDistanceDelta" units closer to the target. This
         * interpolation is in a straight line, and will not overshoot.
         * @param current: The current position.
         * @param target: The destination position.
         * @param maxDistanceDelta: The maximum distance to move.
         * @return: A new vector.
         */
        static inline Vector2 MoveTowards(Vector2 current, Vector2 target,
                                   float maxDistanceDelta);
    
        /**
         * Returns a new vector with magnitude of one.
         * @param v: The vector in question.
         * @return: A new vector.
         */
        static inline Vector2 Normalized(Vector2 v);
    
        /**
         * Creates a new coordinate system out of the two vectors.
         * Normalizes "normal" and normalizes "tangent" and makes it orthogonal to
         * "normal"..
         * @param normal: A reference to the first axis vector.
         * @param tangent: A reference to the second axis vector.
         */
        static inline void OrthoNormalize(Vector2 &normal, Vector2 &tangent);
    
        /**
         * Returns the vector projection of a onto b.
         * @param a: The target vector.
         * @param b: The vector being projected onto.
         * @return: A new vector.
         */
        static inline Vector2 Project(Vector2 a, Vector2 b);
    
        /**
         * Returns a vector reflected about the provided line.
         * This behaves as if there is a plane with the line as its normal, and the
         * vector comes in and bounces off this plane.
         * @param vector: The vector traveling inward at the imaginary plane.
         * @param line: The line about which to reflect.
         * @return: A new vector pointing outward from the imaginary plane.
         */
        static inline Vector2 Reflect(Vector2 vector, Vector2 line);
    
        /**
         * Returns the vector rejection of a on b.
         * @param a: The target vector.
         * @param b: The vector being projected onto.
         * @return: A new vector.
         */
        static inline Vector2 Reject(Vector2 a, Vector2 b);
    
        /**
         * Rotates vector "current" towards vector "target" by "maxRadiansDelta".
         * This treats the vectors as directions and will linearly interpolate
         * between their magnitudes by "maxMagnitudeDelta". This function does not
         * overshoot. If a negative delta is supplied, it will rotate away from
         * "target" until it is pointing the opposite direction, but will not
         * overshoot that either.
         * @param current: The starting direction.
         * @param target: The destination direction.
         * @param maxRadiansDelta: The maximum number of radians to rotate.
         * @param maxMagnitudeDelta: The maximum delta for magnitude interpolation.
         * @return: A new vector.
         */
        static inline Vector2 RotateTowards(Vector2 current, Vector2 target,
                                     float maxRadiansDelta,
                                     float maxMagnitudeDelta);
    
        /**
         * Multiplies two vectors component-wise.
         * @param a: The lhs of the multiplication.
         * @param b: The rhs of the multiplication.
         * @return: A new vector.
         */
        static inline Vector2 Scale(Vector2 a, Vector2 b);
    
        /**
         * Returns a vector rotated towards b from a by the percent t.
         * Since interpolation is done spherically, the vector moves at a constant
         * angular velocity. This rotation is clamped to 0 <= t <= 1.
         * @param a: The starting direction.
         * @param b: The ending direction.
         * @param t: The interpolation value [0-1].
         */
        static inline Vector2 Slerp(Vector2 a, Vector2 b, float t);
    
        /**
         * Returns a vector rotated towards b from a by the percent t.
         * Since interpolation is done spherically, the vector moves at a constant
         * angular velocity. This rotation is unclamped.
         * @param a: The starting direction.
         * @param b: The ending direction.
         * @param t: The interpolation value [0-1].
         */
        static inline Vector2 SlerpUnclamped(Vector2 a, Vector2 b, float t);
    
        /**
         * Returns the squared magnitude of a vector.
         * This is useful when comparing relative lengths, where the exact length
         * is not important, and much time can be saved by not calculating the
         * square root.
         * @param v: The vector in question.
         * @return: A scalar value.
         */
        static inline float SqrMagnitude(Vector2 v);
    
        /**
         * Calculates the polar coordinate space representation of a vector.
         * @param vector: The vector to convert.
         * @param rad: The magnitude of the vector.
         * @param theta: The angle from the X axis.
         */
        static inline void ToPolar(Vector2 vector, float &rad, float &theta);
    
    
        /**
         * Operator overloading.
         */
        inline struct Vector2& operator+=(const float rhs);
        inline struct Vector2& operator-=(const float rhs);
        inline struct Vector2& operator*=(const float rhs);
        inline struct Vector2& operator/=(const float rhs);
        inline struct Vector2& operator+=(const Vector2 rhs);
        inline struct Vector2& operator-=(const Vector2 rhs);
    };
    
    inline Vector2 operator-(Vector2 rhs);
    inline Vector2 operator+(Vector2 lhs, const float rhs);
    inline Vector2 operator-(Vector2 lhs, const float rhs);
    inline Vector2 operator*(Vector2 lhs, const float rhs);
    inline Vector2 operator/(Vector2 lhs, const float rhs);
    inline Vector2 operator+(const float lhs, Vector2 rhs);
    inline Vector2 operator-(const float lhs, Vector2 rhs);
    inline Vector2 operator*(const float lhs, Vector2 rhs);
    inline Vector2 operator/(const float lhs, Vector2 rhs);
    inline Vector2 operator+(Vector2 lhs, const Vector2 rhs);
    inline Vector2 operator-(Vector2 lhs, const Vector2 rhs);
    inline bool operator==(const Vector2 lhs, const Vector2 rhs);
    inline bool operator!=(const Vector2 lhs, const Vector2 rhs);
    
    
    
    /*******************************************************************************
     * Implementation
     */
    
    Vector2::Vector2() : X(0), Y(0) {}
    Vector2::Vector2(float data[]) : X(data[0]), Y(data[1]) {}
    Vector2::Vector2(float value) : X(value), Y(value) {}
    Vector2::Vector2(float x, float y) : X(x), Y(y) {}
    
    
    Vector2 Vector2::Zero() { return Vector2(0, 0); }
    Vector2 Vector2::One() { return Vector2(1, 1); }
    Vector2 Vector2::Right() { return Vector2(1, 0); }
    Vector2 Vector2::Left() { return Vector2(-1, 0); }
    Vector2 Vector2::Up() { return Vector2(0, 1); }
    Vector2 Vector2::Down() { return Vector2(0, -1); }
    
    
    float Vector2::Angle(Vector2 a, Vector2 b)
    {
        float v = Dot(a, b) / (Magnitude(a) * Magnitude(b));
        v = fmax(v, -1.0);
        v = fmin(v, 1.0);
        return acos(v);
    }
    
    Vector2 Vector2::ClampMagnitude(Vector2 vector, float maxLength)
    {
        float length = Magnitude(vector);
        if (length > maxLength)
            vector *= maxLength / length;
        return vector;
    }
    
    float Vector2::Component(Vector2 a, Vector2 b)
    {
        return Dot(a, b) / Magnitude(b);
    }
    
    float Vector2::Distance(Vector2 a, Vector2 b)
    {
        return Vector2::Magnitude(a - b);
    }
    
    float Vector2::Dot(Vector2 lhs, Vector2 rhs)
    {
        return lhs.X * rhs.X + lhs.Y * rhs.Y;
    }
    
    Vector2 Vector2::FromPolar(float rad, float theta)
    {
        Vector2 v;
        v.X = rad * cos(theta);
        v.Y = rad * sin(theta);
        return v;
    }
    
    Vector2 Vector2::Lerp(Vector2 a, Vector2 b, float t)
    {
        if (t < 0) return a;
        else if (t > 1) return b;
        return LerpUnclamped(a, b, t);
    }
    
    Vector2 Vector2::LerpUnclamped(Vector2 a, Vector2 b, float t)
    {
        return (b - a) * t + a;
    }
    
    float Vector2::Magnitude(Vector2 v)
    {
        return sqrt(SqrMagnitude(v));
    }
    
    Vector2 Vector2::Max(Vector2 a, Vector2 b)
    {
        float x = a.X > b.X ? a.X : b.X;
        float y = a.Y > b.Y ? a.Y : b.Y;
        return Vector2(x, y);
    }
    
    Vector2 Vector2::Min(Vector2 a, Vector2 b)
    {
        float x = a.X > b.X ? b.X : a.X;
        float y = a.Y > b.Y ? b.Y : a.Y;
        return Vector2(x, y);
    }
    
    Vector2 Vector2::MoveTowards(Vector2 current, Vector2 target,
                                 float maxDistanceDelta)
    {
        Vector2 d = target - current;
        float m = Magnitude(d);
        if (m < maxDistanceDelta || m == 0)
            return target;
        return current + (d * maxDistanceDelta / m);
    }
    
    Vector2 Vector2::Normalized(Vector2 v)
    {
        float mag = Magnitude(v);
        if (mag == 0)
            return Vector2::Zero();
        return v / mag;
    }
    
    void Vector2::OrthoNormalize(Vector2 &normal, Vector2 &tangent)
    {
        normal = Normalized(normal);
        tangent = Reject(tangent, normal);
        tangent = Normalized(tangent);
    }
    
    Vector2 Vector2::Project(Vector2 a, Vector2 b)
    {
        float m = Magnitude(b);
        return Dot(a, b) / (m * m) * b;
    }
    
    Vector2 Vector2::Reflect(Vector2 vector, Vector2 planeNormal)
    {
        return vector - 2 * Project(vector, planeNormal);
    }
    
    Vector2 Vector2::Reject(Vector2 a, Vector2 b)
    {
        return a - Project(a, b);
    }
    
    Vector2 Vector2::RotateTowards(Vector2 current, Vector2 target,
                                   float maxRadiansDelta,
                                   float maxMagnitudeDelta)
    {
        float magCur = Magnitude(current);
        float magTar = Magnitude(target);
        float newMag = magCur + maxMagnitudeDelta *
            ((magTar > magCur) - (magCur > magTar));
        newMag = fmin(newMag, fmax(magCur, magTar));
        newMag = fmax(newMag, fmin(magCur, magTar));
    
        float totalAngle = Angle(current, target) - maxRadiansDelta;
        if (totalAngle <= 0)
            return Normalized(target) * newMag;
        else if (totalAngle >= M_PI)
            return Normalized(-target) * newMag;
    
        float axis = current.X * target.Y - current.Y * target.X;
        axis = axis / fabs(axis);
        if (!(1 - fabs(axis) < 0.00001))
            axis = 1;
        current = Normalized(current);
        Vector2 newVector = current * cos(maxRadiansDelta) +
            Vector2(-current.Y, current.X) * sin(maxRadiansDelta) * axis;
        return newVector * newMag;
    }
    
    Vector2 Vector2::Scale(Vector2 a, Vector2 b)
    {
        return Vector2(a.X * b.X, a.Y * b.Y);
    }
    
    Vector2 Vector2::Slerp(Vector2 a, Vector2 b, float t)
    {
        if (t < 0) return a;
        else if (t > 1) return b;
        return SlerpUnclamped(a, b, t);
    }
    
    Vector2 Vector2::SlerpUnclamped(Vector2 a, Vector2 b, float t)
    {
        float magA = Magnitude(a);
        float magB = Magnitude(b);
        a /= magA;
        b /= magB;
        float dot = Dot(a, b);
        dot = fmax(dot, -1.0);
        dot = fmin(dot, 1.0);
        float theta = acos(dot) * t;
        Vector2 relativeVec = Normalized(b - a * dot);
        Vector2 newVec = a * cos(theta) + relativeVec * sin(theta);
        return newVec * (magA + (magB - magA) * t);
    }
    
    float Vector2::SqrMagnitude(Vector2 v)
    {
        return v.X * v.X + v.Y * v.Y;
    }
    
    void Vector2::ToPolar(Vector2 vector, float &rad, float &theta)
    {
        rad = Magnitude(vector);
        theta = atan2(vector.Y, vector.X);
    }
    
    
    struct Vector2& Vector2::operator+=(const float rhs)
    {
        X += rhs;
        Y += rhs;
        return *this;
    }
    
    struct Vector2& Vector2::operator-=(const float rhs)
    {
        X -= rhs;
        Y -= rhs;
        return *this;
    }
    
    struct Vector2& Vector2::operator*=(const float rhs)
    {
        X *= rhs;
        Y *= rhs;
        return *this;
    }
    
    struct Vector2& Vector2::operator/=(const float rhs)
    {
        X /= rhs;
        Y /= rhs;
        return *this;
    }
    
    struct Vector2& Vector2::operator+=(const Vector2 rhs)
    {
        X += rhs.X;
        Y += rhs.Y;
        return *this;
    }
    
    struct Vector2& Vector2::operator-=(const Vector2 rhs)
    {
        X -= rhs.X;
        Y -= rhs.Y;
        return *this;
    }
    
    Vector2 operator-(Vector2 rhs) { return rhs * -1; }
    Vector2 operator+(Vector2 lhs, const float rhs) { return lhs += rhs; }
    Vector2 operator-(Vector2 lhs, const float rhs) { return lhs -= rhs; }
    Vector2 operator*(Vector2 lhs, const float rhs) { return lhs *= rhs; }
    Vector2 operator/(Vector2 lhs, const float rhs) { return lhs /= rhs; }
    Vector2 operator+(const float lhs, Vector2 rhs) { return rhs += lhs; }
    Vector2 operator-(const float lhs, Vector2 rhs) { return rhs -= lhs; }
    Vector2 operator*(const float lhs, Vector2 rhs) { return rhs *= lhs; }
    Vector2 operator/(const float lhs, Vector2 rhs) { return rhs /= lhs; }
    Vector2 operator+(Vector2 lhs, const Vector2 rhs) { return lhs += rhs; }
    Vector2 operator-(Vector2 lhs, const Vector2 rhs) { return lhs -= rhs; }
    
    bool operator==(const Vector2 lhs, const Vector2 rhs)
    {
        return lhs.X == rhs.X && lhs.Y == rhs.Y;
    }
    
    bool operator!=(const Vector2 lhs, const Vector2 rhs)
    {
        return !(lhs == rhs);
    }
}