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+/*
+ This file is part of the MinGfx Project.
+ 
+ Copyright (c) 2017,2018 Regents of the University of Minnesota.
+ All Rights Reserved.
+ 
+ Original Author(s) of this File:
+	Dan Keefe, 2018, University of Minnesota
+	
+ Author(s) of Significant Updates/Modifications to the File:
+	...
+ */
+
+#ifndef SRC_VECTOR3_H_
+#define SRC_VECTOR3_H_
+
+#include <iostream>
+
+#include "point3.h"
+
+
+namespace mingfx {
+
+    
+/** A 3D Vector with floating point coordinates, used for storing normals and
+ all sorts of other 3D graphics operations.  Vector3s can be transformed by a
+ Matrix4, and a Vector3 can be created by subtracting two Point3s.  Example:
+ ~~~
+ // subtracting two points creates a vector
+ Point3 a(0,0,0);
+ Point3 b(2,0,0);
+ Vector3 c = b - a;
+
+ // vectors can be transformed by Matrix4s
+ Vector3 dir = c.ToUnit();
+ Matrix4 M = Matrix4::RotateX(GfxMath::ToDegrees(30.0));
+ Vector3 dir_transformed = M * dir;
+
+ // vectors can be added and subtracted
+ Vector3 d(1,0,0);
+ Vector3 e = c + d;
+ 
+ // and we can do the usual dot products and cross products too
+ float f = d.Dot(e);
+ Vector3 g = b.Cross(d);
+
+ // you can access the individual components of the vector in two ways:
+ Vector3 v(1,2,3);
+ float option1 = v.x();
+ float option2 = v[0];
+
+ // to set an individual component of the vector use the [] operator:
+ Vector3 w;
+ w[0] = 0.4;
+ w[1] = 1.2;
+ w[2] = 3.1;
+
+ // you can print the vector by sending it to stdout:
+ std::cout << v << std::endl;
+ ~~~
+ */
+class Vector3 {
+public:
+
+    /// Default constructor to create zero vector
+    Vector3();
+
+    /// Constructs a vector (x,y,z,0), where the 0 comes from the use of
+    /// homogeneous coordinates in computer graphics
+    Vector3(float x, float y, float z);
+
+    /// Constructs a vector given a pointer to x,y,z data
+    Vector3(float *v);
+
+    /// Copy constructor for vector
+    Vector3(const Vector3& v);
+
+    /// Vector destructor
+    virtual ~Vector3();
+
+    /// Check for "equality", taking floating point imprecision into account
+    bool operator==(const Vector3& v) const;
+
+    /// Check for "inequality", taking floating point imprecision into account
+    bool operator!=(const Vector3& v) const;
+
+    /// Vector assignment operator
+    Vector3& operator=(const Vector3& v);
+
+    /// Read only access to the ith coordinate of the vector.
+    float operator[](const int i) const;
+
+    /// Returns a reference to the ith coordinate of the vector.  Use this
+    /// accessor if you wish to set the coordinate rather than just request
+    /// its value.  Example:
+    /// ~~~
+    /// Vector3 a;
+    /// a[0] = 5.0; // set the x-coordinate of the vector
+    /// ~~~
+    float& operator[](const int i);  
+
+    /// Read only access to the x coordinate.  Can also use my_vector[0].  Use
+    /// the my_vector[0] = 1.0; form if you need to set the value.
+    float x() const { return v[0]; }
+    
+    /// Read only access to the y coordinate.  Can also use my_vector[1].  Use
+    /// the my_vector[1] = 1.0; form if you need to set the value.
+    float y() const { return v[1]; }
+
+    /// Read only access to the z coordinate.  Can also use my_vector[2].  Use
+    /// the my_vector[2] = 1.0; form if you need to set the value.
+    float z() const { return v[2]; }
+
+    /// In homogeneous coordinates, the w coordinate for all vectors is 0.0.
+    float w() const { return 0.0; }
+    
+    
+    // --- Vector operations ---
+
+    /** Returns "this dot v", for example:
+     ~~~
+     Vector3 a(1,0,0);
+     Vector3 b(0.5,0,0);
+     float c = a.Dot(b);
+     ~~~
+     */
+    float Dot(const Vector3& v) const;
+
+    /** Returns "this cross v", for example:
+    ~~~
+    Vector3 x(1,0,0);
+    Vector3 y(0,1,0);
+    Vector3 z = x.Cross(y);
+    ~~~
+    */
+    Vector3 Cross(const Vector3& v) const;
+
+    /// Returns the length of the vector
+    float Length() const;
+
+    /// Normalizes the vector by making it unit length.
+    void Normalize();
+
+    /// Returns a normalized (i.e., unit length) version of the vector without
+    /// modifying the original 'this' vector.
+    Vector3 ToUnit() const;
+
+    /// Returns a const pointer to the raw data array
+    const float * value_ptr() const;
+
+    /// Linear interpolation between this vector and another. Alpha=0.0 returns
+    /// this vector, and alpha=1.0 returns the other vector, other values blend
+    /// between the two.
+    Vector3 Lerp(const Vector3 &b, float alpha) const;
+    
+    
+    /// (0,0,0) - a shortcut for a special vector that is frequently needed
+    static const Vector3& Zero();
+
+    /// (1,1,1) - a shortcut for a special vector that is frequently needed
+    static const Vector3& One();
+
+    /// (1,0,0) - a shortcut for a special vector that is frequently needed
+    static const Vector3& UnitX();
+
+    /// (0,1,0) - a shortcut for a special vector that is frequently needed
+    static const Vector3& UnitY();
+
+    /// (0,0,1) - a shortcut for a special vector that is frequently needed
+    static const Vector3& UnitZ();
+    
+
+    /** Returns a new vector that is the unit version of v.  This is just an
+     alternative syntax for ToUnit().  Example:
+     ~~~
+     Vector3 a(100,150,80);
+     Vector3 b = Vector3::Normalize(a);
+     Vector3 c = a.ToUnit();
+     // b and c are the same.
+     ~~~
+     */
+    static Vector3 Normalize(const Vector3 &v);
+    
+    /** Returns v1 cross v2.  This is just an alternative syntax for Cross().
+     Example:
+     ~~~
+     Vector3 x(1,0,0);
+     Vector3 y(0,1,0);
+     Vector3 z1 = Vector3::Cross(x,y);
+     Vector3 z2 = x.Cross(y);
+     // z1 and z2 are the same.
+     ~~~
+     */
+    static Vector3 Cross(const Vector3 &v1, const Vector3 &v2);
+    
+    /** Returns v1 dot v2.  This is just an alternative syntax for Dot().
+     Example:
+     ~~~
+     Vector3 a(1,0,0);
+     Vector3 b(0.5,0,0);
+     Vector3 c1 = a.Dot(b);
+     Vector3 c2 = Vector3::Dot(a,b);
+     // c1 and c2 are the same.
+     ~~~
+     */
+    static float Dot(const Vector3 &v1, const Vector3 &v2);
+    
+    /// Linear interpolation between two vectors.  Alpha=0.0 returns 'a' and
+    /// alpha=1.0 returns 'b', other values blend between the two.
+    static Vector3 Lerp(const Vector3 &a, const Vector3 &b, float alpha);
+    
+private:
+    float v[3];
+};
+
+
+// ---------- Operator Overloads for Working with Vectors ----------
+
+
+// --- Scalers ---
+
+/// Divide the vector by the scalar s
+Vector3 operator/(const Vector3& v, const float s);
+
+/// Multiply the vector by the scalar s
+Vector3 operator*(const float s, const Vector3& v);
+
+/// Multiply the vector by the scalar s
+Vector3 operator*(const Vector3& v, const float s);
+
+/// Negate the vector
+Vector3 operator-(const Vector3& v);
+
+// Note: no -(point) operator, that's an undefined operation
+
+
+// --- Point and Vector Arithmetic ---
+
+/// Adds a vector and a point, returns a point
+Point3 operator+(const Vector3& v, const Point3& p);
+
+/// Adds a point and a vector, returns a point
+Point3 operator+(const Point3& p, const Vector3& v);
+
+/// Adds a vector and a vector, returns a vector
+Vector3 operator+(const Vector3& v1, const Vector3& v2);
+
+// Note: no (point + point) operator, that's an undefined operation
+
+/// Subtracts a vector from a point, returns a point
+Point3 operator-(const Point3& p, const Vector3& v);
+
+/// Subtracts v2 from v1, returns a vector
+Vector3 operator-(const Vector3& v1, const Vector3& v2);
+
+/// Returns the vector spanning p1 and p2
+Vector3 operator-(const Point3& p1, const Point3& p2);
+
+// Note: no (vector - point) operator, that's an undefined operation
+
+    
+    
+    
+// --- Stream operators ---
+
+// Vector3
+std::ostream & operator<< ( std::ostream &os, const Vector3 &v);
+std::istream & operator>> ( std::istream &is, Vector3 &v);
+
+    
+} // end namespace
+ 
+#endif