added 3D Vec3 class and it's operators.

Vec3.h

@@ -0,0 +1,127 @@
+///
+///@Class  Vec3
+///@Brief  Simple 3D vector class
+///@Author PEZY
+///@Date   Sept. 2014
+///@See   
+///
+
+#include <cmath>
+
+namespace B3D
+{
+class Vec3 {
+public:
+  Vec3() {}
+  Vec3(const Vec3 &v) : x(v.x), y(v.y), z(v.z) {}
+  Vec3(float fx, float fy, float fz) : x(fx), y(fy), z(fz) {}
+
+  Vec3 &operator =(const Vec3 &v)
+  {
+    x = v.x; y = v.y; z = v.z;
+    return *this;
+  }
+
+  bool operator ==(const Vec3 &v) const
+  {
+    return x == v.x && y == v.y && z == v.z;
+  }
+  bool operator !=(const Vec3 &v) const
+  {
+    return x != v.x || y != v.y || z != v.z;
+  }
+
+  void zero() { x = y = z = 0.0f; }
+  Vec3 operator -() const { return Vec3(-x, -y, -z); }
+  
+  Vec3 operator +(const Vec3 &v) const
+  {
+    return Vec3(x+v.x, y+v.y, z+v.z);
+  }  
+  Vec3 operator -(const Vec3 &v) const
+  {
+    return Vec3(x-v.x, y-v.y, z-v.z);
+  }
+  Vec3 operator *(float f) const
+  {
+    return Vec3(x*f, y*f, z*f);
+  }
+  Vec3 operator /(float f) const
+  {
+    float oneOverF = 1.f / f;
+    return Vec3(x*oneOverF, y*oneOverF, z*oneOverF);
+  }
+  
+  Vec3 &operator +=(const Vec3 &v)
+  {
+    x += v.x; y += v.y; z += v.z;
+    return *this;
+  }
+  Vec3 &operator -=(const Vec3 &v)
+  {
+    x -= v.x; y -= v.y; z -= v.z;
+    return *this;
+  }
+  Vec3 &operator *=(float f)
+  {
+    x *= f; y *= f; z *= f;
+    return *this;
+  }
+  Vec3 &operator /=(float f)
+  {
+    float oneOverF = 1.f/f;
+    x *= oneOverF; y *= oneOverF;; z *= oneOverF;;
+    return *this;
+  }
+
+  void normalize()
+  {
+    float magSq = x*x + y*y + z*z;
+    if (magSq > 0.0f)
+    {
+      float oneOverMag = 1.0f / std::sqrt(magSq);
+      x *= oneOverMag;
+      y *= oneOverMag;
+      z *= oneOverMag;
+    }
+  }
+
+  float operator *(const Vec3 &v) const
+  {
+    return x*v.x + y*v.y + z*v.z;
+  }
+
+public:
+  float x, y, z;
+
+};
+
+inline float vec3Mag(const Vec3 &v)
+{
+  return std::sqrt(v.x*v.x + v.y*v.y + v.z*v.z);
+}
+
+inline Vec3 crossProduct(const Vec3 &a, const Vec3 &b)
+{
+  return Vec3(
+    a.y*b.z - a.z*b.y,
+    a.z*b.x - a.x*b.z,
+    a.x*b.y - a.y*b.x
+  );
+}
+
+inline Vec3 operator *(float f, const Vec3 &v)
+{
+  return Vec3(f*v.x, f*v.y, f*v.z);
+}
+
+inline float distance(const Vec3 &a, const Vec3 &b)
+{
+  float dx = a.x - b.x;
+  float dy = a.y - b.y;
+  float dz = a.z - b.z;
+  return std::sqrt(dx*dx + dy*dy + dz*dz);
+}
+
+const Vec3 kZeroVec3;
+}

Vec3UTest.cpp

@@ -0,0 +1,81 @@
+///
+///@Brief   Check the exercise of 5.13
+///@Author  PEZY
+///@Date    Sept. 2014
+///@See     class B3D::Vec3
+///
+
+#include <iostream>
+#include "Vec3.h"
+
+using B3D::Vec3;
+using std::cout; using std::endl;
+using B3D::operator *;
+
+int main()
+{
+  ///> Exercise 5.13.1
+  {
+    Vec3 va(3, 7, 0);
+    va = -va;
+    cout << "[" << va.x << "," << va.y << "," << va.z << "]" << endl;
+
+    Vec3 vb(-12, 5, 0);
+    cout << B3D::vec3Mag(vb) << endl;
+
+    Vec3 vc(8, -3, 0.5);
+    cout << B3D::vec3Mag(vc) << endl;
+
+    Vec3 vd(4, -7, 0);
+    vd = 3*vd;
+    cout << "[" << vd.x << "," << vd.y << "," << vd.z << "]" << endl;
+  
+    Vec3 ve(4, 5, 0);
+    ve /= 2;
+    cout << "[" << ve.x << "," << ve.y << "," << ve.z << "]" << endl; 
+  }
+  cout << "----------" << endl; 
+  ///> Exercise 5.13.2
+  {
+    Vec3 va(-12, 5, 0);
+    Vec3 vb(8, -3, 0.5);
+    va.normalize();
+    vb.normalize();
+    cout << "[" << va.x << "," << va.y << "," << va.z << "]" << endl; 
+    cout << "[" << vb.x << "," << vb.y << "," << vb.z << "]" << endl; 
+  }
+  cout << "----------" << endl; 
+  ///> Exercise 5.13.3
+  {
+    Vec3 va1(3, 10, 7);
+    Vec3 va2(8, -7, 4);
+    Vec3 va = va1 - va2;
+    cout << "[" << va.x << "," << va.y << "," << va.z << "]" << endl; 
+
+    Vec3 vb1(1, 2, 3);
+    Vec3 vb2(2, 10, -6);
+    Vec3 vb = 3*vb1 - 4*vb2;
+    cout << "[" << vb.x << "," << vb.y << "," << vb.z << "]" << endl; 
+  }
+  cout << "----------" << endl; 
+  ///> Exercise 5.13.4
+  {
+    Vec3 va1(3, 10, 7);
+    Vec3 va2(8, -7, 4);
+    cout << B3D::distance(va1, va2)  << endl;
+  }
+  cout << "----------" << endl; 
+  ///> Exercise 5.13.5
+  {
+    Vec3 vb(-2, 0, 4);
+    cout <<  3*vb*(Vec3(8, -2, 1.5) + Vec3(0, 9, 7)) << endl;
+  }  
+  cout << "----------" << endl; 
+  ///> Exercise 5.13.8
+  {
+    Vec3 v = B3D::crossProduct(Vec3(3, 10, 7), Vec3(8, -7, 4));
+    cout << "[" << v.x << "," << v.y << "," << v.z << "]" << endl; 
+  } 
+  cout << "----------" << endl; 
+  return 0;
+}