TinyMath.hpp

#ifndef TINYMATH_HPP
#define TINYMATH_HPP
 
#include <cmath>
#include <ostream>
 
// Forward references of each of the structs
struct Vec2D;
struct Matrix3D;
 
// Vec2D performs vector operations with 3-dimensions
// The purpose of this class is primarily for 3D graphics
// applications.
struct Vec2D {
 
    // I'm wrapping all of our member variables in a union.
    // So long as you make sure the byte-size is equivalent, this
    // allows you to access the data in whatever form is most convenient.
    // Meaning I can access Vec2D[0] or equivalently Vec2D.x .
    // I can also pass Vec2D internal array or just individual values if needed conveniently.
    union {
        struct {
            // Note: x,y are a convention
            // x,y could be position, but also any 2-component value.
            float x;
            float y;
            float w; // 'w' is a third hidden component that could be used
            // to determine if this is being used as a vector or a point
            // If w=0 then a vector, if w=1 then a point
            // DO not use 'w' for any computation however.
        };
        float data[3]; // for convenience if you want to access as 'data' or pass Vec2D as an array
    };
 
    // Default conostrutcor
    // 'why default?' https://stackoverflow.com/questions/20828907/the-new-keyword-default-in-c11
    //    Vec2D() = default;
 
    // The "Real" constructor we want to use.
    // This initializes the values x,y, and the 'w' value
    Vec2D(float _x = 0, float _y = 0, float _w = 0) {
        // TODO:
        x = _x;
        y = _y;
        w = _w;
    }
 
    // Index operator, allowing us to access the individual
    // x,y components of our vector.
    float &operator[](int i) {
        // NOTE: Think about why this works.
        //       There is no code to change here.
        return ((&x)[i]);
    }
 
    // Index operator, allowing us to access the individual
    // x,y components of our vector.
    const float &operator[](int i) const {
        // NOTE: Think about why this works.
        //       There is no code to change here.
        return ((&x)[i]);
    }
 
    // General Note
    // You'll observer that some of the operator overloads appear in this class
    // as member functions versus some that are free functions.
    // In general, if you need access to private member variables or the 'this' pointer
    // then you must use a member function. Otherwise, I recommend to 'free your functions'
    // and not make them part of the class for maximum use.
    //
    // Multiplication Operator
    // Multiply vector by a uniform-scalar.
    Vec2D &operator*=(float s) {
        // TODO:
        x *= s;
        y *= s;
 
        return (*this);
    }
 
    // Division Operator
    Vec2D &operator/=(float s) {
        // TODO:
        x /= s;
        y /= s;
 
        return (*this);
    }
 
    // Addition operator
    Vec2D &operator+=(const Vec2D &v) {
        // TODO:
        x += v.x;
        y += v.y;
 
        return (*this);
    }
 
    // Subtraction operator
    Vec2D &operator-=(const Vec2D &v) {
        // TODO:
        x -= v.x;
        y -= v.y;
 
        return (*this);
    }
};
 
// Compute the dot product of a Vec2D
inline float Dot(const Vec2D &a, const Vec2D &b) {
    // TODO:
    return a.x * b.x + a.y * b.y + a.w * b.w;
}
 
/*
// Test for equality
// NOTE: Comparing floats is somewhat tricky, meaning that
//       you will want to take the fabs(lhs.x - lhs.y) < 0.00001
//       of each component to see if they are 'close enough'
bool operator==(Vec2D &lhs, Vec2D &rhs)
{
  bool result = true;
  // TODO
  if (fabs(lhs.x - rhs.x) > 0.00001 || fabs(lhs.y - rhs.y) > 0.00001 || fabs(lhs.w - rhs.w) > 0.00001)
  {
    result = false;
  }
  return result;
}
*/
 
// Multiplication of a vector by a scalar values
inline Vec2D operator*(const Vec2D &v, float s) {
    // TODO:
    Vec2D vec;
 
    vec.x = v.x * s;
    vec.y = v.y * s;
    vec.w = v.w;
 
    return vec;
}
 
inline Vec2D operator*(float s, const Vec2D &v) {
    // TODO:
    Vec2D vec;
 
    vec.x = v.x * s;
    vec.y = v.y * s;
    vec.w = v.w;
 
    return vec;
}
 
// Division of a vector by a scalar value.
inline Vec2D operator/(const Vec2D &v, float s) {
    // TODO:
    Vec2D vec;
 
    vec.x = v.x / s;
    vec.y = v.y / s;
    vec.w = v.w;
 
    return vec;
}
 
// Negation of a vector
// Use Case: Sometimes it is handy to apply a force in an opposite direction
inline Vec2D operator-(const Vec2D &v) {
    // TODO:
    Vec2D vec;
 
    vec.x = v.x * -1.0f;
    vec.y = v.y * -1.0f;
    vec.w = v.w;
 
    return vec;
}
 
// Return the magnitude of a vector
inline float Magnitude(const Vec2D &v) {
    // TODO:
    return sqrt(v.x * v.x + v.y * v.y);
}
 
// Add two vectors together
inline Vec2D operator+(const Vec2D &a, const Vec2D &b) {
    // TODO:
    Vec2D vec;
 
    vec.x = a.x + b.x;
    vec.y = a.y + b.y;
    //?
    vec.w = a.w;
 
    return vec;
}
 
// Subtract two vectors
inline Vec2D operator-(const Vec2D &a, const Vec2D &b) {
    // TODO:
    Vec2D vec;
 
    vec.x = a.x - b.x;
    vec.y = a.y - b.y;
    //?
    vec.w = a.w;
 
    return vec;
}
 
// Vector Projection
inline Vec2D Project(const Vec2D &a, const Vec2D &b) {
    // TODO:
    Vec2D vec;
 
    return b * (float) (Dot(a, b) / (float) pow(Magnitude(b), 2));
}
 
// Set a vectors magnitude to 1
// Note: This is NOT generating a normal vector
inline Vec2D Normalize(const Vec2D &v) {
    // TODO:
    Vec2D vec;
 
    float mag = Magnitude(v);
    vec.x = v.x / mag;
    vec.y = v.y / mag;
    vec.w = v.w;
 
    return vec;
}
 
// a x b (read: 'a crossed b')
// With a 3D vector we would yield another perpendicular cross product
// For 2D cross product, this will yield a scalar.
// You should write this to yield a scalar value.
inline float CrossProduct(const Vec2D &a, const Vec2D &b) {
    // TODO:
    float result;
 
    result = a.x * b.y - b.x * a.y;
 
    return result;
}
 
// Pretty print a vector
// std::ostream& could be 'std::cout' for example'
// This function is primarily used for debugging purposes
inline void PrettyPrint(std::ostream &os, const Vec2D &a) {
    os << "x  : " << a.x << std::endl;
    os << "y  : " << a.y << std::endl;
    os << "(w): " << a.w << std::endl;
}
 
// Matrix 3D represents 3x3 matrices in Math
struct Matrix3D {
private:
    float n[3][3]; // Store each value of the matrix
 
public:
    // Initializes to a identity matrix by default
    Matrix3D() {
        n[0][0] = 1;
        n[0][1] = 0;
        n[0][2] = 0;
        n[1][0] = 0;
        n[1][1] = 1;
        n[1][2] = 0;
        n[2][0] = 0;
        n[2][1] = 0;
        n[2][2] = 1;
    }
 
    // TODO: Row or column major order you decide!
    // Matrix constructor with 9 scalar values.
    Matrix3D(float n00, float n01, float n02,
             float n10, float n11, float n12,
             float n20, float n21, float n22) {
 
        n[0][0] = n00;
        n[0][1] = n01;
        n[0][2] = n02;
        n[1][0] = n10;
        n[1][1] = n11;
        n[1][2] = n12;
        n[2][0] = n20;
        n[2][1] = n21;
        n[2][2] = n22;
    }
 
    // Matrix constructor from three vectors.
    Matrix3D(const Vec2D &a, const Vec2D &b, const Vec2D &c) {
        n[0][0] = a.x;
        n[0][1] = a.y;
        n[0][2] = a.w;
        n[1][0] = b.x;
        n[1][1] = b.y;
        n[1][2] = b.w;
        n[2][0] = c.x;
        n[2][1] = c.y;
        n[2][2] = c.w;
    }
 
    // Index operator with two dimensions
    // Example: M(1,1) returns row 1 and column 1 of matrix M.
    float &operator()(int i, int j) {
        return (n[i][j]);
    }
 
    // Index operator with two dimensions
    // Example: M(1,1) returns row 1 and column 1 of matrix M.
    const float &operator()(int i, int j) const {
        return (n[i][j]);
    }
 
    // Return a row from a matrix as a vector.
    Vec2D &operator[](int j) {
        return (*reinterpret_cast<Vec2D *>(n[j]));
    }
 
    // Return a row from a matrix as a vector.
    const Vec2D &operator[](int j) const {
        return (*reinterpret_cast<const Vec2D *>(n[j]));
    }
};
 
/*
// Matrix Multiplication
Matrix3D operator*(const Matrix3D &A, const Matrix3D &B)
{
  // TODO:
  Matrix3D result;
 
  float a = A(0, 0);
  float b = A(0, 1);
  float c = A(0, 2);
  float d = A(1, 0);
  float e = A(1, 1);
  float f = A(1, 2);
  float g = A(2, 0);
  float h = A(2, 1);
  float i = A(2, 2);
 
  float j = B(0, 0);
  float k = B(0, 1);
  float l = B(0, 2);
  float m = B(1, 0);
  float n = B(1, 1);
  float o = B(1, 2);
  float p = B(2, 0);
  float q = B(2, 1);
  float r = B(2, 2);
 
  result = Matrix3D(
      a * j + b * m + c * p, a * k + b * n + c * q, a * l + b * o + c * r,
      d * j + e * m + f * p, d * k + e * n + f * q, d * l + e * o + f * r,
      g * j + h * m + i * p, g * k + h * n + i * q, g * l + h * o + i * r);
 
  return result;
}
 
// Matrix multiply by a vector
Vec2D operator*(const Matrix3D &M, const Vec2D &v)
{
  // TODO:
  float a = M(0, 0);
  float b = M(0, 1);
  float c = M(0, 2);
  float d = M(1, 0);
  float e = M(1, 1);
  float f = M(1, 2);
  float g = M(2, 0);
  float h = M(2, 1);
  float i = M(2, 2);
 
  float j = v.x;
  float k = v.y;
  float l = v.w;
 
  Vec2D vec = Vec2D(
      a * j + b * k + c * l,
      d * j + e * k + f * l,
      g * j + h * k + i * l);
 
  return vec;
}
 
// Pretty print a matrix
void PrettyPrintMatrix(std::ostream &os, const Matrix3D &a)
{
  for (int i = 0; i < 3; ++i)
  {
    for (int j = 0; j < 3; ++j)
    {
      os << i << ", " << j << ": " << a(i, j) << std::endl;
    }
  }
}
*/
#endif