How can I represent a vector equation of a line segment in C++?

Question

I am working with computer graphics.

I would like to represent a line with two end points, and, then I would like my Line2d class to have a method that

Answer 1

I think there's some confusion because of the following

According to the definition, a vector is composed of a magnitude and a direction.

There is more than one way of representing a vector. I think in your question you mean that a vector can be represented by a magnitude (scalar) and a unit vector indicating a direction. A vector can just be an ordered triplet (for three dimensions) that indicate the magnitude (sqrt(x^2 + y^2 + z^2)) and the direction from the origin.

I think the answer to your question is, you don't need to calculate t. Correct me if I'm mistaken, but I think you're interpreting t as the magnitude? You can calculate that from v with sqrt(x^2 + y^2 + z^2), but v can hold both a magnitude and direction as an ordered triplet by itself.

Edit:

template 
struct Point2d
{
    T x;
    T y;

    Point2d operator + (const Point2d& rhs) const
    {
        return Point2d{x + rhs.x, y + rhs.y};
    }
    Point2d operator - (const Point2d& rhs) const
    {
        return Point2d{x - rhs.x, y - rhs.y};
    }
    // ...

    Point2d operator * (const T value) const
    {
        return Point2d{x*value, y*value};
    }
    Point2d operator / (const T value) const
    {
        return Point2d{x/value, y/value};
    }
    // ...
};

template 
class Vector2d
{
private:
    Point2d p;
public:
    Vector2d(const Point2d& point) : p{point} {}

    /*double Magnitude();
    Point2d Component();
    Vector2d Normal();
    int DotProduct(Vector2d rhs);
    Vector2d& CrossProduct(Vector2d rhs);*/

    Vector2d operator + (const Vector2d& rhs) const
    {
        return p + rhs.p;
    }
    Vector2d operator - (const Vector2d& rhs) const
    {
        return p - rhs.p;
    }
    // ...

    Vector2d operator * (const T value) const
    {
        return p*value;
    }
    Vector2d operator / (const T value) const
    {
        return p/value;
    }
    // ...
};

template 
class LineVector2d
{
private:
    Point2d  p;
    Vector2d v;

public:
    LineVector2d() = default;
    LineVector2d(const Point2d& point, const Vector2d& direction) : p{point}, v{direction} {}

    /// Returns the point on the line for the time/value `t`
    Point2d valueAt(T t)
    {
        return p + v*t;
    }
};