Tuples: Points and Vectors

Tuples: Points and Vectors

The ray tracer is built on a single mathematical primitive: the tuple. A tuple is an ordered list of four numbers — (x, y, z, w).

The w component is the key:

• w = 1 means the tuple is a point — a location in space
• w = 0 means the tuple is a vector — a direction with magnitude

This distinction matters because points and vectors behave differently under transformations. Translating a point moves it; translating a vector does nothing.

The Tuple Class

class Tuple {
public:
    double x, y, z, w;
    Tuple(double x, double y, double z, double w) : x(x), y(y), z(z), w(w) {}

    bool isPoint() const { return this->w == 1.0; }
    bool isVector() const { return this->w == 0.0; }
};

Member variables are accessed with this-> inside methods.

Floating-Point Equality

Since coordinates are stored as double, comparing with == works for w (which is always exactly 0 or 1), but for other comparisons you'll use an epsilon:

const double EPSILON = 0.00001;
bool equal(double a, double b) {
    return abs(a - b) < EPSILON;
}

Your Task

Implement the Tuple class with fields x, y, z, w and methods isPoint() and isVector().

Then create a point p(4, -4, 3, 1) and a vector v(4, -4, 3, 0) and print:

• p.w=1 isPoint=1
• v.w=0 isVector=1