Implement an interval class

[hollasch]

A class that operates on ranges of double values. Use cases:

• aabb class (Refactor AABB class to use interval class #796)
• time interval (Convert time start/end to use interval class #795)
• clamp (Convert clamp() to interval::clamp() #793)
• hittable::hit() (Introduce interval class for hit() methods #786)
• moving_sphere time range (Refactor moving_sphere to use new interval class #797)
• moving_sphere center range (Refactor moving_sphere to use new interval class #797)

Here's a sketch of an interval class (not all methods below need be implemented; only those actually needed):

struct interval {
    double min, max;

    interval() : min(0), max(0) {}
    interval(double x) : min(x), max(x) {}
    interval(double _min, double _max) : min(_min), max(_max) {}

    double size() const {
        return max - min;
    }

    bool contains(double x) const {
        return min <= x && x <= max;
    }

    double clamp(double x) const {
        return (x < min) ? min
             : (x > max) ? max
             : x;
    }

    interval hull(const interval& other) const {
        return interval(std::min(min, other.min), std::max(max, other.max));
    }

    interval intersect(const interval& other) const {
        return interval(std::max(min, other.min), std::min(max, other.max));
    }

    static interval empty    = interval(+std::numeric_limits::infinity, -std::numeric_limits::infinity);
    static interval universe = interval(-std::numeric_limits::infinity, +std::numeric_limits::infinity);
}

This class could also support transforms, such as scale, translate, whatever.

[hollasch]

Hmmm. It appears that "range" is unconventional / inaccurate. Looks like "interval" is more correct.

[hollasch]

From Slack discussion, constant values are interval.empty and interval.universe.

[trevordblack]

Suggest defining const infinity to std::numeric_limits::infinity

[hollasch]

I like it. The better way would be:

using std::numeric_limits::infinity;

[trevordblack]

Yeah, but qualify it's a double:

using std::numeric_limits<double>::infinity;

Edit: that variable is a function

[hollasch]

Oif. Ok,

const auto infinity = std::numeric_limits<double>::infinity();

[hollasch]

ARRRRGGGHHH!!! That looks exactly like the line we already have in src/common/rtweekend.h. X^P

[hollasch]

The remaining three tasks all have to do with time, which is more broadly covered in #799. We'll use interval as appropriate when revisiting time.