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Interval#

The interval is a standard 1D real-valued interval. The class implements a representation and operations on the interval type and guarantees interval validity on construction. Basic operations and accessors are implemented, as well as other common operations. See 'Example Usage' below.

Target use cases#

  • Range or containment checks. The interval class simplifies code that involves checking membership of a value to a range, or intersecting two ranges. It also provides consistent behavior and consistent handling of edge cases.

Properties#

  • empty: An empty interval is equivalent to an empty set. It contains no elements. It is a valid interval, but because it is empty, the notion of measure (length) is undefined; the measure of an empty interval is not zero. The implementation represents the measure of an empty interval with NaN.
  • zero measure: An interval with zero measure is an interval whose bounds are exactly equal. The measure is zero because the interval contains only a single point, and points have zero measure. However, because it does contain a single element, the interval is not empty.
  • valid: A valid interval is either empty or has min/max bounds such that (min <= max). On construction, interval objects are guaranteed to be valid. An attempt to construct an invalid interval results in a runtime_error exception being thrown.
  • pseudo-immutable: Once constructed the only way to change the value of an interval is to overwrite it with a new one; an existing object cannot be modified.

Conventions#

  • All operations on interval objects are defined as static class methods on the interval class. This is a functional-style of programming that basically turns the class into a namespace that grants functions access to private member variables of the object they operate on.

Assumptions#

  • The interval is only intended for floating point types. This is enforced via static assertion.
  • The constructor for non-empty intervals takes two arguments 'min' and 'max', and they must be ordered (i.e., min <= max). If this assumption is violated, an exception is emitted and construction fails.

Example Usage#

#include "geometry/interval.hpp"

#include <iostream>

// using-directive is just for illustration; don't do this in practice
using namespace autoware::common::geometry;

// bounds for example interval
constexpr auto MIN = 0.0;
constexpr auto MAX = 1.0;

//
// Try to construct an invalid interval. This will give the following error:
// 'Attempted to construct an invalid interval: {"min": 1.0, "max": 0.0}'
//

try {
  const auto i = Interval_d(MAX, MIN);
} catch (const std::runtime_error& e) {
  std::cerr << e.what();
}

//
// Construct a double precision interval from 0 to 1
//

const auto i = Interval_d(MIN, MAX);

//
// Test accessors and properties
//

std::cout << Interval_d::min(i) << " " << Interval_d::max(i) << "\n";
// Prints: 0.0 1.0

std::cout << Interval_d::empty(i) << " " << Interval_d::length(i) << "\n";
// Prints: false 1.0

std::cout << Interval_d::contains(i, 0.3) << "\n";
// Prints: true

std::cout << Interval_d::is_subset_eq(Interval_d(0.2, 0.4), i) << "\n";
// Prints: true

//
// Test operations.
//

std::cout << Interval_d::intersect(i, Interval(-1.0, 0.3)) << "\n";
// Prints: {"min": 0.0, "max": 0.3}

std::cout << Interval_d::project_to_interval(i, 0.5) << " "
          << Interval_d::project_to_interval(i, -1.3) << "\n";
// Prints: 0.5 0.0

//
// Distinguish empty/zero measure
//

const auto i_empty = Interval();
const auto i_zero_length = Interval(0.0, 0.0);

std::cout << Interval_d::empty(i_empty) << " "
          << Interval_d::empty(i_zero_length) << "\n";
// Prints: true false

std::cout << Interval_d::zero_measure(i_empty) << " "
          << Interval_d::zero_measure(i_zero_length) << "\n";
// Prints: false false