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Math

The math module is an essential tool for manipulating and combining values of RE:MAKE 2D's base types, whether for position, dimension, or color calculations.

Overview

The math module gathers all the arithmetic and comparison operators usable on RE:MAKE 2D's base types (Vec2d, Dim2d, Fact2d, Grid2d, Area, Color, Date, Clock). These types have no native operators in their respective headers, so the header "remake2d/math.hpp" must be included to use them.

Info

The header "remake2d/math.hpp" already includes "remake2d/all/types.hpp" and "remake2d/clock.hpp", so there is no need to include them separately.

Constant

The header also exposes the mathematical constant pi:

inline constexpr fmax pi = 3.14159265358979;

Arithmetic operators

The Vec2d, Dim2d, Fact2d, Grid2d and Area types support the following set of operators: +, -, /, *, %, along with their assignment equivalents +=, -=, /=, *=, %=:

Vec2d operator+(const Vec2d&, const Vec2d&) noexcept;
Vec2d operator-(const Vec2d&, const Vec2d&) noexcept;
Vec2d operator/(const Vec2d&, const Vec2d&) noexcept;
Vec2d operator*(const Vec2d&, const Vec2d&) noexcept;
Vec2d operator%(const Vec2d&, const Vec2d&) noexcept; // fmod

Vec2d& operator+=(Vec2d&, const Vec2d&) noexcept;
Vec2d& operator-=(Vec2d&, const Vec2d&) noexcept;
Vec2d& operator/=(Vec2d&, const Vec2d&) noexcept;
Vec2d& operator*=(Vec2d&, const Vec2d&) noexcept;
Vec2d& operator%=(Vec2d&, const Vec2d&) noexcept;

The same set of operators is available for Fact2d, Dim2d, Grid2d and Area:

Fact2d operator+(const Fact2d&, const Fact2d&) noexcept;
Fact2d operator-(const Fact2d&, const Fact2d&) noexcept;
Fact2d operator/(const Fact2d&, const Fact2d&) noexcept;
Fact2d operator*(const Fact2d&, const Fact2d&) noexcept;
Fact2d operator%(const Fact2d&, const Fact2d&) noexcept;

Dim2d operator+(const Dim2d&, const Dim2d&) noexcept;
Dim2d operator-(const Dim2d&, const Dim2d&) noexcept;
Dim2d operator/(const Dim2d&, const Dim2d&) noexcept;
Dim2d operator*(const Dim2d&, const Dim2d&) noexcept;
Dim2d operator%(const Dim2d&, const Dim2d&) noexcept;

Grid2d operator+(const Grid2d&, const Grid2d&) noexcept;
Grid2d operator-(const Grid2d&, const Grid2d&) noexcept;
Grid2d operator/(const Grid2d&, const Grid2d&) noexcept;
Grid2d operator*(const Grid2d&, const Grid2d&) noexcept;
Grid2d operator%(const Grid2d&, const Grid2d&) noexcept;

Area operator+(const Area&, const Area&) noexcept;
Area operator-(const Area&, const Area&) noexcept;
Area operator/(const Area&, const Area&) noexcept;
Area operator*(const Area&, const Area&) noexcept;
Area operator%(const Area&, const Area&) noexcept;

Info

For Grid2d and Area, whose members are integers, the % operator performs a classic integer modulo rather than an fmod, unlike Vec2d, Dim2d and Fact2d whose members are floating-point.

Usage

#include <remake2d/math.hpp>

int main(void) {
    rmk::Vec2d vec1 = { 100, 200 };
    rmk::Vec2d vec2 = { 200, 300 };

    rmk::Vec2d vec3 = vec1 + vec2; // { 300, 500 }
    rmk::Vec2d vec4 = vec1 - vec2; // { -100, -100 }
    rmk::Vec2d vec5 = vec1 / vec2; // { 0.5, 0.666... }

    vec1 += vec2; // modifies vec1 directly
}

rmk::Grid2d g1 = { 10, 5 };
rmk::Grid2d g2 = { 3, 2 };

rmk::Grid2d g3 = g1 + g2; // { 13, 7 }
rmk::Grid2d g4 = g1 % g2; // { 1, 1 } (integer modulo)

rmk::Area z1 = { 100, 200, 300, 400 };
rmk::Area z2 = {  50, 100, 100, 200 };

rmk::Area z3 = z1 + z2; // { 150, 300, 400, 600 }
rmk::Area z4 = z1 % z2; // { 0, 0, 0, 0 }

Operators on Color

The Color type only supports the +, - and % operators (as well as +=, -=, %=), since division and multiplication have no meaning on color components:

Color operator+(const Color&, const Color&) noexcept;
Color operator-(const Color&, const Color&) noexcept;
Color operator%(const Color&, const Color&) noexcept;

Color& operator+=(Color&, const Color&) noexcept;
Color& operator-=(Color&, const Color&) noexcept;
Color& operator%=(Color&, const Color&) noexcept;
  • + and -: combine colors by respectively selecting the maximum or minimum of each RGBA component, with a clamp between 0 and 255.
  • %: computes the average of each RGBA component.
rmk::Color purple = rmk::color::red + rmk::color::blue; // { 255, 0, 255, 255 }
rmk::Color mix     = rmk::color::red % rmk::color::blue; // average of the components

Info

For more details on the behavior of these operators, refer to the Color section.

Date and Clock comparisons

The math module also provides the full set of comparison operators for the Date and Clock types, respectively comparing year - month - day and hour - minute - second:

bool operator==(const Date&, const Date&) noexcept;
bool operator!=(const Date&, const Date&) noexcept;
bool operator<(const Date&, const Date&)  noexcept;
bool operator>(const Date&, const Date&)  noexcept;
bool operator<=(const Date&, const Date&) noexcept;
bool operator>=(const Date&, const Date&) noexcept;

bool operator==(const Clock&, const Clock&) noexcept;
bool operator!=(const Clock&, const Clock&) noexcept;
bool operator<(const Clock&, const Clock&)  noexcept;
bool operator>(const Clock&, const Clock&)  noexcept;
bool operator<=(const Clock&, const Clock&) noexcept;
bool operator>=(const Clock&, const Clock&) noexcept;

rmk::Date d1(15, 6, 2026);
rmk::Date d2(20, 6, 2026);

if (d1 < d2) { /* d1 comes before d2 */ }

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