std::lerp

 

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gcd (C++17)

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midpoint (C++20)

lerp (C++20)

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Defined in header <cmath>
constexpr float       lerp( float a, float b, float t ) noexcept;	(1)	(since C++20)
constexpr double      lerp( double a, double b, double t ) noexcept;	(2)	(since C++20)
constexpr long double lerp( long double a, long double b, long double t ) noexcept;	(3)	(since C++20)
constexpr Promoted    lerp( Arithmetic1 a, Arithmetic2 b, Arithmetic3 t ) noexcept;	(4)	(since C++20)

1-3) Computes \(a+t(b−a)\)a+t(b−a), i.e. the linear interpolation between a and b for the parameter t (or extrapolation, when t is outside the range [0,1]).

4) A set of overloads or a function template for all combinations of arguments of arithmetic type not covered by 1-3). If any argument has integral type, it is cast to double. If any other argument is long double, then the return type is long double, otherwise it is double.

Parameters

a, b, t

-

values of floating-point or integral types

Return value

\(a+t(b−a)\)a+t(b−a)

When isfinite(a) && isfinite(b), the following properties are guaranteed:

• If t == 0, the result is equal to a.
• If t == 1, the result is equal to b.
• If t >= 0 && t <= 1, the result is finite.
• If isfinite(t) && a == b, the result is equal to a.
• If isfinite(t) || (!isnan(t) && b-a != 0), the result is not NaN.

Let CMP(x,y) be 1 if x > y, -1 if x < y, and 0 otherwise. For any t1 and t2, the product of CMP(lerp(a, b, t2), lerp(a, b, t1)), CMP(t2, t1), and CMP(b, a) is non-negative. (That is, lerp is monotonic.)

Notes

lerp is available in the global namespace when <math.h> is included, even if it is not a part of C.

Feature testing macro: __cpp_lib_interpolate.

Example

Run this code

#include <iostream>
#include <cmath>
 
int main()
{
    float a=10.0f, b=20.0f;
 
    std::cout << "a=" << a << ", " << "b=" << b << '\n'
              << "mid point=" << std::lerp(a,b,0.5f) << '\n'
              << std::boolalpha << (a == std::lerp(a,b,0.0f)) << ' '
              << std::boolalpha << (b == std::lerp(a,b,1.0f)) << '\n';
 
    for (float t{}; t <= 1.0f; t += 0.1f)
        std::cout << std::lerp(10.f, 20.f, t) << ' ';
    std::cout << '\n';
 
    for (double t{}; t <= 1.0; t += 0.1)
        std::cout << std::lerp(10., 20., t) << ' ';
    std::cout << '\n';
}

Output:

a=10, b=20
mid point=15
true true
10 11 12 13 14 15 16 17 18 19 
10 11 12 13 14 15 16 17 18 19 20

See also

midpoint (C++20)

midpoint between two numbers or pointers (function template)