std:: lerp

Parameters

Return value

\(a + t(b − a)\) a + t(b − a)

When std:: isfinite ( a ) && std:: isfinite ( b ) is true , 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 std:: isfinite ( t ) && a == b , the result is equal to a .
• If std:: isfinite ( t ) || ( b - a ! = 0 && std:: isinf ( t ) ) , 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 ( std :: lerp ( a, b, t2 ) , std :: lerp ( a, b, t1 ) ) ,
• CMP ( t2, t1 ) , and
• CMP ( b, a )

is non-negative. (That is, std::lerp is monotonic.)

Notes

The additional overloads are not required to be provided exactly as (A) . They only need to be sufficient to ensure that for their first argument num1 , second argument num2 and third argument num3 :

Example

#include <cassert>
#include <cmath>
#include <iostream>
 
float naive_lerp(float a, float b, float t)
{
    return a + t * (b - a);
}
 
int main()
{
    std::cout << std::boolalpha;
 
    const float a = 1e8f, b = 1.0f;
    const float midpoint = std::lerp(a, b, 0.5f);
 
    std::cout << "a = " << a << ", " << "b = " << b << '\n'
              << "midpoint = " << midpoint << '\n';
 
    std::cout << "std::lerp is exact: "
              << (a == std::lerp(a, b, 0.0f)) << ' '
              << (b == std::lerp(a, b, 1.0f)) << '\n';
 
    std::cout << "naive_lerp is exact: "
              << (a == naive_lerp(a, b, 0.0f)) << ' '
              << (b == naive_lerp(a, b, 1.0f)) << '\n';
 
    std::cout << "std::lerp(a, b, 1.0f) = " << std::lerp(a, b, 1.0f) << '\n'
              << "naive_lerp(a, b, 1.0f) = " << naive_lerp(a, b, 1.0f) << '\n';
 
    assert(not std::isnan(std::lerp(a, b, INFINITY))); // lerp here can be -inf
 
    std::cout << "Extrapolation demo, given std::lerp(5, 10, t):\n";
    for (auto t{-2.0}; t <= 2.0; t += 0.5)
        std::cout << std::lerp(5.0, 10.0, t) << ' ';
    std::cout << '\n';
}

a = 1e+08, b = 1
midpoint = 5e+07
std::lerp is exact?: true true
naive_lerp is exact?: true false
std::lerp(a, b, 1.0f) = 1
naive_lerp(a, b, 1.0f) = 0
Extrapolation demo, given std::lerp(5, 10, t):
-5 -2.5 0 2.5 5 7.5 10 12.5 15

See also