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Difference between revisions of "cpp/numeric/lerp"

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Revision as of 07:07, 20 September 2020

 
C++
 
Numerics library
Common mathematical functions
Mathematical special functions (C++17)
Mathematical constants (C++20)
Basic linear algebra algorithms (C++26)
Floating-point environment (C++11)
Complex numbers
Numeric array (valarray)
Pseudo-random number generation
Factor operations
(C++17)
(C++17)
Interpolations
(C++20)
lerp
(C++20)
Saturation arithmetic
(C++26)
(C++26)
(C++26)
(C++26)
(C++26)

Generic numeric operations
Bit operations
(C++20)    
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++23)
(C++20)
 
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), 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.

Contents

Parameters

a, b, t - values of floating-point or integral types

Return value

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.)

Examples

Run this code
#include <iostream>
#include <cmath>
 
int main()
{
    float a=10.0f, b=20.0f;
 
    std::cout << "a=" << a << '\n'
              << "b=" << b << '\n'
              << "mid point=" << std::lerp(a,b,0.5f) << '\n'
              << std::boolalpha << (a == std::lerp(a,b,0.0f)) << '\n';
}

Output: 

a=10
b=20
mid point=15
true

See also

(C++20)
 midpoint between two numbers or pointers
(function template) [edit]
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