std::lerp
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 the linear
interpolation between
a and
b, if the parameter
t is inside
[0, 1] (the linear
extrapolation otherwise), i.e. the result of \(a+t(b−a)\)a+t(b−a) with accounting for floating-point calculation imprecision.
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) and isfinite(b), the following properties are guaranteed:
- If
t == 0, the result is equal toa. - If
t == 1, the result is equal tob. - If
t >= 0 && t <= 1, the result is finite. - If
isfinite(t) && a == b, the result is equal toa. - If
isfinite(t) || (b - a != 0andisinf(t)), the result is notNaN.
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
#include <cmath>
#include <cassert>
#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';
}
Possible output:
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
|
(C++20)
|
midpoint between two numbers or pointers (function template) |
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https://en.cppreference.com/w/cpp/numeric/lerp
