Difference between revisions of "cpp/numeric/lerp"
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{{feature_test_macro|__cpp_lib_interpolate|value=201902L|std=C++20|{{tt|std::lerp}}, {{lc|std::midpoint}}}} | {{feature_test_macro|__cpp_lib_interpolate|value=201902L|std=C++20|{{tt|std::lerp}}, {{lc|std::midpoint}}}} | ||
Revision as of 17:05, 12 October 2022
| Defined in header <cmath>
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| 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) 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.
Contents |
Parameters
| a, b, t | - | values of floating-point or integral types |
Return value
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 != 0and 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(lerp(a, b, t2), lerp(a, b, t1)), CMP(t2, t1), and CMP(b, a) is non-negative. (That is, lerp is monotonic.)
Notes
| Feature-test macro | Value | Std | Feature |
|---|---|---|---|
__cpp_lib_interpolate |
201902L | (C++20) | std::lerp, std::midpoint
|
Example
Run this code
#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) |
