29 Numerics library [numerics]

29.7 Mathematical functions for floating-point types [c.math]

29.7.4 Linear interpolation [c.math.lerp]

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constexpr floating-point-type lerp(floating-point-type a, floating-point-type b, floating-point-type t) noexcept;
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Returns: .
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Remarks: Let r be the value returned.
If isfinite(a) && isfinite(b), then:
  • (2.1)
    If t == 0, then r == a.
  • (2.2)
    If t == 1, then r == b.
  • (2.3)
    If t >= 0 && t <= 1, then isfinite(r).
  • (2.4)
    If isfinite(t) && a == b, then r == a.
  • (2.5)
    If isfinite(t) || !isnan(t) && b-a != 0, then !isnan(r).
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.