tmp/tmpd8ioc89a/{from.md → to.md}
RENAMED
|
@@ -0,0 +1,24 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
### Linear interpolation <a id="c.math.lerp">[[c.math.lerp]]</a>
|
| 2 |
+
|
| 3 |
+
``` cpp
|
| 4 |
+
constexpr float lerp(float a, float b, float t) noexcept;
|
| 5 |
+
constexpr double lerp(double a, double b, double t) noexcept;
|
| 6 |
+
constexpr long double lerp(long double a, long double b, long double t) noexcept;
|
| 7 |
+
```
|
| 8 |
+
|
| 9 |
+
*Returns:* a+t(b-a).
|
| 10 |
+
|
| 11 |
+
*Remarks:* Let `r` be the value returned. If
|
| 12 |
+
`isfinite(a) && isfinite(b)`, then:
|
| 13 |
+
|
| 14 |
+
- If `t == 0`, then `r == a`.
|
| 15 |
+
- If `t == 1`, then `r == b`.
|
| 16 |
+
- If `t >= 0 && t <= 1`, then `isfinite(r)`.
|
| 17 |
+
- If `isfinite(t) && a == b`, then `r == a`.
|
| 18 |
+
- If `isfinite(t) || !isnan(t) && b-a != 0`, then `!isnan(r)`.
|
| 19 |
+
|
| 20 |
+
Let *`CMP`*`(x,y)` be `1` if `x > y`, `-1` if `x < y`, and `0`
|
| 21 |
+
otherwise. For any `t1` and `t2`, the product of
|
| 22 |
+
*`CMP`*`(lerp(a, b, t2), lerp(a, b, t1))`, *`CMP`*`(t2, t1)`, and
|
| 23 |
+
*`CMP`*`(b, a)` is non-negative.
|
| 24 |
+
|