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2452 | 2452 | ---------------------------
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2453 | 2453 | Using a diffuse model that scatters vectors evenly about the hemisphere produces a nice and soft
|
2454 | 2454 | diffuse model, but we can definitely do better. A more accurate representation of real diffuse
|
2455 |
| -objects is the _Lambertian_ distribution, which has a scattering distribution that is propertional |
2456 |
| -to $\cos (\phi)$, where $\phi$ is the angle from the normal. This means that a ray is most likely to |
2457 |
| -scatter toward the normal and decreases in likelihood as the direction becomes more tangential. This |
2458 |
| -distribution is notably no longer uniform, but the _Lambertian_ distribution does a better job of |
2459 |
| -modeling objects in the real world than our previous uniform scattering. We can create this |
2460 |
| -distribution by picking random points on the surface of the unit sphere, and then offsetting them |
2461 |
| -along the surface normal. |
| 2455 | +objects is the _Lambertian_ distribution, which scatters reflected rays in a manner that is |
| 2456 | +propertional to $\cos (\phi)$, where $\phi$ is the angle between the reflected ray and the surface |
| 2457 | +normal. This means that a ray is most likely to scatter in directions close to the normal, and less |
| 2458 | +likely to scatter in directions more tangent to the surface. This distribution is notably no longer |
| 2459 | +uniform, but the _Lambertian_ distribution does a better job of modeling objects in the real world |
| 2460 | +than our previous uniform scattering. We can create this distribution by adding a random unit vector |
| 2461 | +to the normal vector. |
2462 | 2462 |
|
2463 | 2463 | At the point of intersection on a surface there is the hit point, $\mathbf{p}$, and there is the
|
2464 | 2464 | normal of the surface, $\mathbf{n}$. At the point of intersection, this surface has exactly two
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