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2450 | 2450 |
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2451 | 2451 | True Lambertian Reflection
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2452 | 2452 | ---------------------------
|
2453 |
| -Using a diffuse model that scatters vectors evenly about the hemisphere produces a nice and soft |
2454 |
| -diffuse model, but we can definitely do better. A more accurate representation of real diffuse |
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 |
| - |
| 2453 | +Scattering reflected rays evenly about the hemisphere produces a nice soft diffuse model, but we can |
| 2454 | + definitely do better. |
| 2455 | +A more accurate representation of real diffuse objects is the _Lambertian_ distribution. |
| 2456 | +This distribution scatters reflected rays in a manner that is proportional to $\cos (\phi)$, where |
| 2457 | + $\phi$ is the angle between the reflected ray and the surface normal. |
| 2458 | +This means that a reflected ray is most likely to scatter in a direction near the surface normal, |
| 2459 | + and less likely to scatter in directions away from the normal. |
| 2460 | +This non-uniform Lambertian distribution does a better job of modeling material reflection in the |
| 2461 | + real world than our previous uniform scattering. |
| 2462 | + |
| 2463 | +We can create this distribution by adding a random unit vector to the normal vector. |
2463 | 2464 | At the point of intersection on a surface there is the hit point, $\mathbf{p}$, and there is the
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2464 | 2465 | normal of the surface, $\mathbf{n}$. At the point of intersection, this surface has exactly two
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2465 | 2466 | sides, so there can only be two unique unit spheres tangent to any intersection point (one
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