Lecture 9: Ray Tracing (23)
sethzhao506

According to the number of real solutions of t, we could determine if the ray intersection occurs. Here, if no real roots, then no intersection; only one real root means that the ray intersects with the sphere at edge; and two real roots means that there two points intersecting with the sphere.

nikyarora

Since r is normally normalized, we can say that a = 1 generally because the result of the dot product of a normalized vector with itself is 1. However, when these rays don't have their direction normalized, we cannot make this generalization.

briana-jin-zhang

The silhouette of an object is when there is exactly one intersection of the ray and object (sphere in this case). Interesting fact: the projection of a sphere onto an image plane in the pinhole camera model will always yield an ellipse.

briana-jin-zhang

Actually I misspoke, it can also appear as a parabola or hyperbola since the rays intersection with the sphere only once will form a cone, and the intersection of planes and cones yield all conic sections.

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