Lecture 9: Ray Tracing & Acceleration Structures (18)
yangbright-2001
linear algebra stuff... The determination of a plane
llejj
From the equation for t we see that if d and N are orthogonal, then t is undefined. This makes sense, since if the ray is parallel to the plane then there won't be an intersection
sparky-ed
It did not come clear at first; therefore, I'd like to talk about details about the mathematical equation here. Notice that in Plane equation, the N is normal vector of the plane and p is any point on the plane and p' is known point on the plane. the reason why the dot product of (p-p`) *N is zero is because if any vector is subtracted by another any vector in the plane, it will be perpendicular to the normal vector. Using this, we can solve for t which is parameter of ray equation!
jlutan
I noticed that these equations are very similar to the ones we used for rasterizing lines of a defined thickness and length. We take the dot product of a vector involving the point with one associated with the object, in this case a plane. I suspect we could also adjust the thickness of the plane if we set bounds instead of testing for intersection.
linear algebra stuff... The determination of a plane
From the equation for t we see that if d and N are orthogonal, then t is undefined. This makes sense, since if the ray is parallel to the plane then there won't be an intersection
It did not come clear at first; therefore, I'd like to talk about details about the mathematical equation here. Notice that in Plane equation, the N is normal vector of the plane and p is any point on the plane and p' is known point on the plane. the reason why the dot product of (p-p`) *N is zero is because if any vector is subtracted by another any vector in the plane, it will be perpendicular to the normal vector. Using this, we can solve for t which is parameter of ray equation!
I noticed that these equations are very similar to the ones we used for rasterizing lines of a defined thickness and length. We take the dot product of a vector involving the point with one associated with the object, in this case a plane. I suspect we could also adjust the thickness of the plane if we set bounds instead of testing for intersection.