It is easy to solve a second-order equation to find the intersection with a circle or third-order sphere. But for a really complex 3D object, its expression might be very complex and is hard to have closed-form solutions.
A better way is to use some nonlinear solver to find the potential solutions. But before that, we should use the bounding box to first filter those impossible roots to accelerate the solving.
StephenYangjz
it's interesting that the intersection test can actually be applied to so many shapes and surfaces. I wonder how common are these implicit surfaces used in real industry? Are these shapes more complicated than necessary, compared to shapes composed of simpler triangles? Are there specific applications where these complicated shapes are used more?
greeknerd1
I think it's really cool how simple the ray tracing method is and yet how well it generalizes to any geometric shape.
It is easy to solve a second-order equation to find the intersection with a circle or third-order sphere. But for a really complex 3D object, its expression might be very complex and is hard to have closed-form solutions.
A better way is to use some nonlinear solver to find the potential solutions. But before that, we should use the bounding box to first filter those impossible roots to accelerate the solving.
it's interesting that the intersection test can actually be applied to so many shapes and surfaces. I wonder how common are these implicit surfaces used in real industry? Are these shapes more complicated than necessary, compared to shapes composed of simpler triangles? Are there specific applications where these complicated shapes are used more?
I think it's really cool how simple the ray tracing method is and yet how well it generalizes to any geometric shape.