Which is the simplest form of ray tracer?
A Minimal Ray-Tracer: Rendering Simple Shapes (Sphere, Cube, Disk, Plane, etc.) Intersecting a ray with a sphere is probably the simplest form of ray-geometry intersection test which is the reason why so many raytracers show images of spheres. It also has the advantage (because of its simplicity) to be very fast.
How to test a ray against a sphere?
We can simply rewrite equation 2 as: where C is the location of the center of the sphere in 3D space. Equation 4 can now be re-written as: | O + tD − C | 2 − R2 = 0. In a more intuitive form, this comes back to say that we can translate the ray by -C and test this transformed ray against the sphere as if it was centered at the origin.
Is the origin of the Ray inside the sphere?
One of the roots can be negative and the other positive which means that the origin of the ray is inside the sphere. There also might be no solution to the quadratic equations which means that the ray doesn’t intersect the sphere at all (no intersection between the ray and the sphere).
Is there an intersection between a ray and a sphere?
Note that they can only be an intersection between the ray and the sphere if tca is positive (if it is negative, it means that the vector L and the vector D points in opposite directions. If there is an intersection, it could potentially be behind the ray’s origin but anything that happens behind the ray’s origin is of no use to us).
How do you calculate the intersection of a ray and a sphere?
We have a ray, and a sphere, we know the ray’s origin point, and it’s direction, and we know the location of the sphere’s center point. What we want to do, is determine if the ray will ever intersect the sphere (spoiler: in this tutorial, it will), and if so, where that intersection occurs.
Which is the correct equation for a sphere?
The equation for a sphere is: Where x, y and z are the coordinates of a cartesian point and R is the radius of a sphere centred at the origin (will see later how to change the equation so that it works with spheres which are not centred at the origin). It says that there is a set of points for which the above equation is true.