I am implementing a conical filter for Gupta-Sproull anti-aliased line algorithm.
Given a cone with the total volume of 1 and a radius of 1. Find the subvolume of the intersection of a line. The line has a size of 1 as well. I need the formula so I can generate a table of values. I could find the total volume of the area under the cone. But then I need to cutout the subvolume of where the line intersects with the cone. I need a formula for this subvolume in terms of height so I can plug in the perpendicular distance from the center (this is what changes depending on where the line is drawn) and output the height. The height will determine the intensity of the pixel because the height decreases as the pixel moves farther away from the center.
So I guess I first need to find the area of that intersection of the line and the circle base....then I can find the volume. How do I find this area since the edges of the circle are arced shaped? I suppose I need to follow the edge of the circle and find out the change in slope of the line between the edges of the line but I do not know how to do it.
The line is flat and only intersects at the base. It marks or cuts out the subsection of the cone.