Not sure it will help, but I'll try to tell it differently...
The initial purpose of conditional is to make sure to have an outline edge around the shape of the part (think "Ligne claire" cartoons characters), so that it can be seen clearly on the background. The edges of a cube are always visible so they are treated as permanent lines. But what to do for rounded shapes? if we put permanent lines, the facets forming the shape will be highlighted - something we don't want. What we need is a mechanism where the line is visible only when it appears on the border of the shape. The magics comes from control points. When projected on screen with current viewing direction, if the two control points are on each side of the conditional line, this mean that the conditional line is in the middle of two visible surfaces, so it is not on the border of the shape and must not be visible. If on the other hand the two control points are projected on the same side of the lines, this means that the conditional line is on the border between shape and background and must be visible. With this verbose explanation and Tim's image, I hope you'll get the hang of it!
The initial purpose of conditional is to make sure to have an outline edge around the shape of the part (think "Ligne claire" cartoons characters), so that it can be seen clearly on the background. The edges of a cube are always visible so they are treated as permanent lines. But what to do for rounded shapes? if we put permanent lines, the facets forming the shape will be highlighted - something we don't want. What we need is a mechanism where the line is visible only when it appears on the border of the shape. The magics comes from control points. When projected on screen with current viewing direction, if the two control points are on each side of the conditional line, this mean that the conditional line is in the middle of two visible surfaces, so it is not on the border of the shape and must not be visible. If on the other hand the two control points are projected on the same side of the lines, this means that the conditional line is on the border between shape and background and must be visible. With this verbose explanation and Tim's image, I hope you'll get the hang of it!