drivermaker
Banned
jsp said:As promised, I detail the aiming system that I use to help supplement the ghost ball method. Refer to the figure below. Before beginning, you must note that I superimposed a set of x/y axes on top of the object and cue balls. These axes will aid in a consistent description of the spatial positioning of the contact points of the balls. The origin of the axes (where the x/y axes intersect) fall at the exact center of the ball, and each axis is parallel to the rails of the table. It is important to note that these axes do not shift or rotate depending on the location of the ball on the table; they remain fixed as how I described it.
The first step is to draw a line going from the center of the intended pocket to the center of the object ball (purple dashed line). Extending this line to the opposite edge of the object ball gives you the object ball contact point (blue dot). To find the contact point of the cue ball, you simply just reflect the location of the cue ball contact point about the axes origin, as shown in the upper left portion of the figure. Geometry tells you that reflecting the object ball CP about the origin will always give you the location of the cue ball CP (red dot) regardless of the location of the cue ball on the table (of course, assuming the shot is still make-able). This is illustrated in the figure with three different locations for the cue ball. For each case, the cue ball CP is in the same location (with respect to the ball’s axes).
Once you have the location of the cue ball CP, the next step is the draw a line through the object ball CP and the cue ball CP (green line). Then, you just simply imagine the line parallel to that line that goes through the center of the cue ball (orange line). This new line is what should direct your aim, since geometry tells you that this line connects the centers of both the cue ball and ghost ball. To make the shot, you just stroke through this line (black arrow).
So to briefly summarize the steps of the system in colors, the order would be purple line, blue dot, red dot, green line, orange line, and black arrow (sorry, the colors didn’t come out correctly in the figure while converting it to a jpeg). In the most basic terms, it’s a contact point to contact point system. The advantage of this system is that you don’t have to estimate the location of the ghost ball’s center. It’s a system I worked out myself, but because of its simplicity I doubt it’s anything novel. If anyone knows the exact name of this system, let me know.
The "Simplicity System".....

