15-462 Graphics Project 2: Camera Movement


If you don't properly keep track of your coordinate system as you move from one position to the next along your spline, then your up vector may end up pointing in a random direction each time, causing your camera to rotate very unpredictably. Below is a summary of a method by Ken Sloan which you might use to move your up vector in a manner which doesn't nauseate the viewer!

Coordinate Transitions

Sloan's method decides each coordinate system using a function of the previous one, to ensure continuity. There are three vectors that we care about for each position P along the length of the spline--these are the tangent, the normal, and the binormal (or T, N, and B). The tangent is already known at each position--it can be acquired from the derivative of your spline function. The vectors which must be decided by this method are N and B.

First, you'll need to generate your starting set of axes at point P0, given T0. The easiest way to do this (perhaps not the best) is as follows: Pick an arbitrary vector V. Make N0 = unit(T0 x V) and B0 = unit(T0xN0), where unit(u) is the normalization of vector u, or u/|u|. You now have a starting set of coordinates.

Now you simply need a function to calculate a set of coordinate vectors given the previous set. Given a previous set at P0 and the desired new set at P1, a good way to do this is to let N1 = unit(B0 x T1) and B1 = unit(T1 x N1).


The coordinates as determined above are useful in two areas of the lab--the first is orienting the camera as it moves along the roller coaster. The second is deciding the orientation of features of the track itself (rails, cross-sections, etc) when you draw them to the screen. Both of these may be accomplished as a function of P, T, N, and B at any given point.

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