| This thesis describes a graphics modeling system, called Sculpt, that maintains physically-valid protein properties while a user interactively moves atoms in a protein model. Sculpt models strong properties such as bond lengths and angles with rigid constraints and models weak properties such as near-neighbor interactions with potential energies. Sculpt continually satisfies the constraints and maintains a local energy minimum throughout user interaction. On a Silicon Graphics 240-GTX, Sculpt maintains 1.5 updates per second on a molecular model with 355 atoms (1065 variables, 1027 constraints, and 3450 potential energies). Performance decreases linearly with increased molecule size. Three techniques yield interactive performance: a constrained minimization algorithm with linear complexity in problem size, coarse-grain parallelism, and variable reduction that replaces model segments with rigid bodies.;The thesis presents a Lagrange multiplier method that finds a constrained minimum and achieves linear computational complexity for articulated figures whose spine contains many more joints than any attached limb (e.g. reptiles, mammals, and proteins). The method computes the Jacobian matrix of the constraint functions, multiplies it by its transpose, and solves the resulting system of equations. A sort of the Jacobian at program initialization yields a constant, band-diagonal pattern of nonzeros. Multiplication and solution of band-diagonal matrices require computation that increases linearly with problem size. One or two iterations of this algorithm typically find a constrained minimum in this application.;The number of functions and variables can be reduced by the use of rigid bodies. A user can specify that a rigid object with few variables replace large segments of a model that should not change. For example, a user can twist a backbone into a helix and then freeze the helix by replacing its atoms and bonds with a cylinder of rigid shape but movable position and orientation.;Two improvements over existing interactive protein modeling systems have been observed in modeling sessions with Sculpt. First, time-consuming model correction is avoided by maintaining a physically-valid model throughout a modeling session. Second, additional cues about model properties can arise when a chemist interactively guides a folding simulation rather than viewing a cine loop from a pre-computed simulation. |
