Abstract: Animation techniques for producing physically-realistic animation while providing the interactivity and control desired by animators. Techniques are provided specifying animation for motion problems that give rise to quadratic optimization functions solvable with linear systems of equations. The resultant splines generalize traditional splines to encompass oscillatory solutions. These problems can be solved at full frame rates, giving animators a keyframe animation tool. Such a formulation is able to address a wide range of oscillatory phenomena while retaining the interactive performance and predictability of traditional splines. The splines may be complex-valued.

Abstract: A system for configuring a chip to perform certain operations is provided. The system includes a CPU. The CPU is in communication with a graphics controller. The graphics controller includes a non-volatile memory for storing a look up table (LUT). The graphics controller further includes a register port. The CPU provides a LUT value to the register port. Look up circuitry, which is in communication with the LUT register port, receives the LUT value from the register port and the LUT circuitry retrieves a corresponding LUT sequence from the LUT. The LUT sequence represents an operation to be performed by the LUT circuitry. The system is further provided with a register block, which can be programmed with values based on the operation to be performed.

Abstract: A processor uses start point fractional values during view screen segment computations that start a view screen segment's computations a particular distance away from a down point. This prevents an excessive sampling density during image generation without wasting processor resources. The processor identifies a start point fractional value for each view screen segment based upon each view screen segment's identifier, and computes a view screen segment start point for each view screen segment using the start point fractional value. View screen segment start points are “tiered” and are a particular distance away from the down point. This stops the view screen segments from converging to a point of severe over sampling while, at the same time, providing a pseudo-uniform sampling density.