A machine-implemented circle-generation method calculates a sequence of coordinates (x.sub.n, y.sub.n) of points approximating a circle or circular arc according to the iterative formula: ##EQU1## or an approximation thereto. This formula is suitable for high-speed computation and approximates a true circle extremely closely. When rounded off to integer coordinates, the starting and ending points of a full circle coincide.

A system for generating a continuous piece-wise linear approximating function that approximately corresponds to a predetermined function over a preselected domain, the approximating function having a selected number of linear segments, the approximating function at the endpoints of the domain falling on the predetermined function. The system first selects an initial error limit, then identifies the points which define the segments. In defining the segments, the system begins at a low endpoint, e...

A digital mixer is supplied with two digitized input signals in complex form. The product of the complex input signals is converted to analog form and provides the desired output signal without any alias terms. The first input signal is desirably stored in a first memory as a sequence of data points corresponding to a complex exponential sinusoid. The second input signal is a baseband excitation waveform that is also stored in complex form in a memory. Operands from these two sources are provide...

A method of stabilizing a halogen-doped silicon oxide film to reduce halogen atoms migrating from said film during subsequent processing steps. A halogen-doped film is deposited over a substrate and then subjected to a degassing step in which the film is briefly heated to a temperature of between about 300 and 550.degree. C. before deposition of a diffusion barrier layer. It is believed that such a heat treatment step removes loosely bonded halogen atoms from the halogen-doped film and thus the ...

A vacuum processing system is provided with a programmable interlock circuit for combining the interlock signals generated by the system into combined interlock signals. The programmable interlock circuit uses a matrix of switches to select which interlocks will be combined to form which combinations. The interlock signals are formed by two lines that are shorted together when the interlock signal is okay and not shorted together when the interlock signal is not okay. When the two lines are shor...

A figure generating apparatus for approximating in a rectangular coordinates system and by line segments a curve which is defined by a parametric cubic curve that includes a parameter, thereby generating a figure in the form of consecutive line segments. A calculator calculates, by using a distance evaluation formula, a distance between a midpoint of a line segment connecting one point of a curve and another point of the same curve which is defined by incrementing a parameter by a first predeter...

A digital plotting system for displaying straight line information. This tem employs a long vector to describe a long straight line on a graph that starts from any point, extends in any direction and has a specific length. The direction is implemented by an eight 45.degree. quadrant system wherein the specific angle within a particular quadrant is derived from binary slope storage and rate generator devices and is referenced from either a vertical adjacent line or a horizontal adjacent line. The...

A variable wave forming circuit is provided which produces signals of various waveforms (e.g., sine, triangular or trapezoidal waves) and various frequencies. A random access memory (memory means) 121 to store wave formation information on waveform is provided. According to the wave formation information stored in the memory means, the updating or keeping of a digital value in an increment/decrement circuit 123 is controlled and the digital value is digital/analog-converted by a digital/analog (...

A variable wave forming circuit is provided which produces signals of various waveforms (e.g., sine, triangular or trapezoidal waves) and various frequencies. A random access memory (memory means) 121 to store wave formation information on waveform is provided. According to the wave formation information stored in the memory means, the updating or keeping of a digital value in an increment/decrement circuit 123 is controlled and the digital value is digital/analog-converted by a digital/analog (...

The curve-generating device serves in particular to produce signals relating to a circular line from simple algorithms. The device comprises means for computing a parameter .DELTA.L defined by ##EQU1## where U is an elementary vector, .theta. is the angle at the center of a polygon of side U+.DELTA.L circumscribed about the circle R, and processing logic circuits for determining the polar direction P.sub.n of the plotted line according to the relation: ##EQU2## where