Digital differential analyzer

Abstract: A scaling apparatus is disclosed for horizontally and vertically scaling scan line information stored in a video memory prior to providing the scan line information to a computer display. Horizontal scaling apparatus is provided in which a first clock signal is provided for graphics portions of scan lines and a second clock signal is provided for video portions of scan lines. The second clock signal is enabled in a manner such that the second clock signal exhibits a predetermined phase relationship with respect to the first clock signal from scan line to scan line. The frequency of the second clock signal is selected to determine the scaling of the video portion of the scan line. Vertical scaling apparatus is provided in which scan line information corresponding to first and second scan lines is retrieved from a video memory. A digital differential analyzer, external to the central processing unit, then determines respective weights for the first and second scan lines dependent on the amount of vertical scaling desired. The weights for the first and second scan lines are then provided to a weighted adder which adds the first and second scan lines according to these weights.

Abstract: A digital differential analyzer is arranged to compute the sum of the first n terms of a Taylor series representing a function of an independent variable where n is an odd integer greater than unity. It includes means for detecting changes in the independent variable and comparing them with two or more standard increment sizes and calculating the effect of an increment of the nearest standard increment size on the value of the function. A specific example for calculating sin theta and cos theta is described.

Abstract: In conventional digital differential analyzers (DDA), the word length used for the transmission of information between integrators is restricted to at most a single magnitude bit and a sign bit. This restriction seriously limits integrator frequency response and has to a large extent been responsible for the failure of DDAs to achieve widespread acceptance as general purpose differential analyzers. In this paper it is shown that DDA speed and accuracy can be greatly improved by using increment word lengths which are approximately one-half the length of integrand registers providing that integration formulas more accurate than Euler integration are used. The programming of such machines for the solution of both linear and nonlinear differential equations is discussed and a quantitative evaluation of performance improvement is presented. At the same time, an effort is made to isolate the principal difficulties in hardware implementation which result from extending the integrator increment resolution.

Abstract: An apparatus and method for mapping data associated with spacial polar angles into a Cartesian coordinate system is disclosed. In the described application, ultrasound returns from a rotating transducer are mapped into a memory to permit presentation on a raster scanned display. A tangent function is used to compute X and Y locations in a digital differential analyzer. The selection of data for these locations is controlled with a secant function by a second digital differential analyzer to minimize quantizing errors.