Digital Differential Analyzer Research Articles

FVDB : A Deep-Learning Framework for Sparse, Large Scale, and High Performance Spatial Intelligence

We present f VDB, a novel GPU-optimized framework for deep learning on large-scale 3D data. f VDB provides a complete set of differentiable primitives to build deep learning architectures for common tasks in 3D learning such as convolution, pooling, attention, ray-tracing, meshing, etc. f VDB simultaneously provides a much larger feature set (primitives and operators) than established frameworks with no loss in efficiency: our operators match or exceed the performance of other frameworks with narrower scope. Furthermore, f VDB can process datasets with much larger footprint and spatial resolution than prior works, while providing a competitive memory footprint on small inputs. To achieve this combination of versatility and performance, f VDB relies on a single novel VDB index grid acceleration structure paired with several key innovations including GPU accelerated sparse grid construction, convolution using tensorcores, fast ray tracing kernels using a Hierarchical Digital Differential Analyzer algorithm (HDDA), and jagged tensors. Our framework is fully integrated with PyTorch enabling interoperability with existing pipelines, and we demonstrate its effectiveness on a number of representative tasks such as large-scale point-cloud segmentation, high resolution 3D generative modeling, unbounded scale Neural Radiance Fields, and large-scale point cloud reconstruction.

The implementation of digital differential analyzer algorithm for route determination’s topographic maps based on android

The route is direction that must be taken from the starting point to the destination point. Determination of the route is usually done for a reference trip that will be taken include the distance, time or slope of the terrain to be passed. In the implementation, the determination of the route is often used by agencies and organizations operating in the open nature where the activities require special expertise that can process geographic information systems. Although the tools and technology for route determination are sufficient, they are still less effective and efficient because to know the distance, time and slope of a terrain on topographic maps are still using conventional calculations, therefore the application of route determination’s topographic maps based android and applying Digital Differential Analyzer algorithm. The algorithm can be used as a line maker to display a slope picture of the field being traversed. This application was developed using the Rational Unified Process (RUP) method which has 4 stages: Inception, Elaboration, Construction, and Transition. This application can be run at least on Android platform version 4.1.

Voxelization Parallelism Using CUDA Architecture

The voxelization process is an essential stage in three dimensional (3D) graphics pipeline. Its implementation should precede displaying objects in the pipeline. In this paper, different Voxelization algorithms are modified and parallelized to accelerate the operation of this stage. The 3D Digital Differential Analyzer (DDA) algorithm is used for line voxelization. This algorithm is utilized in triangle filling using the scan-line and the edge-function algorithms. The first one is designed to produce lines in parallel while the second can produce voxels. All these algorithms are parallelized using CUDA architecture and implemented on GPU processor. The actual implementation of these algorithms is examined and optimized according to the occupancy and block size metrics. The experimental results show that the acceleration amount of 3D DDA was about 4352x max compared to the OpenGL implementation, and the edge function implementation has been executed at a higher speed than the scan-line for object triangles voxelization.

Scheduling system for programed manipulator motion pattern of the parallel structure with flexible links

The use of manipulators with various designs has been recently increasing in the industry. The main construction types of manipulators are considered to be serial and parallel structures. In turn, parallel manipulators can be divided into flexible and rigid joints. The use of manipulators with parallel structures and flexible links in a number of industry fields can increase operational performance, but this type of manipulator remains the least studied. In the present research, an attempt is made to consider a method for planning the motion pattern of a manipulator gripper with parallel structures and flexible links. Planning the movement pattern of gripper is determined by the DDA algorithm (digital differential analyzer). The problem of forming the control actions on the automatic control system of the electrical drive for the links of the manipulator is considered. The results of full-scale modeling on a real model of a cable parallel structure manipulator are presented. The general functional diagram of the manipulator control is also considered in the research.

Extended unit arc length increment interpolation for generalized NURBS curves in multi-axis EDM

Multi-axis electrical discharging machining (EDM) is the main manufacturing approach for shrouded blisks. To maintain a stable discharging, the feedrate of an electrode must be regulated appropriately with respect to a workpiece. The feedrate control in multi-axis EDM is a challenge due to two facts. The first is that the feedrate fluctuations occur at line segment junctions along the feeding trajectory which is expressed in G01 codes. The second is that, with involvement of rotary axes, the feedrate control must consider the nonlinear mapping between the workpiece frame and the machine frame. This paper proposes an extended unit arc length increment interpolation (UALII) for generalized NURBS curves. Given the point coordinates in the machine frame, the coordinates in the workpiece frame can be obtained by the forward kinematics. By using the UALII, the curve parameter is first obtained. To achieve synchronization among involved axes, the curve parameter is substituted into the generalized NURBS curve. Due to the nonlinear mapping, each interpolation of one basic length unit (BLU) can give the axial increments which are more than one BLU. Digital differential analyzer (DDA) is used for a finer interpolation for each axial increment. Machining tests show that the use of UALII for generalized NURBS curves can decrease the machining time by 42.19%, 29.65% and 26.42%, respectively, as compared with the cases of no feedrate planning, the weighted average movement ratio algorithm (WAMRA) and the feedrate post-processing algorithm (FPPA). The extended UALII algorithm can also reduce the electrode wear.

Review and accuracy comparison of various permittivity-averaging schemes for material discontinuities in the two-dimensional FDFD method: implementation using efficient computer graphics techniques.

Several known and widely used averaging techniques aiming to improve the accuracy of the two-dimensional finite-difference frequency-domain (FDFD) method, in the presence of material discontinuities, are reviewed, numerically tested, and compared with respect to their accuracies. Furthermore, all averaging techniques are rigorously and efficiently implemented using the Supercover Digital Differential Analyzer algorithm and a modified Liang-Barsky algorithm suitably adapted from computer graphics applications. The FDFD with Gaussian blurring; the FDFD with volume-polarized effective permittivity; the FDFD with volume-polarized effective permittivity on shifted cells; and the FDFD with anisotropic smoothing [FDFD (AS)] are compared with respect to their accuracies (for both TE and TM polarization), in the case of scattering by an infinite homogeneous cylinder (for which analytical solution exists) comprising a lossless dielectric, a high-index, low-loss dielectric, or a metal. Sample plots of the relative errors are presented for various field components. Absolute error norms (L2 and L∞) are also presented for both polarizations and for two grid-cell sizes for quantitative comparisons. The results show that the FDFD (AS) prevails in accuracy mainly because it satisfies the boundary conditions at the cylinder's boundary the best. However, for the high-index dielectrics and metals, even the FDFD without any averaging gives very good results for the field components parallel to the uniformity direction. However, the FDFD (AS) is always more accurate when the in-plane field components are sought.

Fast exact digital differential analyzer for circle generation

In the first part of the paper we present a short review of applications of digital differential analyzers (DDA) to generation of circles showing that they can be treated as one-step numerical schemes. In the second part we present and discuss a novel fast algorithm based on a two-step numerical scheme (explicit midpoint rule). Although our algorithm is as cheap as the simplest one-step DDA algorithm (and can be represented in terms of shifts and additions), it generates circles with maximal accuracy, i.e., it is exact up to round-off errors.

Control System Design and Trajectory Planning for SCARA Robots

Based on STM32F407ZET6 microprocessor with ARM Cortex-M4 core, we designed a controller for servo motors and servo drivers of a 4-axis Selective Compliance Assembly Robot Arm (SCARA) robot. The forward and inverse kinematic equations are established, circular interpolation equations in three-dimensional space are derived by using the digital differential analyzer method. The adopted circular interpolation algorithm avoids to judge quadrant and feeding direction, which simplifies the program.

A Comparison of Standard One-Step DDA Circular Interpolators with a New Cheap Two-Step Algorithm

We present and study existing digital differential analyzer (DDA) algorithms for circle generation, including an improved two-step DDA algorithm which can be implemented solely in terms of elementary shifts, addition, and subtraction.

Efficient implementation of the 3D‐DDA ray traversal algorithm on GPU and its application in radiation dose calculation

The three-dimensional digital differential analyzer (3D-DDA) algorithm is a widely used ray traversal method, which is also at the core of many convolution∕superposition (C∕S) dose calculation approaches. However, porting existing C∕S dose calculation methods onto graphics processing unit (GPU) has brought challenges to retaining the efficiency of this algorithm. In particular, straightforward implementation of the original 3D-DDA algorithm inflicts a lot of branch divergence which conflicts with the GPU programming model and leads to suboptimal performance. In this paper, an efficient GPU implementation of the 3D-DDA algorithm is proposed, which effectively reduces such branch divergence and improves performance of the C∕S dose calculation programs running on GPU. The main idea of the proposed method is to convert a number of conditional statements in the original 3D-DDA algorithm into a set of simple operations (e.g., arithmetic, comparison, and logic) which are better supported by the GPU architecture. To verify and demonstrate the performance improvement, this ray traversal method was integrated into a GPU-based collapsed cone convolution∕superposition (CCCS) dose calculation program. The proposed method has been tested using a water phantom and various clinical cases on an NVIDIA GTX570 GPU. The CCCS dose calculation program based on the efficient 3D-DDA ray traversal implementation runs 1.42 ∼ 2.67× faster than the one based on the original 3D-DDA implementation, without losing any accuracy. The results show that the proposed method can effectively reduce branch divergence in the original 3D-DDA ray traversal algorithm and improve the performance of the CCCS program running on GPU. Considering the wide utilization of the 3D-DDA algorithm, various applications can benefit from this implementation method.

Optimization of Calculation of Field Orientation Time and Binarization of Fingerprint Images

The field orientation and the binarization in an image are often used in fingerprint identification and authentication, and analysis of textures. The proposed algorithm reuses the additions and multiplications in the calculation of the field orientation using the switching property and uses the Digital Differential Analyzer (DDA) algorithm in the generation of convolution masks for the binarization of fingerprint images. The performance of the processing time and the result of the proposed binarization algorithm compared to the performance of algorithms that use convolutions masks were satisfactory compared to the other algorithms found in literature.

New Digital Differential Analyzer Linear Interpolation Program and Error Analysis

Common digital differential analyzer（DDA）linear interpolation error is lower than a pulse equivalent, and the output pulse along each axis is not uniform. New DDA linear interpolation flow chart was obtained by combining a quick algorithm of DDA interpolation and interpolating algorithm for pulses uniformization with common DDA linear interpolation principle. The relationship between interpolation error and pulse equivalent was demonstrated in detail. As the results shows, the new DDA with high precision machining but simple algorithm, increased interpolating speed; the new algorithm make the generation of uniform pulse series come true, which is of great importance to keep stepping motor rotating steadily without missing steps; At coordinate origin, interpolation error is lower than 0.42 pulse equivalent, while the interpolation point is not at coordinate origin, interpolation error is lower than 0.5 pulse equivalent.

Study on Interpolation of NC Based on VB

This paper discusses the basic principle of numerical control interpolation, including the straight line and arc (Agreeable circle or Negative circle) interpolation method of point by point comparison, Digital Differential Analyzer (DDA) and time-slicing method. By using Visual Basic 6.0 software, the implementation of the interpolation process and dynamic simulation results are displayed on the screen, and the implementation process of interpolation is observed directly, such as continuous interpolation, manual interpolation, step interpolation and interpolation of a closed graph.

A Circular Interpolation Algorithm for NC Machining Trace Control Based on Angle Approximation Theorem

. DDA（Digital Differential Analyzer）circular interpolation algorithm is often applied to NC（Numerical Control） machining trace control, due to the greater error accumulation in DDA interpolation algorithm, the maximum feed speed of machine tool is limited, and the interpolation algorithm is hardly satisfied with the requirements for high-precision and high-speed machining. To solve this problem, a new circular interpolation algorithm based on the angular approximation method was proposed, the fundamental rule, calculation program and calculating process were introduced, and then, this interpolation algorithm was compared with the other DDA interpolation algorithm in error accumulation. It is concluded from comparative analysis and practical application that the new interpolation algorithm does not exist any accumulative error in the speed and outline, the interpolation error is little, the algorithm is simple and easy to be realized as well.

Research on new software compensation method of static and quasi-static errors for precision motion controller

To reduce mechanical vibrations induced by big errors compensation, a new software compensation method based on an improved digital differential analyzer (DDA) interpolator for static and quasi-static errors of machine tools is proposed. Based on principle of traditional DDA interpolator, a DDA interpolator is divided into command generator and command analyzer. There are three types of errors, considering the difference of positions between compensation points and interpolation segments. According to the classification, errors are distributed evenly in data processing and compensated to certain interpolation segments in machining. On-line implementation results show that the proposed approach greatly improves positioning accuracy of computer numerical control (CNC) machine tools.

Design and implementation of integrated non-uniform rational B-spline and digital differential analyser interpolators for computerized numerical control servocontrollers

The purpose of this article is to propose the design and implement an efficient and open real-time non-uniform rational B-spline (NURBS) interpolator for computerized numerical control (CNC) motion control. The proposed architecture of real-time NURBS interpolator integrates the advantages of digital differential analyser (DDA) and the native NURBS interpolator with the help of the data conversion module. First, the desired compensation positions are generated by NURBS interpolator concerning feedrate and curvature for manufacturing accuracy. A data conversion module is then applied to transform the position commands from float to integer. Using this integral-type position command, the pulse trains can be generated by DDA for the AC servomechanism in position mode. The simulation and experimental results validate that this novel real-time NURBS controller is effective and efficient enough to drive the general servomechanism without changing the control scheme of the traditional AC servomotor.

Realization of a Digital Differential Analyzer Using CPLDs

The objective is to design and fabricate a wire programmable discrete version of an analog computer known as the digital differential analyzer (DDA) using the binary rate multiplier (BRM) principle without using analog components like operational amplifiers. The bandwidth of the elements can be more than 50kHz. The BRM enables arithmetic-free signal processing. Programming a DDA based on the BRM principle is very similar to the programming of an analog computer due to the structural similarity. The DDA described in this paper uses two wires each at the input and the output ports. One wire is used for carrying the magnitude of the signal in the pulse-rate form and the other wire for the sign of the signal. The paper aims at simulating and synthesizing various modules of a stand-alone-DDA and downloading the synthesized modules on to complex programmable logic devices (CPLDs). Interconnecting various modules in the CPLD can solve differential equations. The results obtained in real time were verified by simulation using (i) ModelSim, (ii) Simulink and (iii) analytical solution of equivalent Z-domain blocks.

REALIZATION OF A DIGITAL DIFFERENTIAL ANALYZER USING CPLDs

The objective is to design and fabricate a wire programmable discreteversion of an analog computer known as the digital differentialanalyzer (DDA) using the binary rate multiplier (BRM) principlewithout using analog components like operational amplifiers.

Parametric curve machining of a CNC milling EDM

A buffered digital differential analyzer (BDDA) algorithm in a computerized numerical controller (CNC) performs milling electric discharge machining (milling EDM'ing) of a curve constructed from a sequence of segments using a traditional computer-aided manufacturing (CAM) system. The proposed algorithm interpolates more than one segment in a sampling interval and supports the effective machining of a parametric curve when the electrode crosses the connection between the short segments. The accuracy of both the speed and the trajectory of motion can be ensured without the time function of the parameter specified by two terms of a Taylor expansion, such as in a real-time parametric curve interpolator. The proposed algorithm is compared with the reference–word interpolation and real-time polynomial interpolation used in a milling EDM to confirm improvements of erosion speed.

Design and implementation of a linear jerk filter for a computerized numerical controller

The proposed filter is placed in front a buffered digital differential analyzer, and is formed by combining three modified moving average filters. It can export the position commands to ensure smooth and accurate motion of a tool with a linear jerk change. These output commands can guarantee contour accuracy despite the error in the chord height. The acceleration and jerk can be designed simply by specifying the number of registers. The filter can be implemented using three circular buffers to simplify the arithmetic and reduce the computation time. The high precision motion commands are confirmed by installing the filtering algorithm in a digital signal processor of a computerized numerical controller. The radius of the command trajectory does not become distorted at high speed 30 m/min. The commands filtered by the linear jerk filter stabilize the beginning and end of the actual motion of the machine table.