Envelope constrained filter with linear interpolator

1997 ◽  
Vol 45 (6) ◽  
pp. 1405-1414 ◽  
Author(s):  
Ba-Ngu Vo ◽  
A. Cantoni ◽  
Kok Lay Teo
Keyword(s):  
Linear Interpolator

Alternating projections and interpolation of stationary processes

1992 ◽  
Vol 29 (4) ◽  
pp. 921-931 ◽  
Author(s):  
Mohsen Pourahmadi
Keyword(s):  
Missing Values ◽  
Stationary Process ◽  
Dimensional Space ◽  
Stationary Processes ◽  
Finite Dimensional Space ◽  
Alternating Projections ◽  
Von Neumann ◽  
Finite Dimensional ◽  
Explicit Formulae ◽  
Linear Interpolator

By using the alternating projection theorem of J. von Neumann, we obtain explicit formulae for the best linear interpolator and interpolation error of missing values of a stationary process. These are expressed in terms of multistep predictors and autoregressive parameters of the process. The key idea is to approximate the future by a finite-dimensional space.

A GRAPHICS ACCELERATOR FOR HIDDEN SURFACE REMOVAL AND COLOR SHADING

1991 ◽  
Vol 01 (03) ◽  
pp. 239-255
Author(s):  
SEONG-OK BAE ◽  
KYUNG-IL BANG ◽  
CHONG-MIN KYUNG
Keyword(s):  
Reasonable Cost ◽  
Hidden Surface Removal ◽  
Left And Right ◽  
Functional Blocks ◽  
Fast Rendering ◽  
Binary Tree Structure ◽  
The Given ◽  
Linear Interpolator ◽  
Color Shading ◽  
Bit Serial

In this paper, we describe a special purpose hardware called ESEU (Expandable Shading Engine Unit) for fast rendering of 3-D scenes using Gouraud shading model. Each ESEU has three major functional blocks: linear interpolator, multipliers and Edge Painting Tree. Linear interpolator with coupled binary tree structure yields the functional values at all pixels within each zone (zone denotes the smallest interval which encompasses the given span and consists of 2n successive pixels in the x-direction, where n is some integer) by interpolating the functional values, such as z-depth values or color intensities, at the left and right end points of the zone which are calculated by the multipliers. Mask pattern for the removal of data for the pixels outside the original span but within the corresponding zone is generated by the Edge Painting Tree. Since there are no interconnections among ESEU’s, graphics system with any screen size can be easily built using a multitude of the prototype ESEU’s. A prototype ESEU in this work handles 64 pixels; therefore, 16 ESEU’s are required for screens having a 1024-pixel width. The bit-serial nature of the prototype ESEU is suitable for its VLSI implementation at a reasonable cost.

A Quintic Spline Interpolator for Motion Command Generation of Computer-Controlled Machines

1992 ◽  
Author(s):  
D. C. H. Yang ◽  
Fu-Chung Wang
Keyword(s):  
Quintic Spline ◽  
Motion Trajectories ◽  
Command Generation ◽  
Position Data ◽  
Data Points ◽  
On Line ◽  
Computer Controlled ◽  
Speed Accuracy ◽  
Linear Interpolator ◽  
Accuracy Speed

Abstract This paper presents a new method of motion command generation for computer controlled multi-axis machines. The method is based on a quintic spline interpolator (QSI) which generates motion commands to trace a set of desired discrete position data via a composite quintic spline (CQS). This CQS is nearly arc length parametrized and has both tangents and curvatures continuous at the data points. Consequently, the generated motion trajectories are continuous in both velocity and acceleration throughout the motion. A quick motion command generation scheme is also developed. Compared to the existing linear interpolator (LI), the proposed method takes comparable execution time, but is superior in many other aspects, including position accuracy, speed smoothness, acceleration continuity, torque requirement and jerk reduction. Compared to the existing cubic spline interpolator (CSI), the proposed method is able to maintain a similarly smooth composite profile, but better speed accuracy. On-line implementation of this interpolator is believed very promising.

Design of Interpolation Algorithm in the Multi-Axis Motion Control System

2011 ◽  
Vol 411 ◽  
pp. 259-263
Author(s):  
Hai Ming Shen ◽  
Kun Qi Wang ◽  
Yong You Tian
Keyword(s):  
Control System ◽  
Motion Control ◽  
Modular Design ◽  
Interpolation Algorithm ◽  
Interpolation Theory ◽  
Processing Efficiency ◽  
Motion Control System ◽  
Quartus Ii ◽  
Linear Interpolator ◽  
Schematic Diagrams

This paper describes an interpolation algorithm in the multi-axis motion control system, which can achieve six-axis interpolation operations, greatly improving the processing efficiency. Using modular design idea on the Quartus II platform, by DDA interpolation theory, interpolation modules are built through VHDL. And these interpolator modules are connected into schematic diagrams. By those schematic diagrams a linear interpolator, a circular interpolator and a composite interpolator are formed. The corresponding functions of those interpolators have been simulated on the Quartus II platform. The simulation shows that this interpolation algorithm is effective to complex multi-axis motion control system.

Digital linear interpolator

1972 ◽  
Vol 8 (10) ◽  
pp. 256-257
Author(s):  
J.P. Chambers
Keyword(s):  
Linear Interpolator

A Quintic Spline Interpolator for Motion Command Generation of Computer-Controlled Machines

1994 ◽  
Vol 116 (1) ◽  
pp. 226-231 ◽  
Author(s):  
D. C. H. Yang ◽  
Fu-Chung Wang
Keyword(s):  
Quintic Spline ◽  
Motion Trajectories ◽  
Command Generation ◽  
Position Data ◽  
Data Points ◽  
On Line ◽  
Computer Controlled ◽  
Speed Accuracy ◽  
Linear Interpolator ◽  
Accuracy Speed

This paper presents a new method of motion command generation for computer controlled multi-axis machines. The method is based on a quintic spline interpolator (QSI) which generates motion commands to trace a set of desired discrete position data via a composite quintic spline (CQS). This CQS is nearly arc length parametrized and has second order continuous at the data points. Consequently, the generated motion trajectories are continuous in both velocity and acceleration throughout the motion. A quick motion command generation scheme is also developed. Compared to the existing linear interpolator (LI), the proposed method takes comparable execution time, but is superior in many other aspects, including position accuracy, speed smoothness, acceleration continuity, torque requirement, and jerk reduction. Compared to the existing cubic spline interpolator (CSI), the proposed method is able to maintain a similarly smooth composite profile, but better speed accuracy. On-line implementation of this interpolator is believed very promising.

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