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Article
Statistical and Visual Analysis of Error In Interpolating Sculptured Surfaces

Authors: Tahseen F. Abbas --- Aqeel S. Baden --- Muhamed A. Salih
Journal: Engineering and Technology Journal مجلة الهندسة والتكنولوجيا ISSN: 16816900 24120758 Year: 2011 Volume: 29 Issue: 12 Pages: 2520-2538
Publisher: University of Technology الجامعة التكنولوجية

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Abstract

This paper presents a general method for automatic surface interpolation fromrange data and describes the implementation of high order 2D langrangian methodsfor interpolating surfaces from 3rd to 8th order. It uses a modified 2D lagrangianmethod to interpolating, reconstructing and modeling several surfaces, and due to thisinterpolation there will be an error between interpolated surface and the original one,this paper present an algorithm to detect, represent and analyze these interpolatingerrors and statistical criteria to compare the error in representing the sculpturedsurfaces that interpolated with different order basis functions. The comparison isperformed using a mathematically defined data as real data obtained from theproposed models.The system has been implemented for the design of several sculptured surfaces toillustrate the system flexibility. Then the design results have been implemented formanufacturing two of these surfaces using three axis vertical CNC milling machinetool with ball end mill cutter. The method can be used in a variety of CAD/CAMapplications and it has proven to be effective as demonstrated by a number ofexamples using real data from mathematical functions. By applying the proposedsurface interpolating models the percent error was found to be ranged between0.00001% for some model to 3.5% for some other interpolated models with Lagrangemethod.


Article
Surface Fitting and Representation By Using 2D Least Squares Method in CAD Applications

Authors: Tahseen F. Abbas --- Omar A. Raheem --- Abdulwahab N. Abbas
Journal: Engineering and Technology Journal مجلة الهندسة والتكنولوجيا ISSN: 16816900 24120758 Year: 2011 Volume: 29 Issue: 7 Pages: 1425-1437
Publisher: University of Technology الجامعة التكنولوجية

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Abstract

This paper presents a general method for automatic surface fitting fromscattered range data and describes the implementation of three methods for fittingsurfaces: linear, quadratic and cubic. It uses a modified 2D least squares method tofitting, reconstructing and modeling several surfaces and statistical criteria tocompare the three approaches. The comparison is performed using amathematically defined data as real data obtained from the proposed models.The method can be used in a variety of applications such as reverse engineering,automatic generating of a CAD model, etc, and it has proven to be effective asdemonstrated by a number of examples using real data from mathematicalfunctions ( sine, cosine, exponential and cubic). By applying the proposedsurface fitting model the standard deviation was found to be (0.04-0.26), (0.02-0.07) and (0.0-0.12) mm for linear, quadratic and cubic fitting modelsrespectively.


Article
Mathematical Technique for Controlling the Gaps in the Cubic Bezier Curves for Two Dimensional

Author: Ali Hassan Hammadie
Journal: Engineering and Technology Journal مجلة الهندسة والتكنولوجيا ISSN: 16816900 24120758 Year: 2011 Volume: 29 Issue: 9 Pages: 1662-1672
Publisher: University of Technology الجامعة التكنولوجية

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Abstract

Designs are generated in the Bezier curves at most contains gaps in form that isdrawn up in curve. This state is causing misshaping final form that depended oncurves generating.In this research applies of suggested method is making Bezier curve generatingdon't contains upon gaps and can controlled to eliminate gaps by using addedparameters to control it.The research applies modified equations by using different shapes in differentcases and brought shapes (curves) don't contain the gaps and smoothing curves' .


Article
Hardware Implementation of 3D-Bresenham's Algorithm Using FPGA
تنفيذ الكيان المادي لخوارزمية برزنهام ثلاثية الأبعاد باستخدام مصفوفة البوابات المبرمجة حقلياً

Author: Dr. Basma Mohammed Kamal Younis, Lecturer Ne'am Salim Mohammed Sheet
Journal: Tikrit Journal of Engineering Sciences مجلة تكريت للعلوم الهندسية ISSN: 1813162X 23127589 Year: 2013 Volume: 20 Issue: 2 Pages: 37-47
Publisher: Tikrit University جامعة تكريت

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Abstract

Traditional 3D-Bresenham's algorithm is efficient in generating lines on raster systems using only integer calculations. This algorithm is needed as a solution of hidden surface problem using depth-buffer method to calculate z value for each pixel, while calculated values of x and y are used to address frame buffer memory, z value is used to test hidden surface by saving the closest depth in depth buffer.In this paper Bresenham's algorithm for plotting 3D-lines is examined then modified to simplify hardware requirements during implementation phase. Basing on efficiency of the algorithm on the space symmetry an enhanced version of this algorithm is implemented using OpenGL. Experimental results confirm results calculated theoretically for both traditional and modified algorithms.The hardware implementation is accomplished for real time applications, and a graphic sub-system is designed using FPGA. Finally, a comparison is accomplished for Spartan3E utilization which is used to implement the hardware

تعد خوارزمية برزنهام التقليدية خوارزمية كفوءة تستخدم في توليد الخط المستقيم ثلاثي الأبعاد في الأنظمة النقطية باستخدام حسابات القيم الصحيحة فقط. كما أن هذه الخوارزمية تقوم بحل مشكلة الأوجه المخفية التي تستخدم طريقة ذاكرة العمق لحساب قيمة البعد الثالث لكل نقطة شاشة. تستخدم قيم الاحداثي السيني والصادي لحساب عناوين ذاكرة الصورة وقيمة البعد الثالث لفحص الأوجه المخفية بواسطة حفظ العمق الأقرب للناظر في ذاكرة العمق.في هذا البحث تم دراسة خوارزمية برزنهام لرسم الخطوط ثلاثية الأبعاد وتطويرها لتناسب متطلبات مرحلة التنفيذ بالكيان المادي. اعتماداً على خاصية التناظر تم تحسين الخوارزمية باستخدام مكتبة الرسم المفتوحة المعروفة بـ(OpenGL) حيث تم مطابقة النتائج العملية والنظرية لكلتا الخوارزميتين التقليدية والمطورة. تم تنفيذ الكيان المادي لخوارزمية برزنهام ثلاثية الأبعاد بعد تطويرها لأغراض تحقيق الأداء في الزمن الحقيقي, حيث تم تنفيذ منظومة الرسم الفرعية باستخدام البوابات القابلة للبرمجة حقلياُ. وأخيراً تم إجراء مقارنة بين المعماريتين المصممتين من ناحية الاستفادة من مصادر رقاقة Spartan3E المستخدمة للتنفيذ المادي.

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