Eng.&Tech.Journal,Vol.29,No.12 ,2011 *Production and Metallurgy Engineering Department, University of Technology/Baghdad ** Al Anbar Technology Institute/ Al Anbar 2520 Statistical and Visual Analysis of Error In Interpolating Sculptured Surfaces Dr.Tahseen F. Abbas*, Aqeel S. Baden* & Muhamed A. Salih** Received on: 4/4/2011 Accepted on: 21/7/2011 Abstract This paper presents a general method for automatic surface interpolation from range data and describes the implementation of high order 2D langrangian methods for interpolating surfaces from 3 rd to 8 th order. It uses a modified 2D lagrangian method to interpolating, reconstructing and modeling several surfaces, and due to this interpolation there will be an error between interpolated surface and the original one, this paper present an algorithm to detect, represent and analyze these interpolating errors and statistical criteria to compare the error in representing the sculptured surfaces that interpolated with different order basis functions. The comparison is performed using a mathematically defined data as real data obtained from the proposed models. The system has been implemented for the design of several sculptured surfaces to illustrate the system flexibility. Then the design results have been implemented for manufacturing two of these surfaces using three axis vertical CNC milling machine tool with ball end mill cutter. The method can be used in a variety of CAD/CAM applications and it has proven to be effective as demonstrated by a number of examples using real data from mathematical functions. By applying the proposed surface interpolating models the percent error was found to be ranged between 0.00001% for some model to 3.5% for some other interpolated models with Lagrange method. Keywords: Sculptured Surfaces, Bivariate Interpolating, Computer Graphics, Error Analysis, Lagrange Interpolating واﻟ اﻻﺣﺼﺎﺋﻲ اﻟﺘﺤﻠﯿﻞ ﺒﺼﺮي اﻟﻨﺎﺗﺞ اﻟﺨﻄﺄ ﻟﻘﯿﻤﺔ اﺳﺘﻜﻤﺎل ﻣﻦ اﻟﻤﺘﻌﺮﺟﺔ اﻟﺴﻄﻮح اﻟﺨـﻼﺻــﺔ ﯿﺔ اﻟﮭﻨﺪﺳﻄﻮح اﻟﺴﻞ وﺗﻤﺜﯿﺘﻜﻤﺎل ﻻﺳﺔ ﻋﺎﻣﺔ ﻃﺮﯾﻘﺚ اﻟﺒﺤﺬا ھﺪم ﯾﻘﺔ اﻟﻤﺘﻌﺮﺟﺔ ﻃﺮﯾﻘﺘﺨﺪام ﺑﺎﺳ ﻻﻛﺮاﻧﺞﯿﺔ اﻟﮭﻨﺪﺳﺎت ﻟﻠﺘﻄﺒﯿﻘﺔ ﻣﻼﺋﻤﺎ ﻟﺠﻌﻠﮭﺎ وﺗﻄﻮﯾﺮھﺔ اﻟﻌﺪدﯾ ﻟﻠﺘﺤﻠﯿﻼت, ﺎد اﻋﺘﻤﻢ ﺗﺪ وﻗﺎت درﺟﺪة ﻋ ﻟﻼﺳﺘﻜﻤﺎل اﻟﺜﺎﻣﻨﺔ اﻟﺪرﺟﺔ ﻟﻐﺎﯾﺔ اﻟﺜﺎﻟﺜﺔ اﻟﺪرﺟﺔ ﻣﻦ ﻟﺘﻮ اﻟﺴﻄﻮح ﺑﯿﺎﻧﺎت ﻟﯿﺪءﺮا ﺟﻦ ﻣﺎﺗﺞ اﻟﻨﺄ اﻟﺨﻄﻞ وﺗﺤﻠﯿ ﻢ ﺛﺘﻜﻤﺎل اﻻﺳﻖ اﻟﺘﻄﺒﯿﻢ ﺗﺚ ﺣﯿﺚ اﻟﺒﺤﺬا ھﻲ ﻓﺔ اﻟﻤﻘﺘﺮﺣﻄﻮح ﻟﻠﺴﺔ اﻟﺤﻘﯿﻘﯿﺎت اﻟﺒﯿﺎﻧﻊ ﻣﺎﺋﺞ اﻟﻨﺘﺔ ﻣﻘﺎرﻧ ﻷﺔ رﺑﻌﺢﻄﺳ أﺔ ﺗﻜﻌﯿﺒﯿﺔ داﻟ وﯿﺔﺳ أﺔ داﻟ وﺐ اﻟﺠﯿﺪاﻟﺔـ ﺑﺔ ﻣﻤﺜﻠ, ﻤﯿﻤﯿﺔﺼ اﻟﺘﺎت اﻟﺒﯿﺎﻧﺘﺜﻤﺎر اﺳﻢ ﺗ  ﻣﺔ اﻟﻤﺘﻌﺮﺟ ﻟﻠﺴﻄﻮح اﻟﻤﺴﺘﻨﺘﺠﺔﺎت اﻟﺒﯿﺎﻧﺘﻜﻤﺎل اﺳﻼل ﺧ ﻦﺔ اﻟﻤﻘﺘﺮﺣﺮاﻧﺞ ﻻﻛﺔ ﺑﻄﺮﯾﻘﻊﻨﯿﺼ ﻟﺘﻄﺤﯿﻦ ﺳ ﺮﺟﯿﻦ ﻣﺘﻌيﺪد ﻋﻢ ﺗﺤﻜ ذاتﺔ ﻋﻤﻮدﯾﺰﺮﯾﻔ ﺗﺔ ﻣﺎﻛﻨﺘﺨﺪام ﺑﺎﺳﺔﻔ ﻣﺨﺘﻠﺘﻜﻤﺎل اﺳﺪرﺟﺎت وﺑﺎور ﻣﺤﺜﻼث ﺑ ﻛﺮوﯾﺔ ﻧﮭﺎﯾﺔ ذاتﺰﺮﯾﻔ ﺗ وﻋﺪد ﺔ ﯾﻘﺮ اﻟﻄﺔﺎﻋﻠﯿ ﻓﺎﺋﺞ اﻟﻨﺘﺮتﮭﻇ ا وﺎت ﻟﻠﺒﯿﺎﻧﻲﺎﺋﺼ اﻻﺣﻞ اﻟﺘﺤﻠﯿﻼل ﺧﻦ ﻣﺔ اﻟﻤﻘﺎرﻧﺖ وﺗﻤ اﻟﺎﯿﺮھﻏ وبﻮ ﺑﺎﻟﺤﺎﺳ اﻟﻤﻌﺎنﻤﯿﻢﺼ اﻟﺘ و اﻟﻌﻜﺴﯿﺔ اﻟﮭﻨﺪﺳﯿﺔ ﺗﻄﺒﯿﻘﺎت ﻓﻲ اﻟﺴﻄﻮح ﻟﺘﻤﺜﯿﻞ اﻟﻤﻘﺘﺮﺣﺔ ﻤﻄﻮرة PDF created with pdfFactory Pro trial version www.pdffactory.com