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Geometric Modelling Using Subdivision Techniques

Thesis Info

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Author

Nadeem Ahmad

Program

PhD

Institute

University of the Punjab

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2007

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/410

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726338014

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Subdivision techniques are being appreciated in geometric modelling. Curves be- ing the basic ingredient of the surfaces, have their own importance. Since no single scheme can be fit for every situation so, there is always a room to introduce new schemes. In this dissertation the interpolating curve subdivision scheme developed by Weissman [50], has been analyzed, using Laurent polynomial method. More- over, four approximating curve subdivision schemes have been developed. These schemes have also been analyzed, using Laurent polynomial method. The local supports of these schemes are determined as well. Regarding surface generation, a mathematical model of a three dimensional object using cross sectional data has been constructed. An algorithm for generating quadrilateral net is presented. The contours have been generated interpolating the data at each section, using a linear subdivision scheme introduced by Dyn et al. [17]. The contours have been, then, blended using the non-linear subdivision scheme developed Aspert [2]. The im- plementation of the schemes developed have also been depicted through different examples.
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مظلوم بہن کی فریاد

مظلوم بہن کی فریاد

’’اگر مجھے پتہ ہوتا میری حکومت گرانے کے لیے میرے بھائی کو قتل کیا جائے گا ۔تو میں کبھی بھی پرائم منسٹر ہائوس کے لیے نہ لڑتی ۔‘‘

یہ کوئی سیاسی بیان نہیں ایک مظلوم بہن کی اپنے بھائی کے قتل پہ فریاد ہے ۔کنیزِ کر بلا کا یزیدیت کے خلاف مقدمہ ہے ۔مظلومیت کا نوحہ ہے ۔بھٹو خاندان پہ ہو نے والے مظالم ہمار ی تاریخ پہ بد نما داغ ہیں اور اس سے بھی بڑی بے ضمیری یہ ہے کہ قاتل انہیں قتل کرنے کے بعد قتل کا الزام بھی انہی پہ لگاتے رہے ۔

 

وہ دریا دیس سمندر تھی

جو تیرے میرے اندر تھی

وہ سوہنی مٹی سندھڑی کی

وہ لڑکی لال قلندر تھی

یادگارِ کار ساز

ہماری خاک سے خوشبو وطن کی آئے گی

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