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Subdivision Schemes and Their Applications in Geometric Modeling

Thesis Info

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Author

Pakeeza Ashraf

Program

PhD

Institute

The Islamia University of Bahawalpur

City

Bahawalpur

Province

Punjab

Country

Pakistan

Thesis Completing Year

2015

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/6778/1/Pakeeza_Ashraf_Maths_Islamia_Univ_Bahawalpur_2015.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727411573

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Subdivision is a basic tool to describe smooth curves and surfaces in computer aided geometric design. Since no single subdivision scheme can be adequate for every situation so, there is always a space to present new schemes. The main purpose of this dissertation is to introduce different kinds of subdivision schemes for curve and surface designing based on arity and complexity. Several explicit formulae for generation of mask of subdivision schemes are presented. Many well known existing schemes are special cases of our proposed schemes. Convergence and smoothness of stationary and non-stationary subdivision schemes are evaluated by using Laurent polynomial method and asymptotic equivalence technique respectively. Some of remarkable properties of proposed subdivision schemes like Hölder regularity, support of basic limit function, error bounds, total absolute curvature, artifact, shrinkage effect, limit stencil, convexity preservation, affine invariance and reproduction are discussed. The applications of the schemes developed have also been depicted through different examples.
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بسم اللہ الرحمن الرحیم
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ملاوٹ کرپشن ہے سب کا مزاج
خدا جانے بدلے گا کب یہ سماج
صاحبِ صدر!
انٹی کرپشن یعنی انسداد بدعنوانی کے لفظ سے ہی یہ بات مترشحّ ہورہی ہے کہ بدعنوانی کو :
کوئی معاشرہ ، کوئی قوم، کوئی خاندان کسی لحاظ سے بھی مستحسن قرارنہیں دیتا، جس مضمون کا عنوان ہی غیر مناسب اور ناموزوں ہو اس میں موجود موادکبھی اچھے نتائج برآمد نہیں کرسکتا۔
کرپشن کے لفظ میں سینکڑوں برائیاں ، سینکڑوں نازیبا حرکات پنہاں ہیں ، کرپشن کا اژدہا معاشرے کے حسن کو اپنی بھیانک شکل سے شب بیماراں کرنے کے درپے ہے۔ کرپشن جس مقام پر بھی ہو تو اس کی شائستگی اور شیفتگی کا قلع قمع کر دیتی ہے۔
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مجاہد سرحد پر کھڑ اتساہل اور غفلت کا شکار ہے تو وہ بھی کرپشن کر رہا ہے۔ مسیحااپنے فرائضِ منصبی بطریقِ احسن سرانجام نہیں دے رہا تو وہ بھی بدعنوانی اور کرپشن کا شکار ہے۔ اس کی لا پرواہی سے مریض لقمہ اجل بن رہے ہیں تو اس عظیم پیشہ سے وابستہ شخص گویا انتہائی درجے کابدعنوان اور کرپٹ ہے۔
معزز سامعین!
کر پشن اور بدعنوانی کے حامل شخص سے خلاصی انتہائی ناگزیر ہے۔ بدعنوانی کے خوفناک سالوں سے نکلنے کے لیے دیانتداری اور ایمان داری کی شمع کو منور کرنا ہوگا۔ اسلام کے گلشن سے گلہائے رنگارنگ کا نظارہ کرنا ہوگا، جرأت اور جوانمردی کے اسپ تازی کی شاہسواری کرنی ہوگی۔
صدرِ ذی وقار!
کرپشن اور بدعنوانی ایسی نہیں کہ ناپ تول میں کمی کی جائے ، ہر غیر اخلاقی...

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