تصميم خوارزمية استيفاء تحليل رقمي تفاضلي عالية الدقة

Authors

  • إبراهيم الشامي

Abstract

تبحث هذه الورقة  في تحليل و مقارنة دقة التوليد بخوارزميات الاستيفاء المستندة على التحليل الرقمي التفاضلي ، ويتم طرح خوارزمية جديدة تتصف بدقة توليد أعلى من جميع الخوارزميات المعروفة حالياً. تعتمد المقارنة على حساب معين مصفوفة الانتقال T ، حيث ترتبط الإحداثيات الحالية Pi بالإحداثيات الآتية Pi+1 بالعلاقة العودية Pi+1=T.Pi، ويكون بشكل عام .

وتعتمد الخوارزمية المقترحة على فرض قيمة cosθ بحيث تساوي، وحساب sinθ بحيث يكون معين مصفوفة الانتقال أقرب ما يمكن للواحد الصحيح ، وتستخدم مصفوفة الانتقال في حساب إحداثيات أول نقطة مولدة، وتحسب إحداثيات باقي النقاط من علاقة هنرييه:

{ Pi+2= (2cosθ).Pi+1-Pi }    i >0 .

In this paper the writer presents a new algorithm for circular interpolation DDA. The accuracy of this algorithm is much higher than all others compared in this paper.

The comparison in algorithms of interpolation depends on calculating a determinant of the rotation matrix T. We may obtain the following recurrence formula: , where {Pi} i>0 is an equidistance point sequence on circular arc and T is a rotation matrix: .

Our method is based on imposing a value of cosθ as: (cosθ ) and calculating the value of sin where the determinant |T| equals unity. This results that: .

We used cosθ and sinθ calculating the value of coordinates a single point which comes after the initial point directly. The rest of the interpolation points are calculated by Henrie's equation: { Pi+2= (2cosθ).Pi+1-Pi }    i >0 .

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Published

2019-01-24

How to Cite

1.
الشامي إ. تصميم خوارزمية استيفاء تحليل رقمي تفاضلي عالية الدقة. Tuj-eng [Internet]. 2019Jan.24 [cited 2024Nov.24];29(1). Available from: https://journal.tishreen.edu.sy/index.php/engscnc/article/view/6974

Issue

Vol. 29 No. 1 (2007): العلوم الهندسية

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Articles

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