Visualization with Nurbs Using Simulated Annealing Optimization Technique
نویسنده
چکیده
ACKNOWLEDGEMENTS In the name of Allah, Most Gracious, Most Merciful All praise and glory to Almighty Allah (Subhanahu Wa Taalaa) who gave me courage and patience to carry out this work. Peace and blessing of Allah be upon last Prophet Muhammad (Peace Be Upon Him). Acknowledgment is due to King Fahd University of Petroleum & Minerals for supporting this research. My unrestrained appreciation goes to my advisor, Dr. Muhammad Sarfraz, for all the help and support he has given me throughout the course of this work and on several other occasions. I simply cannot begin to imagine how things would have proceeded without his help, his support, and his patience. I also wish to thank my thesis committee members Dr. Wasfi Ghassan Al-Khatib and Dr. Onur Toker for their help, support, and contributions. I also acknowledge my colleagues and friends as I had a pleasant, enjoyable and fruitful company with them. Finally, I wish to express my gratitude to my family members for being patient with me and offering words of encouragements to spur my spirits, at moments of depression. Figure (3.8b) A quadratic curve using the basis functions of figure 3.8a. (Youssef [35]) 30 Figure (3.9) The strong convex hull property for a quadratic B-Spline curve; for) , [ 1 + ∈ i i u u u ,) (u C is in the triangle i i i P P P 1 2 − −. Figure (3.10) The strong convex hull property for a cubic B-Spline curve; for) , [ 1 + ∈ i i u u u ,) (u C is in the quadrilateral i i i i P P P P 1 2 3 − − −. Figure (3.11) A quadratic B-Spline curve on } 1 , 1 , 1 , 5 / 4 , 5 / 3 , 5 / 2 , 5 / 1 , 0 , 0 , 0 { = U. The curve is a straight line between) / (5 2 C and) / (5 3 C. Figure (3.12) A cubic curve on } 1 , 1 , 1 , 1 , 4 / 3 , 2 / 1 , 4 / 1 , 0 , 0 , 0 , 0 { = U ; moving 4 P (to / 4 P) changes the curve in the interval) 1 , 4 / 1 [. x Figure (3.13) B-Spline curves (b) A quadratic curve using …
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