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Curves and Surfaces for Data Visualization Using Splines

Thesis Info

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External Link

Author

Shaikh, Tahira Sumbal

Program

PhD

Institute

University of the Punjab

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2013

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/2630/1/3103S.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676725807404

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This thesis deals with the visualization of regular and irregular (scattered) data using spline curves and surfaces. For the spline curves, a 1 C rational cubic spline is proposed and developed with two free parameters together the error analysis discussed. The proposed rational spline is used to develop three new curve schemes to visualize the shaped data of the positive, monotone and convex data. Algorithms have been developed for the three shape preserving curves schemes. These curve schemes are practically demonstrated for various data in literature. For the visualization of regular grid data, the proposed curve interpolants are extended to their surface counter parts (rational bi-cubic functions) over the rectangular grid. Each boundary curve of the rectangular grid is constructed by the rational cubic functions having two free parameters in its description. This work has been further extended to device three new surface schemes for the visualization of shaped data by imposing data dependent constraints on free parameters; first scheme for the visualization of positive data, second for the visualization of monotone data and third for the visualization of convex data. The algorithms have been designed, for each of surface schemes, to efficiently compute the proposed shape preserving surfaces. The proposed surface schemes are practically demonstrated to shape preserving data. The degree of smoothness attained is 1,1 C . Lastly three schemes are introduced for the visualization of scattered data in the view of positive, monotone and convex surfaces. The given scattered data is triangulated over the domain and piecewise rational cubic function is used for the interpolation of boundary and the radial curves. The final visualized surface is the convex combination of boundary and the radial curves facilitating twelve parameters in each triangular patch. The data dependent constraints are derived on six of the free parameters for visualization of positive, monotone and convex shape of scattered data, while remaining six parameters are free for shape modification. These proposed schemes are local, computationally economical, do not constrain step length, and are equally applicable to data with derivatives and without derivatives.
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عقل مند بادشاہ

عقل مند بادشاہ

کسے شہر وچ اک غریب بندہ رہندا سی۔ انتہائی نیک تے محنتی، سارا دن محنت کردا تے جو کجھ ملدا اوس اتے ربّ دا شکر ادا کردا۔ بچت کر کے اوس دس ہزار روپے جمع کر لئے سن۔ اچانک اوس نوں ضروری کم لئی دوجے شہر جانا پیا۔ اوس پیسے نال لے جاون دیبجائے اپنے گوانڈھی کول امانت رکھوا دتے۔ پر امانت دیندے ویلے کوئی گواہ نئیں سی موجود تے نہ ای اوس امانت دی کوئی رسید لئی۔

چھ مہینیاں پچھوں جدوں اوہ بندہ واپس آیا تاں اوس نے گوانڈھی کولوں اپنی امانت منگی۔ تاں گوانڈھی صاف مکر گیا۔ الٹا اوس دی بے عزتی وی کیتی۔ اوہ ہر روز امانت لین جاندا پر گوانڈھی اوس دی کوئی گل نہ سندا۔ شام نوں اوہ تھک کے گھر واپس آ جاندا۔ آخر کار اوس نے فیصلہ کیتا کہ اوہ اپنا مقدمہ بادشاہ دی عدالت وچ لے کے جاوے گا۔ اوہ بادشاہ دی عدالت وچ اپڑیا تے بادشاہ نوں دسیا کہ اوس کولوں غلطی ہوئی اے کہ اوس بغیر کسے گواہ تے رسید دے دس ہزار روپے گوانڈھی کول امانت راکھوے سن پر ہن اوہ اوس دی امانت واپس نئیں کردا۔ ایس لئی میرے پیسے مینوں واپس لے کے دیو۔

بادشاہ نے اوس نوں آکھیا کہ بناں ثبوت دے میں اوس نوں گرفتار نئیں کر سکدا۔ پر اک تجویز اے کہ میں کل عصر دی نماز توں بعد سیر کردا اوس بندے دی دوکان اتے آوے گا۔ توں وی اوتھے آ جاویں۔ میں تینوں جھک کے سلام کراں گا۔ توں بڑی لاپرواہی نال اوس دی جواب دیویں ایسے طرں میں تیرے نال جو وی گلاں کراں توں انتہائی لاپرواہی نال اوہناں دا جواب دینا ایں۔

بادشاہ دے دسے ہوئے منصوبے دے تحت اگلے اوہ بندہ...

امن کے حوالہ سے اسلام پر کئے جانے والے اعتراضات و شبہات کا جائزہ

In the present age, a great conflict has become the source of clash between Islām and the rest of the world, especially, the western world. The world of Islām is accused of having and breeding the fanatical elements, who help promote terrorism in the world. The Western world and the media leave no opportunity to malign the name of the most peaceful religion of the world. This article illumines that Islām is a peace loving religion and does not approve terrorism. Those elements, involved in disrupting peace are not the true representative of Islām. They make a very minor portion of the Islamic world. The majority of Muslims are peace loving people and they need to be given a due coverage by the media. This research article is an attempt to present a very soft, peaceful and noble image of Islām before the world, especially, the western world. The two main sources of Islām: al-Qur’ān and the sayings of the Prophet of Islām, the prophet Muḥammadﷺ, have been quoted extensively, to prove that the religion and the meanings of the world, ‘Islām’, all reflect peace, fraternity, friendship and altruism. The Western scholars have also been quoted appropriately to support the said premise.

Seroprevalence of Toxoplasmosis, Hematological and Serum Biochemical Profile in Sheep in Multan and Khanewal Districts Punjab Pakistan

The present study was conducted to determine the seroprevalence of toxoplasmosis, hematological and serum biochemical changes in sheep naturally infected with Toxoplasma gondii and compared between T. gondii positive and negative sheep in Multan and Khanewal districts, Punjab (Pakistan). Blood samples were collected from 500 sheep and T. gondii antibodies were tested by latex agglutination test (LAT) and Enzyme Linked Immunosorbent Assay (ELISA). Information related to hosts and herds were recorded on questionnaire basis such as gender, age of animals, aborted or non-aborted sheep, cats association with herd, method of disposing aborted fetuses and herd size. The overall prevalence of toxoplasmosis in sheep was 33.6% by latex agglutination test (LAT) and 27.4% by ELISA (P-value = 0.033, OR = 1.341, 95 % CI = 1.023, 1.757). The area wise prevalence of toxoplasmosis was 34.02% and 33. 01 % by LAT (P-value = 0.813, OR = 1.031, 95 % CI = 0.802, 1.324) in Multan and Khanewal and 28.12 % and 26.41 % by ELISA (P-value = 0.672, OR = 1.065, 95 % CI = 0.796, 1.424) in Multan and Khanewal respectively. Difference was statistically non-significant (P>0.05). The seroprevalence of toxoplasmosis was compared between aborted and non-aborted sheep and according to these results infection rate was 51.66% and 31.10% in aborted and non-aborted sheep by LAT (P-value = 0.002, OR = 1.661, 95 % CI = 1.248, 2.211) and 41.66 % and 26.22% in aborted and non-aborted sheep by ELISA (P-value = 0.013, OR = 1.589, 95 % CI = 1.128, 2.238) respectively. Difference was statistically significant (P<0.05) by both techniques. The relationship between sex of sheep and toxoplasmosis showed that infection was 31.37% and 33.85 % by LAT (P-value = 0.722, OR = 0.927, 95 % CI = 0.605, 1.419) in males and females respectively. Similarly prevalence was 19.6 % and 28.28% by ELISA (P-value = 0.188, OR = 0.693, 95 % CI = 0.390, 1.232) in males and females respectively. The prevalence was higher in females than males and difference was statistically non-significant (P>0.05) by both techniques. The prevalence of T. gondii was compared between different age groups and according to these findings infection rate was higher in age group 60-73 months (64.5% and 38.7%) and lowest in age group 4-17 months (26.4% and 22.4%) by LAT (P-value = 0.001) and ELISA (P-value = 0.404). Difference was statistically significant (P<0.05) by LAT and non-significant (P>0.05) by ELISA. Risk factors associated with prevalence of toxoplasmosis in sheep were also studied and according to these results a large flock size, presence of cats, and the aborted fetuses openly left on ground were all statistically significant (P≤0.05) risk factors that were positively associated with prevalence of toxoplasmosis in sheep flocks. Hematological and serum biochemical parameters were studied between T. gondii positive and negative sheep and according to these results mean values of haemoglobin, glucose, cholesterol, AST, ALT and LDH were 9.5 ± 2.6 g/dL, 50.6 ± 11.3 mg/dL, 211.6 ± 79.6 mg/dL, 216.4 ± 144.4 U/L, 79.0 ± 64.1 U/L, 613.9 ± 297.2 U/L in T. gondii positive sheep by LAT and 9.9 ± 3.1 g/dL, 52.3 ± 11.3 mg/dL, 198.5 ± 73.6 mg/dL, 209.44 ± 629.3 U/L, 98.7 ± 228.7 U/L, 578.3 ± 292.9 U/L in T. gondii negative sheep respectively. Similarly mean values of haemoglobin, glucose, cholesterol, AST, ALT and LDH were 9.5 ± 2.5 g/dL, 50.6 ± 11.3 mg/dL, 214.6 ± 79.9 mg/dL, 217.3 ± 140.7 U/L, 77.8 ± 66.4 U/L, 606.8± 291.5 U/L in T. gondii positive sheep by ELISA and 9.9 ± 3.1 g/dL, 52.3 ± 11.2 mg/dL, 198.4± 73.8 mg/dL, 209.6 ± 605.1 U/L, 97.6 ± 219.8 U/L, 583.8 ± 295.7 U/L in T. gondii negative sheep respectively. Hemoglobin, glucose and ALT concentration was lower in T. gondii positive sheep as compared to T. gondii negative sheep. Cholesterol, AST and LDH concentration was higher in T. gondii positive sheep than T. gondii negative sheep. Haemoglobin, Glucose, AST, ALT and LDH values varied statistically non-significantly (P>0.05) between T. gondii positive and negative sheep whereas cholesterol level varied statistically significantly (P<0.05) between T. gondii positive and negative sheep. In conclusion, cholesterol level was found higher in sheep infected with toxoplasmosis which may lead to certain complications including coronary artery diseases, myocardial infarction, atherosclerosis, hypertension, hemorrhage and vascular thrombosis in infected sheep. T. gondii is a blood parasite which can cause abortion, fetal death, stillbirth, neonatal death in sheep which can lead toward economic losses such as reduction in fur, wool, meat, milk and other dairy products etc. The results indicated the overall high rates of seroprevalence of T. gondii in sheep that warranted the threat to public health especially farmers and abattoir workers via zoonotic transmission of toxoplasmosis. Keeping in view, the medical and veterinary importance of T. gondii it is recommended that human population (especially farmers and abattoir workers), other livestock species and stray cats present in study area must also be screened for the Toxoplasma infection in the public interest.