The Aims of the Prophetic Hijrah and its Teaching and Guidance

The aim of Hijrah is not to run away from problem that occurred in the process of giving da'wah, but rather to establish the resolve in solving the problem. Hijrah as a movement carried out by the Prophet Muhammad (PBUH) and his companions from Makkah to Madinah, aimed to keep, maintain and uphold the message of Allah, in the form of Islamic aqeedah and shari’a, in order to achieve the mercy and pleasure of Allah SWT. This move, as we can see in the seerah, later brought a great impact to the success of the Islamic da’wah which was increasingly evolving. Hence the fundamental problem that has led to the migration has been solved. In fact, the Hijrah brought a significant impact not just to the Islamic world but also to world civilisation. The story and background of the migration of Rasulullah (PBUH) from Makkah to Madinah is touched in this writing to show that there were a lot of lessons and guidance that can be inferred. It did not merely signify a final destination for Makkah Muslims, but was also the beginning of a continuous effort to establish a strong and resilient ummah. The event of Hijrah in fact had changed the world after that forever. It highlighted the perseverance of the Rasulullah (PBUH) and the early Muslims through the difficult times. Hijrah demonstrates that for people with faith, there is hope for ease after difficulties. There was also a great unity model among Muslims of different backgrounds. The Hijrah had also marked the beginning of the Islamic State under the leadership of Rasulullah (PBUH) which then became a reference for all state governance everywhere in the future

Data Visualization Using Spline Functions

Accurate visualization of regular and scattered surface data requires that the surface characteristics or shape is preserved. This is desirable in most computer aided engineering applications, including; geometric modelling, sectional drawing, designing pipe systems in chemical plants, surgery; designing car bodies, ship hulls and airplanes; physical and chemical processes, geology, meteorology. Three basic surface data shape characteristics, namely positivity, monotonicity and convexity are of general interest. For examples rainfall data is positive, the rate of dissemination of drugs in the blood is positive and monotone, data generated in an optimization problem may be convex. Within a data visualization environment, a user is usually interested in graphically. This requires the use of interpolating schemes which themselves must possess certain characteristics like shape preservation, shape control, etc. Many authors derived the constraints on derivatives to visualize the shape of data. These schemes fail to preserve the shape of data, when data are given with the derivatives at the data points. Some existing schemes are global, the disadvantages of these schemes: modification of data or constraints in one of the interval will affect the graphical display of the data over the whole domain. In the visualization of monotone scattered data, some existing schemes transform the scattered data in to the regular data. These schemes are not feasible to industrial applications where bulk of data is under consideration. The focus of this thesis is on the graphical display of regular and scattered surface data which possess positive, monotone and convex shape features. The aim is to develop the data visualization schemes that are local, computationally economical, visuallyv pleasing that are applicable to both data and data with derivatives and above all provide automotive techniques for appropriate choice of parameters. Data visualization schemes for regular data are developed using rational bi-cubic function and rational bi-cubic partially blended function to preserve positivity, monotonicity and convexity of surface data. Simple sufficient data dependent shape preserving constraints are derived in terms of the free parameters of rational bi-cubic and rational bi-cubic partially blended function. The problem of data visualization of constrained data is also addressed when the data is lying above the plane and the interpolating surface is required to lie on the same side of the plane. Finally, data visualization schemes are developed for scattered data arranged over the triangular grid.