# Software Listing of Author : "Dr. Murtaza Khan"

(1) CubicBezier1.m : Evaluates Cubic Bezier Curve for given four Control Points and interval. (2) PlotBezier1.m : Plots Bezier Curve, Control Points, Control Polygon (3) TestCircleApproxByCubicBezier.m : Test Program. Pass Control Points that approximate unit radius circle using cubic Beizer curves. (4) ApproxofCirclebyCubicBezier.pdf: Explains theroy.

• Platform: Matlab, Scripts

(1) bezierInterp.m ------------------- A function for Bezier interpolation for given four control points. Each control point can be in N-Dimensional vector space. Optionally a vector t can be pass then bezier curve would be evaluated at values stored in vector t. By default bezier curve would be evaluated at 101 values between 0 and 1. Ouput of function is evaluated values in N-Dimensional vector space. (2) bezierInterpTest.m ----------------------- A test program that perform shows Bezier interpolation for four sample control points in 1D, 2D, 3D, 4D vector space.

• Platform: Matlab, Scripts

INPUT: x: vector of numeric values, x should already be sorted in ascending order (e.g. 2,7,20,...120) sval: numeric value to be search in x OUTPUT: index: index of sval with respect to x. If sval is not found in x then index is empty.

• Platform: Matlab, Scripts

Computes Direction Cosine Matrix from Euler angles (in radians) for six basic sequence of rotations around X(Roll),Y(Pitch) and Z(Yaw) axis. Allowed rotations sequences: xyz, xzy, yxz, yzx, zxy, zyx OR rpy, ryp, pry, pyr, yrp, ypr ---------------------------- dcmfromeuler.m function to compute DCM from Euler angles dcmfromeulerTest.m A simple test program to test dcmfromeuler.m

• Platform: Matlab, Scripts

Euler Angles To Quaternion Conversion for six basic sequence of rotations around X(Roll),Y(Pitch) and Z(Yaw) axis. Allowed Sequences: xyz, xzy, yxz, yzx, zxy, zyx.

• Platform: Matlab, Scripts

mergesorted.m ------------------ If we have two individually sorted vectors "a" and "b" but they are not sorted with respect to each other and we want to merge them into vector "c" such that "c" is also a sorted vector. Then c=mergesorted(a,b) can be used. This function most likely make difference for very large vectors (may be elements in million). On P-4 machine when length of "a" is 2 million and length of "b" is 2.5 million then c=mergesorted(a,b) is around 3 times faster than using MATLAB builtin function c=sort([a,b]). testmergesorted.m ---------------------- A simple test program to that test "mergesorted" and builtin "sort" function and compare their performance.

• Platform: Matlab, Scripts

Quadtree decomposition of RGB image of size M-by-N-by-3. Three thresholds for red,green and blue components are used. For any R or G or B block if the maximum value of the block elements minus the minimum value of the block elements is greater than its respective threshold then the RGB block is split into 4 blocks. For lossy encoding (individual) mean value R,G,B are assign to RGB block. Image is padded if its size is not power of 2, so that image can be divided until block of size 1. Thresholds are specified as a value between 0 and 1 (0 for lossless encoding). If Image is of type uint8 then threshold value is multiplied by 255, if Image is of type uint16 then threshold value is multiplied by 65535, to determine the actual threshold. No toolbox required. main.m --------- Test program for Quadtree decomposition (Encoding) and...

• Platform: Matlab, Scripts

Search value 'v' in sorted vector 'x' and find index and value with respect to vector x that is equal or closest to 'v'. If more than one value is equal then anyone can be returned (this is property of binary search). If more than one value is closest then first occurred is returned (this is property of linear search). Algorithm First binary search is used to find v in x. If not found then range obtained by binary search is searched linearly to find the closest value. INPUT: x: vector of numeric values, x should already be sorted in ascending order (e.g. 2,7,20,...120) v: numeric value to be search in x OUTPUT: i: index of v with respect to x. cv: value that is equal or closest to v in x

• Platform: Matlab, Scripts

reshape1dto2dbalance.m ---------------------- If possible then reshapes 1D array (vector) 'A' into 2D array 'B' such that: abs(NC-NR) is minimized where NR=number of rows in B NC=number of columns B Note: Elements of A are placed column-wise in B. reshape1dto2dbalanceTest.m -------------------------- A simple test program

• Platform: Matlab, Scripts
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