# lab6 - MATLAB DSP Graphics Module No CM0268 Laboratory...

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MATLAB, DSP, Graphics Module No: CM0268 Laboratory Worksheet 6: Geometric Computing with MATLAB Dr Y Lai Aims and Objectives After working through this worksheet you should be familiar with: The basic theoretic knowledge of geometric computing The rendering of geometric primitives such as lines and circles with MATLAB The intersections (relationship) between lines and circles, and how to solve them with MATLAB The interpolation of polynomial curves with constraints, including Lagrangian and Hermite interpolation. None of the work here is part of the assessed coursework for this module 1

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Geometric Computing with MATLAB For all the following exercises, please download MATLAB Computational Geometry demo code from http://www.cs.cf.ac.uk/Dave/CM0268/Lecture Examples/Computational Geometry/all.zip , and unpack it to your local directory. MATLAB functions that are used will be given in the questions. For given functions, look at the code ﬁrst and understand how it works. In the following, ( x 0 ,y 0 ) represents a 2D point with x coordinate x 0 and y coordinate y 0 , or a 2D vector with the corresponding direction. 1. Line representations and intersection : Given four points P 1 = (1 , 6) , P 2 = (0 , 2) , P 3 = (3 , 3) , P 4 = (5 , 5) Represent line L 1 = P 1 P 3 and L 2 = P 2 P 4 in the parametric form and convert them to the implicit representation (using line par2imp 2d.m ). Calculate the intersection point between two lines without us-
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lab6 - MATLAB DSP Graphics Module No CM0268 Laboratory...

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