Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 33.1, Problem 3E
Program Plan Intro
To calculate a pseudo code to sort the sequence of n points with respect to their polar angles where a point is given. The procedure must take time equal to
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Let l be a line in the x-yplane. If l is a vertical line, its equation is x = a for some real number a.
Suppose l is not a vertical line and its slope is m. Then the equation of l is y = mx + b, where b is the y-intercept.
If l passes through the point (x₀, y₀), the equation of l can be written as y - y₀ = m(x - x₀).
If (x₁, y₁) and (x₂, y₂) are two points in the x-y plane and x₁ ≠ x₂, the slope of line passing through these points is m = (y₂ - y₁)/(x₂ - x₁).
Instructions
Write a program that prompts the user for two points in the x-y plane. Input should be entered in the following order:
Input x₁
Input y₁
Input x₂
Although the plot function is designed primarily for plotting standard xy graphs, it
can be adapted for other kinds of plotting as well.
b. Make a plot of the curve, which is defined parametrically by the equations
x = 2cosθ + cos2θ, y = 2sinθ - sin2θ,
where 0 < θ < 2π. Take a set of values of θ between zero and 2π and calculate x
and y for each from the equations above, then plot y as a function of x.
b. Taking this approach a step further, one can make a polar plot r = f(θ) for some
function f by calculating r for a range of values of θ and then converting r and
θ to Cartesian coordinates using the standard equations x = r cosθ, y = r sinθ.
Use this method to make a plot of the function
r = ecosθ – 2 cos(4θ) + sin5 (θ/12)
in the range 0 <= θ <= 24π.
use python code to answer the highlight one
Write what each of the following means in computer graphics:
1) Geometrical Transformations which includes,
2D Transformations
Homogenous Coordinates
2D Matrix Transformations
Composition of Transformations
3D Matrix Transformation
Chapter 33 Solutions
Introduction to Algorithms
Ch. 33.1 - Prob. 1ECh. 33.1 - Prob. 2ECh. 33.1 - Prob. 3ECh. 33.1 - Prob. 4ECh. 33.1 - Prob. 5ECh. 33.1 - Prob. 6ECh. 33.1 - Prob. 7ECh. 33.1 - Prob. 8ECh. 33.2 - Prob. 1ECh. 33.2 - Prob. 2E
Ch. 33.2 - Prob. 3ECh. 33.2 - Prob. 4ECh. 33.2 - Prob. 5ECh. 33.2 - Prob. 6ECh. 33.2 - Prob. 7ECh. 33.2 - Prob. 8ECh. 33.2 - Prob. 9ECh. 33.3 - Prob. 1ECh. 33.3 - Prob. 2ECh. 33.3 - Prob. 3ECh. 33.3 - Prob. 4ECh. 33.3 - Prob. 5ECh. 33.3 - Prob. 6ECh. 33.4 - Prob. 1ECh. 33.4 - Prob. 2ECh. 33.4 - Prob. 3ECh. 33.4 - Prob. 4ECh. 33.4 - Prob. 5ECh. 33.4 - Prob. 6ECh. 33 - Prob. 1PCh. 33 - Prob. 2PCh. 33 - Prob. 3PCh. 33 - Prob. 4PCh. 33 - Prob. 5P
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