Suppose a computer program needs to apply an affine transformation to a complex three-dimensional object made up of 3000 points. The transformation is composed of 8 matrices (call them M¡ through Mg), so for each point (x, y, z) in the object, the following operation is performed. JI M1 M2 M3 M7 M8 Each multiplication of a matrix times a column vector involves 16 multiplications (of one number by another) and 12 additions, for a total of 28 arithmetic operations. Each multiplication of a matrix times another matrix involves 64 multiplications and 48 additions, for a total of 112 arithmetic operations. (These numbers are not made up or chosen randomly; they are facts about 4 x 4 matrix multiplication.) The most inefficient way of applying the transformation to the 3000 points would be to begin on the left, multiplying M, by M2, then that result by M3, and so on along the list from left to right, and doing the same 8 multiplications again for each of the 3000 points. How many arithmetic operations would this require for transforming one point? How many would it require in total for transforming all 3000 points?

Suppose a computer program needs to apply an affine transformation to a complex three-dimensional object made up of 3000 points. The transformation is composed of 8 matrices (call them M¡ through Mg), so for each point (x, y, z) in the object, the following operation is performed. JI M1 M2 M3 M7 M8 Each multiplication of a matrix times a column vector involves 16 multiplications (of one number by another) and 12 additions, for a total of 28 arithmetic operations. Each multiplication of a matrix times another matrix involves 64 multiplications and 48 additions, for a total of 112 arithmetic operations. (These numbers are not made up or chosen randomly; they are facts about 4 x 4 matrix multiplication.) The most inefficient way of applying the transformation to the 3000 points would be to begin on the left, multiplying M, by M2, then that result by M3, and so on along the list from left to right, and doing the same 8 multiplications again for each of the 3000 points. How many arithmetic operations would this require for transforming one point? How many would it require in total for transforming all 3000 points?

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Related questions

Q: Thinking again about specific GUI applications that you use regularly: Select one element of poor…

A: Solution :: What is GUI ? Answer:: The graphical user (connecting point/way of interacting with…

Q: Use numpy.arange() to generate a 1-dimenstional array with 100 odd numbers 1, 3, 5, …, 199. Then use…

A: import numpy as np a=np.arange(1, 200, step=2).reshape(10,10) print("Shape of 2-D array is:\n ")…

Q: Write a C program to obtain transpose of a 4 x 4 matrix. The transpose of a matrix is obtained…

Q: Use nested for...loops to create a (6x6) matrix in which the value of an element is three times its…

A: The objective of the question is to create a 6x6 matrix using nested for loops. The value of each…

Q: Use loops to create a (8x8) matrix in which the value of each element is four times its row number…

A: The objective of the question is to create an 8x8 matrix using loops in Matlab. The value of each…

Q: Matlab：Create six numbers in column vector array by the uniform distribution. Show them in…

A: Matlab: Syntax: rng('default'); r1 = rand(1,6,1); A = Rand(1,6,'single'); class(A)

Q: If memory read cycle takes 100 ns and a cache read cycle takes 20 ns, then for four continuous…

A: Memory Read cycle : 100nsCache Read cycle : 20ns Four continuous reference is done - one reference…

Q: Given an array of integers, print a sum triangle from it such that the first level has all array…

A: Given: The integer array.

Q: Use nested for...loops to create a (6×6) matrix in which the value of an element is three times its…

A: Algorithm to Create a (6×6) Matrix with Given Conditions:1. Initialize a 6x6 matrix (let's call it…

Q: Given an 8-element array: A = {x1, x2, X3, X4, X5, X6, 27, x8}, we would like to find its 3rd…

A: Start with an 8-element array A: {X1, X2, X3, X4, X5, X6, X7, X8}. Let x1 be the larger of X1 and…

Q: For a matrix (two-dimensional array)utilizing for loops.USE following numbers to read from monitor…

A: For a matrix (two-dimensional array)utilizing for loops.USE following numbers to read from monitor…

Q: Write in Python

A: Function Definition :Function Name and Parameter: The function determinant_3x3 is defined to take…

Q: The goal of this problem is to walk from cell (0, 0) to cell (m, n) of a two-dimensional array.…

A: Create a two-dimensional array dp of the same dimensions as the toll matrix, initialized with…

Concept explainers

Use of XOR function

XOR function or exclusive OR function was introduced in Excel 2013. This function is available under excel logical functions. For the given statement, the XOR function will return true only when either of the statements is true. It returns false when both the statements are true or when both the statements are false.

Question

Suppose a computer program needs to apply an affine transformation to a complex three-dimensional object made up of 3000
points. The transformation is composed of 8 matrices (call them M1 through M3), so for each point (x, y, z) in the object, the
following operation is performed.
|-|-|-|-||
y
M1
M2
M3
M7
M8
Each multiplication of a matrix times a column vector involves 16 multiplications (of one number by another) and 12 additions,
for a total of 28 arithmetic operations. Each multiplication of a matrix times another matrix involves 64 multiplications and 48
additions, for a total of 112 arithmetic operations. (These numbers are not made up or chosen randomly; they are facts about
4 x 4 matrix multiplication.)
The most inefficient way of applying the transformation to the 3000 points would be to begin on the left, multiplying M1 by
M2, then that result by M3, and so on along the list from left to right, and doing the same 8 multiplications again for each of
the 3000 points. How many arithmetic operations would this require for transforming one point?
How many would it require in total for transforming all 3000 points?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.

Similar questions

Write a C Program to read a matrix and find sum, product of all elements of two dimensional (matrix) array
Suppose the weekly hours for all employees are stored in a two-dimensional array. Each row records an employee's seven-day work hours with seven columns. For example, the following array stores the work hours for eight employees. Su MTW Th F Sa Su Employeel 0 Employee2 1 Employee3 2 Employee4 3 Employees 7 Employee6 5 Employee7 6 Employee8 7 52 2 2 13 7 34 4 3. 4 4 34 9 34 6 8 3 3. 32 2 by Java code 3 4 6. 3 4 4 6 3 4 374 8 3 8 6 35 9 87 4 4 27 Write a program that Prompt the user to enter number of employees Prompt the user to enter the employees names and save their names in a one dimensional array. (Check for availability if name exist, no duplicate names) For each employee, enter the seven-day work hours and save them in a two dimensional array. Compute the total hours worked by each employee and save them in one dimensional array. Compute the wages of employees as follows: up to 40 hours per week the hour price is 20 otherwise the overtime hour price is 1.2 regular hour price.…
Create a python program that will except a 3x3 matrix and unit for translation, then conduct a basic 2D transformation of translation on the matrix.
How does alpha and beta get initialized in the above since you did show it in either the flowchart or a comment within the code.
MATLAB. write code for all parts
jupyter nootebook python with julia 1: Modify your models and coding of Chebyshev center and building a house to get the right anwsers. # Given matrix A and vector b A = [2 -1 2; -1 2 4; 1 2 -2; -1 0 0; 0 -1 0; 0 0 -1]b = [2; 16; 8; 0; 0; 0]
Write a function in matlab that takes a matrix with m rows and n columns and returns the sum of all of the odd numbers inside of that matrix.