Consider a composite transformation, a translation to left/down followed by rotation, answer the following RADIA UNIVERSITY 1. Find a single 3*3 matrix that can implement them. 2. Find the equation formula based on matrix in step 1 3. Apply any one matrix or equation) to the object points (3.2), (8.2), (8,3), (5.3) (5.6) (3,6) with translation factor = (-2,-2), rotation by angle -45, then discuss the results.

Consider a composite transformation, a translation to left/down followed by rotation, answer the following RADIA UNIVERSITY 1. Find a single 3*3 matrix that can implement them. 2. Find the equation formula based on matrix in step 1 3. Apply any one matrix or equation) to the object points (3.2), (8.2), (8,3), (5.3) (5.6) (3,6) with translation factor = (-2,-2), rotation by angle -45, then discuss the results.

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

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Consider the transformation necessary to scale a 2-dimensional object centred at (-1, 3) by 4 in the y-direction. The resulting object is still to be centred at (-1, 3). List the sequence of steps necessary to accomplish this transformation. Write the individual transformation matrices needed to implement each of the steps in (a) above. Hint: Use homogeneous coordinates. Compute the composite transformation matrix which will accomplish the entire transformation?
SOLVE IN MATLAB. What is the code for this in matlab?
Please note that neither the center of projection nor the projection plane is at the origin. So please use the appropriate general perspective projection matrix to solve this problem. I have attached an image of the projection matrix that you have to use where Qdx is the x coordinate of the center of projection, Qdy is the y coordinate of the center of projection, and zp is the z coordinate of the center of the projection plane. Let a 3D point (423, -423, 423) be projected on a projection plane. Given that the center of the projection plane is (0.0, 0.0, -423.0) and the coordinate of the COP is (4, 2, 3). Determine the coordinate of that 3D point on the projection plane using a general purpose perspective projection matrix.
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Problem 4. Consider the function Ik = g(k) = sin (). el-k/20). Construct the vector g = (go, ..., 9T) for T = 30 on MATLAB. Visualise the values of gr's using a stem plot.
QUESTION 1 Suppose that a transformation from object space to world space is given by a square matrix M. Choose the best answer. O The transformation is linear. The transformation could be a translation. The transformation is not affine. We cannot say anything from above until we know the dimensions of the object and world spaces.
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Convergence of iterative methods like the Conjugate Gradient Method can be accelerated by the use of a technique called preconditioning. The convergence rates of iterative methods often depend, directly or indirectly, on the condition number of the coefficient matrix A. The idea of preconditioning is to reduce the effective condition number of the problem. The preconditioned form of the n X n linear system Ax = b is where M is an invertible n x n matrix called the preconditioner. When A is a symmetric positive-definite n x n matrix, we will choose a symmetric positive-definite matrix M for use as a preconditioner. A particularly simple choice is the Jacobi preconditioner M = D, where D is the diagonal of A. The Preconditioned Conjugate Gradient Method is now easy to describe: Replace Ax = b with the preconditioned equation M-¹Ax = M-¹b, and replace the Euclidean inner product with (v, w) M. To convert Algorithm 2 in Section 3.3 to the preconditioned version, let zk = M-¹b - M-¹ Axk =…
Q3: Consider a composite transformation, a translation to left/down followed by rotation, answer the following 1. Find a single 3*3 matrix that can implement them. 2. Find the equation formula based on matrix in step 1 3. Apply any one( matrix or equation) to the object points (3,2), (8,2), (8,3), (5,3) (5,6) (3,6) with translation factor = (-2,-2), rotation by angle= -45, then discuss the results.
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Please answer all parts of this questions for me with clear steps and explanations, thanks in advance.