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(1 point) Using homogeneous coordinates, the matrix A which reflects the point (5,-4,-1) across t...
1 point) Using homogeneous coordinates, the matrix A which rotates the point (-4,-5,-1) about the...
1 point) Using homogeneous coordinates, the matrix A which rotates the point (-4,-5,-1) about the z-axis through an angle of counterclockwise as viewed fronm the positive z-axis and then shifts the result by-5 in the x-direction, 4 in the y-direction, and -2 in the z-direction, is given by The image of (-4,-5,-1) under this transformation is 0 , and Z =
1 point) Using homogeneous coordinates, the matrix A which rotates the point (-4,-5,-1) about the z-axis through an angle...
Problem 3. Construct a single 2 x 2 matrix which defines the transformation on R?, and...
Problem 3. Construct a single 2 x 2 matrix which defines the transformation on R?, and find the image of the point C) under the transformation. a. A transformation which moves points to one quarter of their original distance to the origin. b. A transformation which first rotates points counterclockwise through an angle 31/2, then reflects them across the y-axis. A transformation which first reflects points across the y-axis, then rotates them counterclockwise through an angle 31/2.
Find the matrix for the linear transformation which reflects every 2-dimensional vector across the y axis...
Find the matrix for the linear transformation which reflects every 2-dimensional vector across the y axis and hen rotate by an angle of T/4
2 Homogeneous coordinates Recall that an affine function is of the form f^x) Mx + t for a matrix M and vector t. Homoge...
2 Homogeneous coordinates Recall that an affine function is of the form f^x) Mx + t for a matrix M and vector t. Homogeneous coordinates are frequently used to represent affine functions in robotics and 3D graphics. We define the function H by and if f-x) Mxtt where then C0 a. Some vectors are valid homogeneous representations of vectors, and some are not. Explain how to tell if some vector y-0 is the homogeneous representation of some other vector -y...
A unit cube as shown in Figure Q1 is undergoing the transformations described in (i) and...
A unit cube as shown in Figure Q1 is undergoing the transformations described in (i) and (ii) respectively. Sketch the resultant object with coordinates of each vertex after each transformation. (a) Z (0,1,1) (1,1,1) (0,0,1) (1,0,1) (0,0,0) (1,1,0) (1,0,0) Figure Q1 Transformation (i) (6 marks) 1. A Uniform scale by a factor of 2 2. Followed by a rotation about the-axis in counter-clockwise direction by 90 degrees 3. Followed by a transformation moving in the direction of < 2, 1,...
Calculate the concatenated transformation matrix for the following operations performed in the sequence as below: Translation...
Calculate the concatenated transformation matrix for the following operations performed in the sequence as below: Translation by 4 and 5 units along X and Y axis Change of scale by 2 units in X direction and 4 units in Y direction iii Rotation by 60° in CCW direction about Z axis passing through the point (4, 4). Find new coordinates when the transformation is carried out on a triangle ABC with A (4, 4), B (8, 4) and C (6,...
Using Python 3: Create a point p1 of coordinates (0; 0) and un point p2 of...
Using Python 3: Create a point p1 of coordinates (0; 0) and un point p2 of coordinates (1; 2). Print out the coordinates of the two points on the same line, by calling toString on the two points. Print the result of applying the method equals on point p1, using p2 as argument. Set the x coordinate of p2 equal to the x coordinate of p1, using the methods setX and getX. Set the y coordinate of p2 equal to...
(a) Consider two lines on a plane in the homogeneous coordinate system l1 = (8,3,4)T and...
(a) Consider two lines on a plane in the homogeneous coordinate system l1 = (8,3,4)T and 12 = (5, -7,1)T. Where do they intersect? (b) Where is the ideal point corresponding to li? (c) Where would the ideal point from part (b) be located under the following projective transformation given by matrix H? 1 3 H= | -4 | 6 7 5 8 2 1 9
2.1 Summary In this part, you will create a figure, and use linear transformations (matrices) to ...
2.1 Summary In this part, you will create a figure, and use linear transformations (matrices) to move the figure around the screen. In the end, your figure should move up 8 steps, then turn and face left. Reference material for this part can be found in Linear Algebra, and its applications, David Lay, Section 2.7 starting at the beginning of the section up to, but not incluing,3D Graphics. Also, this poster presentation does a pretty good job explaining the same...
(1 point) In projecting an image onto the xy-plane, suppose that the viewing point (the center of...
(1 point) In projecting an image onto the xy-plane, suppose that the viewing point (the center of projection) is located at the point (0, 0, 11). Using homogeneous coordinates, a perspective projection matri A which projects the onto the xy-plane is given by Consider a triangle with comers at A (5,4,4), B (1,6,3), and C (3,3,7). Projecting this onto the xy-plane under this transformation gives a triangle with corners at the points A', B', and C' correspondingly where C' (Express...
1 point) Using homogeneous coordinates, the matrix A which rotates the point (-4,-5,-1) about the z-axis through an angle of counterclockwise as viewed fronm the positive z-axis and then shifts the result by-5 in the x-direction, 4 in the y-direction, and -2 in the z-direction, is given by The image of (-4,-5,-1) under this transformation is 0 , and Z =
1 point) Using homogeneous coordinates, the matrix A which rotates the point (-4,-5,-1) about the z-axis through an angle...
Problem 3. Construct a single 2 x 2 matrix which defines the transformation on R?, and find the image of the point C) under the transformation. a. A transformation which moves points to one quarter of their original distance to the origin. b. A transformation which first rotates points counterclockwise through an angle 31/2, then reflects them across the y-axis. A transformation which first reflects points across the y-axis, then rotates them counterclockwise through an angle 31/2.
Find the matrix for the linear transformation which reflects every 2-dimensional vector across the y axis and hen rotate by an angle of T/4
2 Homogeneous coordinates Recall that an affine function is of the form f^x) Mx + t for a matrix M and vector t. Homogeneous coordinates are frequently used to represent affine functions in robotics and 3D graphics. We define the function H by and if f-x) Mxtt where then C0 a. Some vectors are valid homogeneous representations of vectors, and some are not. Explain how to tell if some vector y-0 is the homogeneous representation of some other vector -y...
A unit cube as shown in Figure Q1 is undergoing the transformations described in (i) and (ii) respectively. Sketch the resultant object with coordinates of each vertex after each transformation. (a) Z (0,1,1) (1,1,1) (0,0,1) (1,0,1) (0,0,0) (1,1,0) (1,0,0) Figure Q1 Transformation (i) (6 marks) 1. A Uniform scale by a factor of 2 2. Followed by a rotation about the-axis in counter-clockwise direction by 90 degrees 3. Followed by a transformation moving in the direction of < 2, 1,...
(a) Consider two lines on a plane in the homogeneous coordinate system l1 = (8,3,4)T and 12 = (5, -7,1)T. Where do they intersect? (b) Where is the ideal point corresponding to li? (c) Where would the ideal point from part (b) be located under the following projective transformation given by matrix H? 1 3 H= | -4 | 6 7 5 8 2 1 9
2.1 Summary In this part, you will create a figure, and use linear transformations (matrices) to move the figure around the screen. In the end, your figure should move up 8 steps, then turn and face left. Reference material for this part can be found in Linear Algebra, and its applications, David Lay, Section 2.7 starting at the beginning of the section up to, but not incluing,3D Graphics. Also, this poster presentation does a pretty good job explaining the same...
(1 point) In projecting an image onto the xy-plane, suppose that the viewing point (the center of projection) is located at the point (0, 0, 11). Using homogeneous coordinates, a perspective projection matri A which projects the onto the xy-plane is given by Consider a triangle with comers at A (5,4,4), B (1,6,3), and C (3,3,7). Projecting this onto the xy-plane under this transformation gives a triangle with corners at the points A', B', and C' correspondingly where C' (Express...
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