Cgm Quiz 2 -cse B

Homogeneous coordinates and matrix representation are used to treat all three transformations (scaling, rotation, and shearing) in a consistent way. By representing the transformations as matrices, it becomes easier to apply multiple transformations to an object without losing information. The homogeneous coordinates allow for the representation of points at infinity, which is useful in computer graphics and geometric calculations. Overall, using homogeneous coordinates and matrix representation ensures a unified approach to handling different transformations efficiently and accurately.

Shear is a transformation that causes a distortion in the shape of an object. It involves shifting one part of the object in a parallel direction, while keeping the other parts fixed. This results in a sheared or skewed shape. Unlike reflection, rotation, and scaling, shear specifically affects the shape of the object by stretching or compressing it along a particular axis.

When the scaling factors sx and sy are assigned unequal values, it results in differential scaling. This means that the object will be scaled differently in the x and y directions, causing it to stretch or compress in one direction more than the other. This results in a non-uniform scaling effect, where the object's proportions are changed.

The figures represent a reflection across the x-axis because the x-coordinates of each point remain the same, while the y-coordinates are negated. This results in the figures being flipped upside down with respect to the x-axis.

To change the position of a circle or ellipse, one needs to translate the center coordinates and redraw the figure in a new location. This means that the center point of the circle or ellipse is moved to a different position, and then the entire shape is redrawn accordingly. This process allows for the circle or ellipse to be repositioned without altering its size or shape. Therefore, the correct answer is "Center coordinates and redraw the figure in new location."

The correct answer is P’=T*P because in homogeneous coordinates, translation is represented by a translation matrix T. Multiplying the translation matrix T with the point matrix P will result in the transformed point matrix P'. This is the correct representation for translation in homogeneous coordinates.

The correct answer is A(0,0), B(-2,0), C(-2, -2), D(0, -2). When a reflection is applied about the x-axis, the y-coordinate of each point is negated. When a reflection is applied about the y-axis, the x-coordinate of each point is negated. In this case, both reflections are applied simultaneously, resulting in the negation of both the x and y coordinates for each point. Therefore, the new coordinates of A, B, C, and D are A(0,0), B(-2,0), C(-2, -2), D(0, -2).

Scaling is the correct answer because it refers to the transformation in which the dimension of an object is changed relative to the axes. Scaling can either increase or decrease the size of an object along the x, y, or z-axis. This transformation does not involve any rotation, reflection, or translation of the object, but solely focuses on changing its size.

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In the Cohen-Sutherland line clipping algorithm, the endpoint region codes represent the position of the endpoints of the line segment with respect to the clipping window. The region codes are typically binary numbers that indicate whether the endpoint is inside or outside the window.

If the bitwise logical OR of the endpoint region codes is zero, it means that both endpoints are inside the window. This indicates that the line segment is completely visible and does not need to be clipped.