set-4

Answer: 3. Translation.

Explanation:

• Translation is a rigid body transformation that moves objects without deformation.

• In mathematical terms, translation can be represented as:

  $$\begin{pmatrix} x' \\ y' \\ z' \end{pmatrix} = \begin{pmatrix} x \\ y \\ z \end{pmatrix} + \begin{pmatrix} t_x \\ t_y \\ t_z \end{pmatrix}$$

  where $(t_x, t_y, t_z)$ are the translation distances along the x, y, and z axes, respectively.

Answer: 1. Rotation.

Explanation:

• Rotation is a transformation that repositions an object along a circular path in the xy plane.

• The rotation of a point $(x, y)$ by an angle $\theta$ can be represented as:

  $$\begin{pmatrix} x' \\ y' \end{pmatrix} = \begin{pmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix}$$

Answer: 3. Multiplicative.

Explanation:

• Successive scaling operations are multiplicative because each scaling transformation is applied by multiplying the current coordinates by a scaling matrix.

• For example, scaling a point $(x, y)$ by factors $(s_x, s_y)$ can be represented as:

  $$\begin{pmatrix} x' \\ y' \end{pmatrix} = \begin{pmatrix} s_x & 0 \\ 0 & s_y \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix}$$

Answer: 3. Rigid motion.

Explanation:

• Rigid motion refers to a transformation that changes the coordinate positions of an object without altering its shape or size.
• This includes translations and rotations, which preserve distances between points.

Answer: 2. Composite transformation.

Explanation:

• Composite transformations often involve inverse matrix calculations because they combine multiple transformations, and sometimes it is necessary to reverse one or more of these transformations.
• For example, if you have a transformation matrix $T$, its inverse $T^{-1}$ can be used to undo the transformation.

Answer: 4. Reflection.

Explanation:

• Reflection is a transformation that produces a mirror image of an object.

• For example, reflecting a point $(x, y)$ across the x-axis can be represented as:

  $$\begin{pmatrix} x' \\ y' \end{pmatrix} = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix}$$

Answer: 3. Surface rendering.

Explanation:

• Surface rendering is used to display objects with color or shaded surfaces.
• This involves calculating the interaction of light with the object’s surface to determine its appearance.

Answer: 4. Lighting specifications.

Explanation:

• Lighting specifications include the intensity and positions of light sources and general background illumination required for a scene.
• These specifications are crucial for realistic rendering of objects in a scene.

Answer: 4. Shadow regions.

Explanation:

• In surface rendering, procedures are applied to generate the correct illumination and shadow regions of the scene.
• Shadows are created by determining which parts of the scene are occluded from light sources.

Answer: 1. Depth cueing.

Explanation:

• Depth cueing is a technique where the intensity of lines decreases from the front to the back of the object, giving a sense of depth.
• This helps in perceiving the relative distances of objects in a scene.

Answer: 3. Cutaway view.

Explanation:

• A cutaway view removes part of the visible surfaces to show the internal structure of an object.
• This is commonly used in technical drawings and illustrations.

Answer: 1. Reflecting.

Explanation:

• Reflecting a raster scan image from a vibrating flexible mirror can produce three-dimensional views.
• This technique is used in some types of 3D displays.

Answer: 2. 2.

Explanation:

• Stereoscopic devices present two views of the scene, one for each eye, to create a 3D effect.
• This mimics the way human eyes perceive depth.

Answer: 2. Axis of reflection.

Explanation:

• The mirror image for a two-dimensional reflection is generated relative to an axis of reflection by rotating the object 180 degrees about this axis.

• Mathematically, this can be represented as:

  $$\begin{pmatrix} x' \\ y' \end{pmatrix} = \begin{pmatrix} \cos(180^\circ) & -\sin(180^\circ) \\ \sin(180^\circ) & \cos(180^\circ) \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix}$$

Answer: 2. 180.

Explanation:

• The mirror image for a two-dimensional reflection is generated by rotating the object 180 degrees about the reflection axis.
• This rotation effectively flips the object across the axis.

Answer: 2. Shear.

Explanation:

• Shear transformations can be used to modify the shape of an object by slanting it along one or more axes.

• For example, a shear transformation along the x-axis can be represented as:

  $$\begin{pmatrix} x' \\ y' \end{pmatrix} = \begin{pmatrix} 1 & sh_x \\ 0 & 1 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix}$$

  where $sh_x$ is the shear factor.

Answer: 3. Real Number.

Explanation:

• Real numbers can be assigned as shear parameters because shear transformations can involve any real-valued factor.
• This allows for precise control over the degree of shearing.

Answer: 4. 2D transformation.

Explanation:

• Translation, rotation, scaling, and reflection are examples of 2D transformations.
• These transformations are fundamental in computer graphics for manipulating objects in a two-dimensional space.

Answer: 1. Vertex table.

Explanation:

• The vertex table can be expanded so that vertices are cross-referenced to corresponding edges.
• This helps in efficiently storing and retrieving geometric data.

Answer: 2. 2.

Explanation:

• Every vertex is the endpoint for at least two edges.
• This is because a vertex is typically shared between two edges in a polygonal mesh.

Answer: 1. 1.

Explanation:

• Each polygon has at least one shared edge.
• This is because polygons are typically connected to other polygons in a mesh.

Answer: 3. Object boundaries.

Explanation:

• Object boundaries can be constructed with various combinations of plane and curved surfaces.
• This allows for the creation of complex 3D models.

Answer: 1. Cross sectional.

Explanation:

• Graphics packages often provide routines for displaying internal components or cross-sectional views of solid objects.
• This is useful for visualizing the internal structure of objects.

Answer: 2. Surface.

Explanation:

• Surface rendering algorithms must be applied if a realistic rendering of the scene is required.
• These algorithms simulate the interaction of light with surfaces to produce realistic images.

Answer: 4. Position and orientation.

Explanation:

• The coordinate reference defines the position and orientation for the plane of the camera film.
• This is crucial for determining how the scene is projected onto the film.

Answer: 1. Parallel.

Explanation:

• The easiest rotation axes to handle are those that are parallel to the coordinate axes.
• This simplifies the rotation transformation because it aligns with the standard coordinate system.

Answer: 2. Shear.

Explanation:

• Shear transformations can be used to modify the shape of an object by slanting it along one or more axes.
• This is useful for creating effects like slanting or skewing.

Answer: 4. Purple line.

Explanation:

• The line joining the red and violet spectral points is called the purple line.
• This line represents the transition between the red and violet ends of the visible spectrum.

Answer: 4. White.

Explanation:

• Different tints are produced by adding white pigment to the original color.
• This lightens the color, creating a tint.

Answer: 1. Graphical kernel system.

Explanation:

• GKS stands for Graphical Kernel System.
• It is a standard for 2D graphics programming.

Answer: 2. 630.

Explanation:

• Visual pigment red has a peak sensitivity at a wavelength of about 630 nm.
• This is within the red part of the visible spectrum.

Answer: 2. Hue.

Explanation:

• The dominant frequency is also called hue.
• Hue represents the color itself, such as red, green, or blue.

Answer: 2. Virtual.

Explanation:

• A data glove is used to grasp virtual objects.
• It is commonly used in virtual reality environments.

Answer: 2. Solids.

Explanation:

• Space partitioning representation describes interior properties by partitioning the spatial region containing an object into a set of small, non-overlapping contiguous solids.
• This is useful for representing complex 3D objects.

Answer: 4. Boundary representations.

Explanation:

• Boundary representations for a three-dimensional graphics object are a set of surface polygons that enclose the object interior.
• This is a common way to represent 3D objects in computer graphics.

Answer: 1. Polygon facets.

Explanation:

• A polygon mesh approximation to a curved surface can be improved by dividing the surface into smaller polygon facets.
• This increases the resolution and accuracy of the approximation.

Answer: 4. Geometric data.

Explanation:

• A way of storing geometric data is to create lists, namely vertex table, edge table, and polygon table.
• These tables help in efficiently storing and retrieving the geometric properties of objects.

Answer: 1. Vertex table.

Explanation:

• The edge table contains pointers back to the vertex table to identify vertices for each polygon edge.
• This helps in maintaining the connectivity between vertices and edges.

Answer: 2. Parallel projection.

Explanation:

• In a parallel projection, parallel lines in the world coordinate scene project into parallel lines on the two-dimensional display plane.
• This type of projection preserves parallelism and is commonly used in technical drawings.

Answer: 4. Perspective projection.

Explanation:

• In perspective projection, parallel lines in the scene that are not parallel to the display plane are projected into converging lines.
• This creates a sense of depth and realism in the rendered image.

Answer: 1. Depth cueing.

Explanation:

• Depth cueing is applied by choosing maximum and minimum intensity values and a range of distances over which the intensities are to vary.
• This technique helps in perceiving the depth of objects in a scene.

Answer: 3. Object interior.

Explanation:

• The side of the plane that faces the object interior is called the inside face.
• This is important for determining the orientation of surfaces in 3D models.

Answer: 1. Object exterior.

Explanation:

• The side of the plane that faces the object exterior is called the outward face.
• This is important for determining the visibility of surfaces in 3D rendering.

Answer: 1. 3.

Explanation:

• When polygons are specified with more than three vertices, it is possible that the vertices may not all lie in one plane.
• This can lead to issues in rendering and shading.

Answer: 2. Beizer polynomial.

Explanation:

• The number of control points in a Bezier curve is called the Bezier polynomial.
• The degree of the polynomial is one less than the number of control points.

Answer: 2. Fractal geometry.

Explanation:

• Natural objects can be realistically described with fractal geometry.
• Fractals are used to model complex natural shapes like mountains, clouds, and coastlines.

Answer: 3. Fractal dimension.

Explanation:

• The representation of the amount of variation in object detail is represented with fractal dimension.
• Fractal dimension quantifies the complexity of a fractal shape.

Answer: 3. Decreasing intensity.

Explanation:

• In depth cueing, the lines farther away are displayed with decreasing intensity.
• This helps in perceiving the relative distances of objects in a scene.

Answer: 4. Dashed.

Explanation:

• A technique commonly used for engineering drawing is to display the non-visible lines as dashed lines.
• This helps in distinguishing between visible and hidden parts of an object.

Answer: 4. Boundary representations.

Explanation:

• Boundary representations describe a three-dimensional object as a set of surfaces that separate the object interior from the environment.
• This is a common way to represent 3D objects in computer graphics.