Curves and Surfaces Questions and Answers

Answer: A

Solid modeling is based on complete, valid and unambiguous geometric representation of a physical object. The representation must be complete, with enough information to answer any geometric question, valid, with points joined in a real solid, and unambiguous, so that it stands for one object only. 'Incomplete', 'varying' and 'undefined' go against this requirement. A solid model that is valid and unambiguous can be used to compute volume, mass and other properties, which is the reason such a model is used in design.

Answer: A

The interpolation methods are Inverse Distance Weighted, Kriging, Natural Neighbor, Spline and Topo to raster, which are i to v. A compiler translates a program into machine code and has nothing to do with interpolation, so vi is wrong and the option that includes it is incorrect. The other options leave out some of the five methods. Kriging and IDW are both used, for example, to make surfaces of rainfall or elevation from scattered measuring points.

Answer: D

Ambient light is light illuminated due to reflection from various surfaces.

In Hearn and Baker's illumination model, a surface that is not directly exposed to any light source can still be seen because nearby objects reflect light onto it. The combined reflections from all the surfaces in a scene produce a uniform background illumination, the ambient light, which is modelled as a constant intensity reaching every surface equally from all directions.

Light coming from a single source or from several sources is direct illumination, handled by the diffuse and specular terms. The definition rests on reflection alone, so the option combining direct light from sources with reflection does not describe ambient light.

Answer: C

The table that is not part of the scheme is the Point table.

The standard geometric tables for polygon surfaces are three: a vertex table holding the coordinates of each vertex, an edge table holding pointers to the two vertices of each edge, and a polygon-surface table holding pointers to the edges of each polygon. Splitting the data this way lets shared vertices and edges be stored once and checked for consistency.

Vertex, edge and polygon surface tables are all in the scheme. There is no separate 'point table': points are the vertices, already stored in the vertex table.

Answer: D

The parameter is 2.

A superellipse is given by

\[ \begin{aligned} &\left(\frac{x}{r_x}\right)^{2/\rho} \\ &\quad + \left(\frac{y}{r_y}\right)^{2/\rho} = 1 \end{aligned} \]

With \(r_x = r_y = r\) and \(\rho = 2\) the exponents become 1, so \(|x| + |y| = r\): four straight edges meeting at the axes, which is exactly the diamond shown.

\(\rho = 1\) gives the ordinary ellipse, here a circle. Values below 1, such as 0.5, bulge outwards towards a square with rounded corners, and values between 1 and 2, such as 1.5, give a shape between the circle and the diamond, with curved sides.

Answer: D

The highest specular reflection coefficient is that of silver.

Silver reflects about 95 per cent or more of visible light across the spectrum, the highest of common materials, which is why it is used for mirrors. Gold also reflects strongly, but less in the blue and green, which gives it its colour.

Water and glass are dielectrics: at 45 degrees of incidence they reflect only a few per cent of the light and transmit the rest.