Solution

The correct answer is A - IV, B - III, C - I, D - II 

Key Points

• A. Bezier curves and IV (painting drawing CAD):
  • Bezier curves are mathematical descriptions of curves that can accurately describe various shapes. They are widely used in computer graphics, including painting, drawing, and Computer-Aided Design (CAD), because of their power to model smooth and flexible curves with just a few parameters.
• B. B-Splines and III (Bias and tension):
  • B-splines, short for Basis Splines, are a highly generalized version of Bezier curves and can represent the same curves, but also provide more control over curves' shapes. The notion of bias and tension are key features of design layouts which B-Splines can often accommodate. They allow for control over how "tight" or "loose" a curve is and in which direction the curve tends to lean. Thus these tools can offer accurate control over graphical structures, matching the B-Splines with tense and biased controls.
• C. Sweep representations and I (3 dim objects that have translation rotational symmetry):
  • Sweep representations refer to the methods in computer graphics and solid modeling that represent a 3D object as a 2D profile swept along a path. These methods are capable of creating complex 3D objects with translation and rotational symmetry, as the same pattern is repeated in different orientations and positions.
• D. Natural objects and II (Fractal geometry):
  • Many natural objects - like mountain ranges, clouds, trees, and more - show a self-similar pattern: they have parts that resemble the whole, at many scales of magnification. Fractal geometry is a special form of graphical representation of mathematical functions or set of numbers generated by a mathematical function. This helps to explain structures in the world which have complexity, detail and hierarchy, such as those found in natural landscapes. As a result, fractal geometry has wide-ranging applications in many fields, including the representation of natural objects in computer graphics.