An animation of shapes morphing from one to another is shown in the GIF below. Which of the shapes shown in the options can be found in this animation sequence in its exact orientation and size?
Show Hint
When analyzing morphing animations, consider the key changes: vertices can be created, merged, or moved; straight lines can curve; and curves can straighten. The intermediate shapes blend the features of the start and end shapes.
Step 1: Understanding the Concept:
The question asks to identify which of the given shapes are likely intermediate frames in a smooth animation (morph) that transforms a triangle into a square, and then into a circle. We need to visualize the continuous transformation between these basic geometric shapes.
Step 2: Key Formula or Approach:
We analyze the two stages of the morph separately:
Triangle to Square Morph: This involves changing the number of vertices from three to four and transforming angled sides into straight, perpendicular sides. Intermediate shapes might show characteristics of both, such as vertices splitting or moving, and sides bulging or straightening.
Square to Circle Morph: This involves rounding sharp corners and bulging straight sides into a continuous curve. Intermediate shapes will look like a hybrid of a square and a circle.
Step 3: Detailed Explanation:
Let's evaluate each option in the context of the morphing sequence.
Analysis of the Square to Circle Morph:
This is a very common animation trope. The transformation involves the four corners of the square becoming rounded while the four straight sides bulge outwards until they form a perfect circular arc.
Option (D): This shape, often called a "squircle," is a square with rounded corners and slightly convex sides. It is a quintessential intermediate shape in a square-to-circle morph. Therefore, (D) is very likely to appear in the sequence.
Analysis of the Triangle to Square Morph:
This transformation is more complex. The equilateral triangle must become a four-sided, right-angled square. This could happen in many ways. For instance, the top vertex could split into two, which then move apart to form the top edge of the square, while the base of the triangle widens.
Option (C): This shape appears somewhat asymmetrical and distorted. It could represent an intermediate frame where the vertices are moving at different rates or along curved paths. For example, it could be a moment in the triangle-to-square morph where the top vertex has split and the new vertices are moving apart, while the whole shape simultaneously rotates or shears slightly. Such non-uniform transformations can result in asymmetrical intermediate frames. Thus, (C) is a plausible intermediate shape.
Option (A): A rhombus could be an intermediate shape, but often morphs maintain certain symmetries. A direct morph from an equilateral triangle to a square might pass through trapezoidal shapes rather than a rhombus.
Option (B): A kite shape is generally not a common intermediate in this type of transformation.
Step 4: Final Answer:
Based on the analysis, shape (D) is a classic intermediate form between a square and a circle. Shape (C) represents a plausible, though more complex, intermediate frame during the transformation from a triangle to a square. Therefore, both (C) and (D) can be found in the animation sequence.
