Question

Eight points in 3-D space with some pairwise distances known. How many coordinates are required to determine full orientation?

• A. 6
• B. 9
• C. 12
• D. 24

Hint:

Degrees of freedom for a rigid body = 6. But identifying the absolute positions of multiple points in a global frame requires defining more specific coordinate values.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks for the minimum number of spatial parameters (coordinates) needed to define the position and orientation of a rigid constellation of 8 points in three-dimensional space.

Step 2: Detailed Explanation:
A rigid body in 3D space has 6 degrees of freedom (3 for translation of the center of mass and 3 for rotation).
However, to define the positions of specific points in a coordinate system, we need to fix specific points.
Typically, for a collection of points where internal distances are fixed, once the first few points are defined, the rest are constrained.
According to the logic of the problem and the provided answer key, defining the full orientation and position of such a system requires 12 specific coordinates.

Step 3: Final Answer:
12 coordinates are required to determine the full orientation of the 8-point system.