Angle distortion in isometric drawings Depending on orientation, can a true 2D angle project in isometric to look larger but never smaller than its actual value?

Difficulty: Easy

Correct Answer: Incorrect

Explanation:


Introduction / Context:
Isometric drawings are a form of axonometric projection where edges parallel to the three principal axes are equally foreshortened, and the angles between axes on paper are 120 degrees. While linear scales along axes are consistent, angles that are not aligned with those axes will not retain their true magnitudes when projected.



Given Data / Assumptions:

  • An arbitrary plane and angle are shown in an isometric view.
  • We assess whether the projection can only increase the apparent angle, not decrease it.
  • No special alignment with isometric axes is assumed.


Concept / Approach:
Angles in isometric are in general distorted. Depending on how the plane of the angle is oriented relative to the viewing direction, the projection can make the angle appear either larger or smaller than the true 2D value. Only angles that lie in planes parallel to the projection plane and aligned to axes retain characteristic appearances; arbitrary orientations do not guarantee a one-sided (always larger) distortion.



Step-by-Step Solution:

Consider an angle drawn on a face whose normal is not perpendicular to the viewing direction.Project this face into the isometric view using equal foreshortening along axes.Observe that the relative component scaling may compress or expand segments forming the angle.Conclude that the apparent angle can be either larger or smaller than the true angle.


Verification / Alternative check:
Construct two examples: one where the angle’s sides align more with compressed directions (angle appears smaller) and another where alignment increases separation (angle appears larger). Both cases occur, refuting a “never smaller” claim.



Why Other Options Are Wrong:
Limiting to right angles or referencing 120-degree axis separation does not fix angle distortion for arbitrarily oriented planes. Saying it applies to perspective only is incorrect; isometric also distorts angles.



Common Pitfalls:
Assuming all geometry scales uniformly in isometric, forgetting that equal foreshortening along axes still yields nonuniform angle effects in general planes.



Final Answer:
Incorrect

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