Question

Given below are different properties of 3d projections from a-d. identify the correct order on the basis of property true of

(i) a perspective projection only,
(ii) an orthographic projection only,
(iii) both orthographic and projective transformations and
(iv) neither orthographic nor projective transformation, respectively.

(a) straight lines are mapped to straight lines.
(b) distances and angles are (in general) preserved.
(c) far away objects appear the same size as closer ones.
(d) requires homogeneous coordinates in order for it to be encoded into a linear

(A) d, c, b, a
(B) b, c, d, a
(C) d, c, a, b
(D) c, d, b, a

Answer 1

The correct order for the properties of 3D projections is (A) d, c, b, a, which corresponds to perspective projection only, orthographic projection only, both transformations, and neither transformation respectively.

Step-by-step explanation:

The correct order based on the properties true for different types of 3D projections is (A) d, c, b, a. This order corresponds to (i) a perspective projection only, (ii) an orthographic projection only, (iii) both orthographic and projective transformations, and (iv) neither orthographic nor projective transformation, respectively.

• (d) requires homogeneous coordinates in order for it to be encoded into a linear transformation. This is a property of perspective projections, as they need to account for the depth and convergence of lines at a vanishing point.
• (c) far away objects appear the same size as closer ones. This is not a property of orthographic projections which maintain the scale of objects regardless of their distance from the viewer but is a characteristic of perspective projections.
• (b) distances and angles are (in general) preserved. This is true for orthographic projections since they do not represent depth and maintain the true dimensions and angles of the subject.
• (a) straight lines are mapped to straight lines. This property holds for both orthographic and perspective projections.