Three Dimensional Transformations and Projection Questions and Answers

Q: From modeling coordinates to device coordinates in general 3D transformation pipeline, identify the correct order of other coordinates involved :(i) Viewing coordinates(ii) Projection coordinates(iii) World coordinates

The order is (iii), (i) and (ii): world, viewing, projection.In the general 3D viewing pipeline, modelling coordinates are first transformed into world coordinates (placing objects in the scene), then into viewing coordinates (as seen from the camera), then into projection coordinates (after perspective or parallel projection), then normalised and finally mapped to device coordinates.Every other option puts viewing or projection before the world coordinate stage, which reverses the pipeline.

Which of the following statements is/are INCORRECT about the Z-buffer algorithm in computer graphics?

Statements:
i) It is an image space method to detect visible surface.
ii) In this method, a depth buffer is used to store the depth values of each position and a refresh (frame) buffer is used to store the intensity values or colour values for each position.
iii) In this method, object edges can be anti aliased.
iv) This method can only find one visible surface at each pixel position.

A.ii, iii and iv only
B.i, ii, iii and iv
C.i, ii, and iv only
D.iii only

Exam Year(s)

DSSSB TGT - 2023,

Answer: D

Only statement iii is incorrect. The Z-buffer algorithm is an image-space method of detecting visible surfaces (i), and it keeps a depth buffer for the depth value of each position and a refresh (frame) buffer for the intensity or colour (ii). It finds only one visible surface at each pixel position (iv), and because it keeps no information about the surfaces behind it, object edges cannot be anti-aliased, so statement iii is the false one. The other options mark true statements as incorrect.

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From modeling coordinates to device coordinates in general 3D transformation pipeline, identify the correct order of other coordinates involved :

(i) Viewing coordinates
(ii) Projection coordinates
(iii) World coordinates

A.(i), (ii) and (iii)
B.(ii), (i) and (iii)
C.(iii), (i) and (ii)
D.(ii), (iii) and (i)

Exam Year(s)

MH SET - 2020, SET Exam - 2020,

Answer: C

The order is (iii), (i) and (ii): world, viewing, projection.

In the general 3D viewing pipeline, modelling coordinates are first transformed into world coordinates (placing objects in the scene), then into viewing coordinates (as seen from the camera), then into projection coordinates (after perspective or parallel projection), then normalised and finally mapped to device coordinates.

Every other option puts viewing or projection before the world coordinate stage, which reverses the pipeline.

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The Z-buffer algorithm is used for Hidden surface removal of objects. The maximum number of objects that can be handled by this algorithm shall

A.Depend on the application
B.be arbitrary no. of objects
C.Depend on the memory availability
D.Depend on the processor

Exam Year(s)

UGC NET - 2012,

Answer: B

The Z-buffer algorithm compares the depth of each pixel from every object with the value stored in the buffer, and it handles the objects one at a time, so it does not need to hold or sort all objects. For this reason the number of objects that it can handle is arbitrary, and is not limited by the application, the memory or the processor, which limit only the size of the picture and the speed. The keyed answer is that it can be an arbitrary number of objects.

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The perspective projection matrix, on the view plane z = d where the centre of projection is the origin (0, 0, 0) shall be

A.\(\begin{bmatrix}0&0&0&d\\0&0&d&0\\0&d&0&0\\d&0&0&1\end{bmatrix}\)
B.\(\begin{bmatrix}d&0&0&0\\0&d&0&0\\0&0&d&0\\0&0&1&0\end{bmatrix}\)
C.\(\begin{bmatrix}0&0&0&d\\0&0&d&0\\0&d&0&0\\1&0&0&0\end{bmatrix}\)
D.\(\begin{bmatrix}d&0&0&0\\0&d&0&0\\0&0&d&0\\0&0&0&1\end{bmatrix}\)

Exam Year(s)

UGC NET - 2012,

Answer: B

For perspective projection with the centre of projection at the origin onto the plane z = d, a point (x, y, z) goes to (xd/z, yd/z, d). In homogeneous form this is the matrix with d on the first three diagonal places and a 1 in the last row under the third column, so that the fourth coordinate becomes z and the division by it gives the projected point. That is option (B). Option (D) is a plain scaling with a 1 in the corner, which gives no perspective division, and options (A) and (C) are not the projection matrix.

Three Dimensional Transformations and Projection Questions and Answers

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