Give the number of principal vanishing point(s) along with their direction for the standard perspective transformation :
Only one in the direction K
A principal vanishing point arises for each coordinate axis that the view plane cuts, because lines parallel to that axis converge on the projection.
In the standard perspective transformation the centre of projection lies on the z-axis and the view plane is the xy-plane, so only the z-axis meets the view plane.
Lines parallel to the x and y directions stay parallel to the view plane and do not converge, so I and J give no vanishing point.
Therefore there is exactly one principal vanishing point, in the K direction.
Hence, Only one in the direction K.
Similar Questions
Match the following :
a. Cavalier Projection i. The direction of projection is chosen so that there is no foreshortening of lines perpendicular to the xy plane. b. Cabinet Projection ii. The direction of projection is chosen so that lines perpendicular to the xy planes are foreshortened by half their lengths. c. Isometric Projection iii. The direction of projection makes equal angles with all of the principal axis. d. Orthographic Projection iv. Projections are characterized by the fact that the direction of projection is perpendicular to the view plane. Codes :
a b c d
In __________curve the last and the first vertices of the polygon lie on the curve and all other vertices define the derivatives, order and shape of the curve.
Which of the following statement(s) is/are correct with reference to curve generation ?
I. Hermite curves are generated using the concepts of interpolation.
II. Bezier curves are generated using the concepts of approximation.
III. The Bezier curve lies entirely within the convex hull of its control points.
IV. The degree of Bezier curve does not depend on the number of control points.
In perspective projection, if a line segment joining a point which lies in front of the viewer to a point in back of the viewer is projected to a broken line of infinite extent. This is known as _______.
Important Questions from Three Dimensional Concepts
- A normalized matrix that maps a 3D window specified by coordinates (1, 1, 1) and (4, 5, 6) on to a viewport specified by coordinates (2, 4, 2) and (8, 10, 8) is
Which of the following statements are true.
A. Painters' algorithm is also called depth sort algorithm.
B. Gourad shading is on interpolating shading method.
C. Gourad shading is an averaging shading method.
D. The Z-buffer algorithm finds the largest depth value Z.
Choose the correct answer from the options given below:
In the context of 3D Computer graphics, which of the following statements is/are correct?
(A) Under perspective projection, each set of parallel lines in the object do not stay parallel in the image (except those that are parallel to the viewplane to start with).
(B) Applying a perspective transformation in the graphics pipeline to a vertex involves dividing by its 'z' coordinate.
(C) Perspective transformation is a linear transformation.
Choose the correct answer from the options given below:
In 3D graphics, which statements are true?
P: Back-face culling is an example of image-precision visible-surface determination.
Q: In single-sample rasterization, a Z-buffer stores a depth value for each pixel and uses depth comparisons to determine visible surfaces; its numerical precision depends on the implementation.
In 3D Graphics, which of the following statements about perspective and parallel projection is/are true?
P: In a perspective projection, the farthest an object is from the center of projection, the smaller it appears.
Q: Parallel projection is equivalent to a perspective projection where the viewer is standing infinitely far away
R: Perspective projections do not preserve straight lines.
