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.
Bezier curve
Approximating curves in computer graphics are defined by a control (characteristic) polygon. A Bezier curve of degree n uses n+1 control points and the Bernstein basis functions; it always interpolates the first and last control points, while the intermediate points only pull the curve.
For a Bezier curve, P(0) = P0 and P(1) = Pn, so the first and last vertices of the polygon lie on the curve. The inner vertices set the end tangent directions (derivatives), the degree (order = number of vertices) and the overall shape. This matches the description in the question.
A B-Spline curve generally does not pass through its end control points unless a special clamped knot vector is used, and its order is chosen independently of the number of vertices. Boxline curve and Gaussian curve are not curve-design schemes based on a control polygon.
Bezier curve option is correct.
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
Give the number of principal vanishing point(s) along with their direction for the standard perspective transformation :
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.
