a) What is the difference between a parallel projection and a perspective projection? Explain with examples.
b) What will be the perspective projection of a unit cube on the plane x = y if it is viewed from the point (1,2,0)? Justify your answer.
c) Transform the scene in the world coordinate system to the viewing coordinate system with viewpoint at (1,1,2). The view plane normal vector is(−4,2,5) and the view up vector is (1,4,0).
### a) Difference between Parallel Projection and Perspective Projection - Parallel Projection: In parallel projection, objects are projected onto a plane in such a way that their relative proportions remain unchanged regardless of their depth. The projection lines are parallel to each other and to the projection plane. The distance from the object to the projection plane does not affect the object's size or shape. This type of projection is commonly used for technical drawings, architectural plans, and maps. Example: A blueprint of a building, where all lines are parallel, and the dimensions do not change regardless of how far the building is from the observer. - Perspective Projection: In perspective projection, objects appear smaller as they move farther from the observer, simulating how the human eye perceives objects in three-dimensional space. The projection lines converge at a point called the vanishing point. The depth of the object affects its size and position in the image. Example: A road leading off into the distance, where ________ ___ __________ _______ ______ _________ _______ __________ _____ ____ ________ __________.
_______ _____ _____ ___ ___.
__________ ______ ________ _________ _________ _______ __________ ________ _________ ___ ____.
____ ____ _____ _____ _________ __________ __________ ___.
__________ _______ ____ ______ ______ _______ ____ ______ _______ __________ ___ __________.
____ ___ ________ ___ ______.
__________ __________ ________ _____ ___ _________ _________ _____ __________ ________ _________.
__________ ______ _____ ____ ____ ___ ________ ________ _______ __________.
____ ____ __________ ___ __________ ______ _________ ________ ______ ______ _______ ____.
______ _______ ___ ___ ___.
__________ ________ ___ _______ ___ __________ _______ __________.
_____ _____ ____ ________ __________ ____ _____ _____ _____ _____ _______ __________.
_______ ________ _________ ______ _________ ________ ______ _____.
_______ ______ _____ ________ __________ _________ __________ ________ _________ _________ ____.
__________ _______ __________ __________ __________ ______ ________ __________ ______.
_______ _____ _______ __________ ____ ________ ______ _______ ________ ________ ________ ______.
_____ ___ __________ _____ __________ ________ _________ __________ ____ ____ _________ ____.
____ ______ __________ __________ __________ _______ ______.
_______ ____ ______ ______ __________ _______ ______ _________ ____.
______ ____ _____ _________ ________ _____ ___ _________ ________ ________ ____ ______.
_________ _________ ________ ________ ________ __________ __________ __________ ______ _________ _______.
______ __________ ____ _______ ____ _______.
____ ________ _________ _______ __________ ______ ______ ______ _______ ___ _____ ___.
_____ ________ ________ ___ __________ _________ __________ ________ ___ ________ ____ ______.
_______ _______ _______ ___ __________.
__________ _____ _______ __________ ______ ______ ____ ____.
_________ _____ ___ _______ ___ ___ ____.
_____ ______ _________ ____ ______ _______ __________ _____ ____ ________ __________ _________.
_________ _________ _________ ______ _______.
_______ _____ __________ _______ ________ ________.
_____ ___ __________ ___ ________.
_________ ____ _________ __________ _________.
_____ ______ ________ __________ ___ ________ ______ ______ _______.
____ _______ _______ _______ _______ ____ ______ ____ __________ ______.
______ _____ __________ _____ ______ _____ ________ __________ ______.
________ ___ ____ ___ ____.
___ __________ _________ ____ ____ ________ _________ ________ ________ ________.
_______ _______ ________ ____ _____ _____ __________ _____ ________ ________ _____.
__________ ______ _________ _____ ______ ______ ________ ________ __________ _______ ___.
_________ _____ _______ ___ _________ ________ __________ _________ ______ ________ _______ ______.
_________ ____ __________ ____ ________ ______ _______ ______ _________ ____.
_____ ______ _____ __________ ____ ___ ____ _______ ___.
________ ______ _______ ________ __________ ____ _______ _____ _________ __________ _________.
_______ ____ _______ _______ ______ ____ ____ _________.
___ ______ _______ __________ _____ __________ __________ ___.
_______ ____ ____ ____ ________ _____ _____ __________ _______ ________ ________ _________.
____ _____ _________ _________ __________ _________ _________ ________ ___ ____ _______.
______ __________ ____ ____ _______ _____ ____ ________ ____.
______ ____ _______ ______ _____ ____ _______ __________ _____ _____ __________ __________.
___ ____ _________ ____ __________ ___ ___ _______ __________ _____.
______ ________ ___ ________ ______ ________ __________ ______.
_____ ____ ______ _______ __________ ___ ____.
___ ________ _________ ________ ____ __________ ___ ____ ______.
_____ ___ _______ _________ _______ ___ ___ ____ _____ ____ _____.
Get Full Answer on WhatsApp
a) Transform the quadrilateral ABCD with vertices A(1,0),B(4,−1),C(5,3) and D(−1,5) under a translation by the point (4, 5) followed by a counter-clockwise rotation by an angle of 45◦
.b) If you perform an x-direction shear transformation, and then a y-direction shear transformation, will the result be the same as the one which is obtained when it is simultaneous shear in both the directions? Justify your answer.
c) Let W be a window with corners (0,0),(8,0),(8,4) and (0,4). Clip a triangle with vertices (1,1),(10,2) and (5,9) against the window W by tracing Liang Barskey line clipping algorithm
a) Write a boundary fill procedure to fill an 8-connected region.
b) Let W be the window having two diagonally opposite corners at (10, 2) and (30, 15). Trace the Cohen-Sutherland line clipping algorithm for the line segment joining the points (0,0) and (15, 30).
a) What is the difference between a parallel projection and a perspective projection? Explain with examples.
b) What will be the perspective projection of a unit cube on the plane x = y if it is viewed from the point (1,2,0)? Justify your answer.
c) Transform the scene in the world coordinate system to the viewing coordinate system with viewpoint at (1,1,2). The view plane normal vector is(−4,2,5) and the view up vector is (1,4,0).
a) Consider a polygon with vertices at (5, 20), (12, 5), (15, 15), (25, 5), (30, 25), and (15, 30). Prepare a sorted edge list, and then make the active edge list for the
scanlines y = 5,10,15,20,25,30.
b) Develop and implement the flood fill algorithm.
c) Prove or disprove: "Multiplication of transformation matrices for two successive rotations is commutative."
a) If the origin is taken as the centre of projection, then what will be the perspective projection when the projection plane passes through the point P(4,5,3) and has normal vector (1,2,−1).
b) Write a program that produces different views of a cuboid, that is, how the cuboid looks from the top, from the front or from the right.
c) Write a code to continuously rotate a pentagon about a corner point in the anti-clockwise direction.
a) Explain what do you understand by the terms persistence, refresh rate, resolution, aspect ratio, horizontal and vertical retrace.
b) Compute the pixel positions along the line path of the lien joining the points A and B(10,8).
c) Using the midpoint method and symmetry in account, develop an efficient method
for scan converting the curve n the interval [0, 10].
a) Devise an efficient algorithm that takes advantage of symmetry properties to display a sine function.
b) Prove that the reflection along the line y = −x is equivalent to reflection along the y-axis followed by a counter-clockwise rotation by 90◦ .
c) Shear a square whose opposite vertices are at (1,1) and (2,2) by i) 2 units along the x-axis and reference line y = 0
ii) 4 units along the y-axis and reference line x = 0.