In Cyrus-Beck algorithm for line clipping the value of t parameter is computed by the relation : (Here P1 and P2 are the two end points of the line, f is a point on the boundary, n1 is inner normal)
\(\frac{(f_i - P_1)\cdot n_i}{(P_2 - P_1)\cdot n_i}\)
Cyrus-Beck writes the line in parametric form \(P(t) = P_1 + t\,(P_2 - P_1),\ 0 \le t \le 1\), so t = 0 at P1 and t = 1 at P2.
For edge i of the convex window, with a point \(f_i\) on that edge and inner normal \(n_i\), a point P(t) lies exactly on the edge when \(n_i \cdot \left(P(t) - f_i\right) = 0\) (inside gives a positive value, outside a negative one).
Substituting: \(n_i \cdot (P_1 - f_i) + t\, n_i \cdot (P_2 - P_1) = 0\), which gives \(t = \frac{(f_i - P_1)\cdot n_i}{(P_2 - P_1)\cdot n_i}\). The sign of the denominator tells whether the line is entering or leaving through that edge.
The expression with \((P_1 - f_i)\) in the numerator is the negative of this t. The two expressions built from P2 measure the parameter from the other end point, i.e. they give 1 – t, not the t of the parametric line starting at P1.
Hence, the answer is \(\frac{(f_i - P_1)\cdot n_i}{(P_2 - P_1)\cdot n_i}\).
Similar Questions
Which of the following statement(s) is/are incorrect ?
(a) Mapping the co-ordinates of the points and lines that form the picture into the appropriate co-ordinates on the device or workstation is known as viewing transformation.
(b) The right-handed cartesian co-ordinates system in whose co-ordinates we describe the picture is known as world co-ordinate system.
(c) The co-ordinate system that corresponds to the device or workstation where the image is to be displayed is known as physical device co-ordinate system.
(d) Left - handed co-ordinate system in which the display area of the virtual display device corresponds to the unit (|x|) square whose lower left-hand corner is at the origin of the co-ordinate system, is known as normalized device co-ordinate system.
Codes :
Consider a window bounded by the lines : x = 0; y= 0; x = 5 and y = 3. The line segment joining (-1, 0) and (4, 5), if clipped against this window will connect the points
Arrange the 2-D viewing transformation pipeline.
A. Convert world-coordinates to viewing coordinates
B. Map viewing coordinates to normalized viewing coordinates using window - viewpoint specifications
C. Construct world - coordinates scene using modeling - coordinates transformations
D. Map normalized viewpoint to device coordinates
Choose the correct answer from the options given below:
Let R be the rectangular window against which the lines are to be clipped using 2D Sutherland-Cohen line clipping algorithm. The rectangular window has lower left-hand corner at (– 5, 1) and upper right-hand corner at (3, 7). Consider the following three lines for clipping with the given end point co-ordinates :
Line AB : A (– 6, 2) and B (–1, 8)
Line CD : C (– 1, 5) and D (4, 8)
Line EF : E (–2, 3) and F (1, 2)
Which of the following line(s) is/are candidate for clipping ?
Important Questions from Two Dimensional Viewing
- Which of the following technique is used for Clipping?
Rearrange steps involved in two dimensional viewing transformation.
I. Map normalized viewport to device Co-ordinates
II. Convert world co-ordinate to viewing co-ordinates
III. Construct world – co-ordinate scene using modeling coordinate transformation
IV. Map viewing co-ordinates to normalized viewing co-ordinates using window-viewportspecification
Which of the following statement(s) is/are incorrect ?
(a) Mapping the co-ordinates of the points and lines that form the picture into the appropriate co-ordinates on the device or workstation is known as viewing transformation.
(b) The right-handed cartesian co-ordinates system in whose co-ordinates we describe the picture is known as world co-ordinate system.
(c) The co-ordinate system that corresponds to the device or workstation where the image is to be displayed is known as physical device co-ordinate system.
(d) Left - handed co-ordinate system in which the display area of the virtual display device corresponds to the unit (|x|) square whose lower left-hand corner is at the origin of the co-ordinate system, is known as normalized device co-ordinate system.
Codes :
Consider a window bounded by the lines : x = 0; y= 0; x = 5 and y = 3. The line segment joining (-1, 0) and (4, 5), if clipped against this window will connect the points
Arrange the 2-D viewing transformation pipeline.
A. Convert world-coordinates to viewing coordinates
B. Map viewing coordinates to normalized viewing coordinates using window - viewpoint specifications
C. Construct world - coordinates scene using modeling - coordinates transformations
D. Map normalized viewpoint to device coordinates
Choose the correct answer from the options given below:
