Given a clipping window with boundaries: XWmin = 4, XWmax = 10 YWmin = 4,…
Given a clipping window with boundaries:
XWmin = 4, XWmax = 10
YWmin = 4, YWmax = 10
Find the region codes for the endpoints of the line P1(2, 2) to P2(12, 12). Determine the visibility of the line and calculate the intersection points if necessary.
Attempted by 17 students.
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Detailed Solution
Step 1: Assign Region Codes (Outcodes)
The region code is assigned as [Top, Bottom, Right, Left].
For P1(2, 2):
y < YWmin (2 < 4): Bottom bit is 1.
x < XWmin (2 < 4): Left bit is 1.
Region Code (P1) = 0101
For P2(12, 12):
y > YWmax (12 > 10): Top bit is 1.
x > XWmax (12 > 10): Right bit is 1.
Region Code (P2) = 1010
Step 2: Visibility Check
Trivial Acceptance: 0101 OR 1010 = 1111 (Not 0000, so not completely inside).
Trivial Rejection: $0101 AND 1010 = 0000 (Result is zero, so the line is a clipping candidate).
Step 3: Calculate Intersections
The slope (m) of the line is:
m = (y2 - y1)/(x2 - x1) = (12 - 2)/(12 - 2) = 10/10 = 1
Intersection with the Bottom Boundary (y = 4):
Using x = x1 + (y - y1)/m:
x = 2 + (4 - 2)/1 = 2 + 2 = 4
New point: P'1(4, 4). Its code is 0000 (Inside).
Intersection with the Top Boundary (y = 10):
Using x = x1 + (y - y_1)/m:
x = 12 + (10 - 12)/1 = 12 - 2 = 10
New point: P'2(10, 10). Its code is 0000 (Inside).
Final Result:
The clipped line segment lies between P'1(4, 4) and P'2(10, 10).