1. Type to enter a caption.
Computer Graphics
Week 5 Lecture 1

2. Polygon Clipping

3. Polygon Basics Convex Polygon Non Convex Polygon
A line joining any two interior points lie completely inside the polygon
A line joining any two interior points does not lie completely inside the polygon

4. Polygon Basics Postively Oriented Polygon:
If the tour of vertices in the given order produces a counter clockwise circuit
e.g. ABCDE → +vely oriented
AEDCB → not +vely oriented

5. Mathematical defination of +ve orientation
NOTE:
If we tour along the edges of +vely oriented polygon our left hand would always point towards the inside of the polygon
Let A(x1,y1) and B(x2,y2) be a directed line segment, Then a point P(x,y) will be to the left of line segment if
C = (x2-x1)(y-y1) - (y2-y1)(x-x1) is +ve

6. Mathematical defination of Convex Polygon
So if a point P(x,y) , that lies inside the polygon, is to the right of any edge , then the polygon is not Convex polygon
(Given positive orientation)

7. Sutherland Hodgeman Algo
For Clipping any polygon against a convex clipping window
Successively , clips the polygon against the infinite edges of clipping window

8. S-H Algo Input : Vertices of polygon to be clipped (v1,v2, … , vn)
Output : Produces a clipped polygon by introducing new vertices at places where the polygon gets clipped.
Algo:
The algo starts from the edge vn to v1, moves around the edges of polygon until it reaches back to vn.
At each step , it examines the relationship between the polygon edge and the clipping boundary.
Based on the relationship , adds zero,one or two vertices to the list of output vertices (that will define the clipped polygon)
Explanation on board

9. SO,
There could be 4 cases based on how polygon edge crosses the clipping boundary

10. Case:
Both Vertices, of polygon edge (v1 and v2) , are inside the clipping boundary
Output:
Add v2 to output list
Case 1

11. Case 2 Case: v1 is inside v2 is outside Output:
Intersection point of polygon edge with the clipping boundary , i , is output
Case 2

12. Case:
Both v1 and v2 are outside
Output:
no output
Case 3

13. Case:
v1 is outside and v2 is inside
Output:
i and v2
Case 4

14. Example

15. Left Edge Clipping Input vertices : v1 to v8
Output vertices: i1,i2,v8,v7,v6,v5,v4,v3,v2

16. Bottom Edge Clipping Input vertices : i1,i2,v8,v7,v6,v5,v4,v3,v2
Output vertices: i2,v8,i3,i4,v6,v5,v4,v3,v2,i1

17. Right Edge Clipping Input vertices : i2,v8,i3,i4,v6,v5,v4,v3,v2,i1
Output vertices: i5,i6,v4,v3,v2,i1,i2,v8,i3,i4,v6

18. Top Edge Clipping Input vertices : i5,i6,v4,v3,v2,i1,i2,v8,i3,i4,v6
Output vertices: i7,i8,v2,i1,i2,v8,i3,i4,v6,i5,i6,v4

19. The End

20. Slide 1

21. Text

23. Text