1. AMS 345/CSE 355 Computational Geometry
Lecture: Geometric Primitives
Joe Mitchell
Code/figures from
[O’Rourke]: Computational Geometry in C: Chap 1

2. Cross Products c b a

3. Cross Products Example: ab × ac = [2,1] × [2,2] = (2*2-2*1) = 1
ab × ad = [2,1] × [0,-1] = (2*(-1)-0*1) = -2
c=(2,2)
b=(2,1) a
d=(0,-1)

4. Determinant Form

5. Area of Convex Polygon

6. Area of Simple Polygon

7. Point Type

8. Vertex Structure

9. NEW and ADD

11. b c a

12. Proper Segment Intersection
Fact: ab and cd properly intersect if and only if (1) points a and b are on opposite sides of line cd, AND (2) c and d are on opposite sides of line ab

14. Improper Segment Intersection

15. Between b c a b c a

16. Segment Intersection

17. Diagonalie
Test if segment ab, joining vertices a and b, forms a “diagonalie” = an interior or exterior diagonal for P.
Check: does the segment ab avoid intersecting all edges of P, except those that share endpoints with ab? a a b a b b

18. InCone

19. InCone b a0 a1 a b a a1 a0

20. Diagonal

21. Additional Primitives
ConvexVertex(a,P) – returns T iff a is a convex vertex of P
RaySegIntersectProp
RayRayIntersectProp
RaySegIntersect, RayRayIntersect
SegSegShareEndptOnly
SegSegT-Intersect
PointInTriangle
SegInPolygon
Etc, etc

22. From Practice Midterm

23. From Practice Midterm