Geometric Primitives Code and Examples

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

2. Cross Products c b a

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

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 b a 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