1. Essential Geometry

2. Equations Implicit – F(x,y) = 0 Parametric – P(t) = x – Q(t) = y – 0 <= t <= 1

3. Geometric Operations Bounding box – Efficiency Distance from a point – Selection Nearest Point – Snapping Inside/Outside – Selection

4. Geometric Operations Cx,Cy R

5. Geometric Operations Top LeftRight Bottom

6. Geometric Operations B Cx,Cy A

7. Geometric Operations

9. Piecewise Continuity C(0) – same end point C(1) – same slope at the shared endpoint (Smooth joint) C(2) – Smooth second derivative at the joint

10. Parametric form P(t) = at 3 + bt 2 + ct + d = x Q(t) = et 3 + ft 2 + gt + h = y

11. Bezier A0 A2 A1 A3

12. Bezier A0 A2 A1 B0 A3 B1 B2 B3

13. Bezier Convex Hull A0 A2 A1 A3

14. B-Spline A0 A2 A1 A4 A3 A5

15. Catmull-Rom A0 A2 A1 A4 A3 A5

16. Matrix Forms