1. Point To Triangle(intro)
The minimum distance between and a triangle where
: the values corresponding to the point on the triangle closest to
Squared-distance

2. Point To Triangle(intro2)
Where
Positivity :
Minimum of Q(s,t) over D
-an interior point of D where
-at a point on the boundary of D

3. Point To Triangle(parameter plane)
Parameter plane for Triangle 2 a b c

4. Point To Triangle(Quadratics)

5. Point To Triangle(algorithm)
Occurrence of in region 1,3,5 : region 1 : minimum is at a region 3 : minimum is at b region 5 : minimum is at c
Occrrence of in region 2(4, 6) : minimum is either at a or at b choice based on the signs of and

6. Point To Triangle(implementation)
The solution of : 
Definition :

7. Point To Triangle(implementation2)
Determination of region :

8. Point To Triangle(implementation3)
Then handling by region
Region 0 :

9. Point To Triangle(imple4-region1)

10. Point To Triangle(imple5-region3,5)

11. Point To Triangle(imple6-region2,4,6)

12. Point To Triangle(imple6-region2,4,6)

13. Linear Component To Triangle(intro)
Minimum distance between a linear component : and a triangle : for where
Squared-distance :

14. Linear Component To Triangle(intro2)
Regions are extruded along the r-axis and split based on whether
Solution to in region minimum occurs at an interior point
Otherwise, minimum occurs on a face separating regions
The determinant of the system for linear component is parallel to triangle

15. Point To Rectangle(characteristics)
Parameter domain is
Parameter plane : nine regions

16. Point To Rectangle(comparison)
Parameter plane for Triangle 2

17. Point To Rectangle(characteristics2)
Triangle : The zero of the gradient of the quadratic is region 2,4,6  the minimum of Q occurs on one of two edges
Rectangle : (s, t) for is in region 2,4,6,8  the minimum of Q must occur at the vertex

18. Point To Rectangle(Quardratics)

19. Point To Rectangle(algorithm)
: The closest point on the rectangle to the  Projection of onto the plane of the rectangle
is inside the rectangle : is the closest point
is in regions 1,3,5,7 : Projection point of onto the rectangle edge for that region is the closest point

20. Point To Rectangle(algorithm2)
is in regions 2,4,6,7 : The rectangle vertex of that region is the closest point

21. Point To Rectangle(implementation)
Definition :
Projection onto the plane of the rectangle :

22. Point To Rectangle(pseudocode)

23. Point To Rectangle(pseudocode2)

24. Linear Component To Rectangle(intro)
Minimum distance between a linear component : and a rectangle : for where
Squared-distance :

25. Linear Component To Rectangle(intro2)
Regions are extruded along the r-axis and split based on whether
Solution to in region minimum occurs at an interior point
Otherwise, minimum occurs on a face separating regions
The determinant of the system for linear component is parallel to rectangle

26. Line To Rectangle(pseudocode)

27. Line To Rectangle(pseudocode2)

28. Line To Rectangle(pseudocod3)

29. Line To Rectangle(pseudocode4)

30. Line To Rectangle(pseudocode5)