1 Pertemuan 20 Understanding Continued Matakuliah: T0264/Intelijensia Semu Tahun: Juli 2006 Versi: 2/1

2 Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : >

3 Outline Materi Materi 1 Materi 2 Materi 3 Materi 4 Materi 5

Understanding as Constraint Satisfaction There are two important steps in the use of constraints in problem solving 1.Analyze the problem domain to determine what the constraint are. 2.Solve the problem by applying a constraint satisfaction algorithm that effectively uses the constraints from step 1 to control the search.

5 Understanding as Constraint Satisfaction contd’ A Line Drawing An Obscuring Edge  A boundary between objects, or between objects and the background A Concave Edge  An edge between two faces that form an acute angle when viewed from outside the object A Convex Edge  An edge between two faces that form an obtuse angle when viewed from outside the object

6 Trihedral Figures Some Trihedral Figures

7 Nontrihedral Figures Some Nontrihedral Figures

8 Line-Labeling Line-Labeling Conventions:

9 Line-Labeling contd’ An Example of line Labeling :

10 The Four Trihedral Vertex Type FORK : Sudut 90 o

11 A Figure Occupying One Octant Consider the drawing, which accupies one of the eight octant formed by the intersection of the planes corresponding to the faces of vertex A.

12 The Vertices of a Figure Occupying One Octant

13 The Eighteen Physically Possible Trihedral Vertices

14 A Simple Example of the Labeling Process

15 Algorithm : Waltz 1.Find the lines at the border of the scene boundary and label them. These lines can be found by finding an outline such that no vertices are outside it. We do this first because this labeling will impose additional constraints on the other labelings in the figure. 2.Number the vertices of the figure to be analyzed. These number will correspond to the order in which the vertices will be visited during the labeling process. To decide on a numbering, do the following :

16 Algorithm : Waltz a. Start at any vertex on the boundary of the figure. Since boundary lines are known, the vertices involving them are more highly constrained than are interior ones. b. Move from the vertex along the boundary to an adjacent unnumbered vertex and continue until all boundary vertices have been numbered. c. Number interior vertices by moving from a numbered vertex to some adjacent unnumbered one. By always labeling a vertex next to one that has already been labeled, maximum use can be made of the constraints.

17 Algorithm : Waltz 3. Visit each vertex V in order and attempt to label it by doing the following : a. Using the set of possible vertex labelings given in figure (the eighteen physically possible trihedral vertices), attach to V a list of its possible labelings. b. See whether some of these labelings can be eliminated on the basis of local constraints. To do this, examine each vertex A that is adjacent to V and that has already been visited. Check to see that for each proposed labeling for V, there is a way to label the line between V and A in such a way that at least one of the labelings listed for A is still possible. Eliminate from V’s list any labeling for which this is not the case.

18 Algorithm : Waltz c. Use the set of labelings just attached to V to constraint the labelings at vertices adjacent to V. For each vertex A that was visited in the last step, do the following : i)Eliminate all labelings of A that are not consistent with at least one labeling of V. ii). If any labelings were eliminated, continue constraint propagation by examining the vertices adjacent to A and checking for consistency with the restricted set of labeling now attached to A. iii). Continue to propagate until there are no adjacent labeled vertices or until there is no change made to the existing set of labelings.

19 > End of Pertemuan 20 Good Luck