By Michal Forišek, Monika Steinová
There is an important distinction among designing a brand new set of rules, proving its correctness, and instructing it to an viewers. while educating algorithms, the teacher's major aim could be to show the underlying rules and to aid the scholars shape right psychological versions concerning the set of rules. This technique can frequently be facilitated through the use of compatible metaphors. This paintings presents a collection of novel metaphors pointed out and built as compatible instruments for instructing a number of the "classic textbook" algorithms taught in undergraduate classes world wide. every one bankruptcy offers workouts and didactic notes for lecturers in accordance with the authors’ reviews whilst utilizing the metaphor in a school room setting.
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3 Winding Number 49 1 B2 1 B1 2 −1 1 1 1 Fig. 19 Computing the winding number by counting passes in both direction. The boy at B1 witnesses two passes counter-clockwise and one pass clockwise. The boy at B2 observes two passes in each direction. (The dashed rays represent the boys’ lines of sight) The canonical way of doing this calculation is by using the arctangent function. More specifically, we compute the angle α1 between the half-axis x + and the vector (x1 , y1 ), and the angle α2 between x + and (x2 , y2 ).
In the middle the shortest distance is between a pair of endpoints. On the right, the shortest distance is between one endpoint and its perpendicular projection to the other line segment Fig. 8 One of the more involved cases in three dimensions which students often miss. For a better perception the two line segments (black lines) are located on a cube surface. The shortest connecting straight line between the two line segments is represented by the dotted line straightforward—consider all the possible cases, find the one that applies, and compute the distance using the corresponding formula.
A polygon is a closed polyline that never touches or intersects itself. The word “polygon” is also used for the entire area enclosed inside such a polyline, including the boundary. ) We will consider another traditional problem in two-dimensional computational geometry: testing whether a given point is contained in a given polygon. 3 Winding Number 6 45 y 5 4 3 A 2 B D C E F 1 0 −1 −1 x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Fig. 15 Some of the special cases in the ray casting algorithm: We are checking whether A lies inside the polygon.