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The first two values, Δ(1) and Δ(2), refer to the unit line segment and unit square respectively. For the three-dimensional case, the mean line segment length of a unit cube is also known as Robbins constant, named after David P. Robbins. This constant has a closed form, [6]
Given two different points (x 1, y 1) and (x 2, y 2), there is exactly one line that passes through them. There are several ways to write a linear equation of this line. If x 1 ≠ x 2, the slope of the line is . Thus, a point-slope form is [3]
In C and C++, the + operator is not associated with a sequence point, and therefore in the expression f()+g() it is possible that either f() or g() will be executed first. The comma operator introduces a sequence point, and therefore in the code f(),g() the order of evaluation is defined: first f() is called, and then g() is called.
The Shamos–Hoey algorithm [1] applies this principle to solve the line segment intersection detection problem, as stated above, of determining whether or not a set of line segments has an intersection; the Bentley–Ottmann algorithm works by the same principle to list all intersections in logarithmic time per intersection.
two different references to the same object, e.g., two nicknames for the same person; In many modern programming languages, objects and data structures are accessed through references. In such languages, there becomes a need to test for two different types of equality: Location equality (identity): if two references (A and B) reference the same ...
A constraint logic program is a logic program that contains constraints in the body of clauses. An example of a clause including a constraint is A (X, Y):-X + Y > 0, B (X), C (Y). In this clause, X + Y > 0 is a constraint; A(X,Y), B(X), and C(Y) are literals as in regular logic programming.
Two segments are said to be equipollent when they have the same length and direction. Two equipollent segments are parallel but not necessarily colinear nor overlapping , and vice versa. For example, a segment AB , from point A to point B , has the opposite direction to segment BA ; thus AB and BA are not equipollent.
This observation about De Morgan's laws shows that is not left distributive over or because only the following are guaranteed in general: () = () () = where equality holds for one (or equivalently, for both) of the above two inclusion formulas if and only if =.